Browse Algebra problems Studdy Solved!

Problem 23801

Упростите выражение: $2 \log _{4} k-3 \log _{4} 6$

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Problem 23802

In Exercises 1-4, find the domain of the function $f$ . Use limits to describe the behavior of $f$ at value(s) of $x$ not in its domain.
1. $f(x)=\frac{1}{x+3}$
2. $f(x)=\frac{-3}{x-1}$
3. $f(x)=\frac{-1}{x^{2}-4}$
4. $f(x)=\frac{2}{x^{2}-1}$

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Problem 23803

Q3. A car of mass 800 kg is travelling along a straight horizontal road. A constant retarding force of FN reduces the speed of the car from $18 \mathrm{~ms}^{\wedge}-1$ to $12 \mathrm{~ms}^{\wedge}-1$ in 2.4 s . Calculate: (a) the value of $F$
Answer: $\square$

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Problem 23804

Find the domain of the function $f(x) = \sqrt{1-x} + \sqrt{x-1}$ .

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Problem 23805

3. $x+5=\frac{14}{x}$
5. $x+\frac{4 x}{x-3}=\frac{12}{x-3}$

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Problem 23806

10. $11 k+2=24$

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Problem 23807

10. $x+\frac{6}{x}=-7$
12. $2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}$

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Problem 23808

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS:

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Problem 23809

Factor the expression: $3c^3 + 24$ .

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Problem 23810

1. Let $a_{n}=-n^{2}+18 n-56$ where $n \in \mathbb{N}$ . What is the smallest $n_{0} \in \mathbb{N}$ such that $a_{n}$ is decreasing for all $n \geqslant n_{0}$ .
ANS:

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Problem 23811

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$
ANS: $\qquad$

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Problem 23812

5. If a savings account offers a nominal interest rate of $3 \%$ per year, compounded every four months, then how many years will it take for a deposit to double in value?
ANS:

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Problem 23813

Identify the coefficient and degree of the term: $-10 x^{4} b^{4}$ The coefficient is $\square$ and the degree is $\square$ Question Help: Video Written Example

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Problem 23814

Given that Alice and Bob are using the block cipher $\varepsilon_{k}(\cdot)$ with the 5 -bit block $b: b_{1} b_{2} b_{3} b_{4} b_{5}$ and the 5 -bit key $k: k_{1} k_{2} k_{3} k_{4} k_{5}$ to encrypt according to the rule $\varepsilon_{k}(b)=k \oplus b$ . Additionally, to encrypt multiple blocks using the primitive $\mathcal{E}_{k}(\cdot)$ , Alice and Bob are using the counter (CTR) mode. Assume the key agreed upon is $(\mathbf{1 0 0 0 1})_{2}$ and the initialization vector (IV) generated at encryption time is $(\mathbf{1 0 0 1 1})_{2}$ . What is the ciphertext that Bob receives when Alice sends the plaintext $(0101001010)_{2}$ ?

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Problem 23815

ANS: $x \in(1,5) \cup 18 ;+$
3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS: $N=10$

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Problem 23816

5p 2. Fie expresia $E(x)=\left(\frac{1}{x-3}+\frac{x}{9-x^{2}}\right): \frac{3}{(x-3)(x+3)}$ , unde $x \in \mathbb{R} \backslash\{ \pm 3\}$ . (2p) a) Arată că $E(-1)=1$ . (3p) b) Calculează numărul $z=E(1)+2 E(2)+3 E(3)+\ldots+2022 E(2022)$ .

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Problem 23817

5) Complete the table using the function $y=3 x-4$ .

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Problem 23818

(iii) Evaluate the following without using log tables: $2 \log 5+\log 3+3 \log 2-\frac{1}{2} \log 36-2 \log 10$

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Problem 23819

EXERCICE 12 Soit le polynôme complexe $\mathrm{P}(\mathrm{z})$ de la variable complexe z $P(z)=z^{3}-(7+9 i) z^{2}+(39 i-14) z+50$
1-Montrer que l'équation $\mathrm{P}(\mathrm{z})=0$ admet une racine $\mathrm{z}_{0}$ imaginaire pure. 2- Résoudre l'équation $\mathrm{P}(\mathrm{z})=0$ . On notera $\mathrm{z}_{1}$ la racine non imaginaire pur ayant la plus petite partie réelle et $\mathrm{z}_{2}$ la troisième. 3-Dans le plan affine euclidien rapporté au repère ( $\mathrm{o}, \mathrm{i}, \mathrm{j}$ ) orthonormé on considère les points $\mathrm{A}, \mathrm{B}$ , et C d'affixes respectives $\mathrm{z}_{0} ; \mathrm{z}_{1} ; \mathrm{z}_{2}$ . Déterminer et construire l'ensemble des points M du plan tels que : $\mathrm{MA}^{2}-\mathrm{MB}^{2}+\mathrm{MC}^{2}=4$ .

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Problem 23820

2. 4. What is the conductance of a $39 \Omega$ resistor? Ans. 25,6 mS.

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Problem 23821

Quiz Review: Factor each completely. 1) $50 b^{2}-40 b+8$ 2) $45 x^{2}-80$ 3) $75 r^{2}-27$ 4) $75 a^{2}-30 a+3$ 5) $64 u^{4}-125 u$ 6) $27+x^{3}$ 7) $u^{4}+64 u$ 8) $x-125 x^{4}$ 9) $14 n^{3}+6 n^{2}+21 n+9$ 10) $30 r^{3}+35 r^{2}-6 r-7$

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Problem 23822

8. 11. The conductance of a wire is $2,5 \mathrm{~S}$ . Another wire of the same material and at the same temperature has a diameter one-forth as great and the length twice as great. Find the conductance of the second wire. Ans. $78,1 \mathrm{mS}$ .

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Problem 23823

14. 17. Find the temperature coefficient of resistance of iron at $20^{\circ} \mathrm{C}$ , if iron has an inferred zero resistance temperature $-162^{\circ} \mathrm{C}$ ? Ans $0,00551 /{ }^{\circ} \mathrm{C}-$

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Problem 23824

Graph each equation. 5) $y=x^{2}-2 x-3$
Identify the $\min / \max$ value of each. Th

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Problem 23825

Problem 8. An e.m.f. of 250 V is connected across a resistance and the current flowing through the resistance is 4 A . What is the power developed? Ans. 1 kW.

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Problem 23826

Write the function whose graph is the graph of $y=\sqrt{x}$ but is shifted down 3 units.

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Problem 23827

31. The sum of two numbers is 37 . One number is 5 more than the other. Find the numbers.

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Problem 23828

19. Use voltage division twice to find the voltage $U$ in the circuit given below. Ans. 36V.

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Problem 23829

For each pair of functions $f$ and $g$ below, find $f(g(x))$ and $g(f(x))$ . Then, determine whether $f$ and $g$ are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all $x$ in the domain of the composition. You do not have to indicate the domain.) (a) $f(x)=-\frac{2}{x}, x \neq 0$ (b) $f(x)=3 x+5$ $\begin{array}{l} g(x)=-\frac{2}{x}, x \neq 0 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other $f$ and $g$ are not inverses of each other

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Problem 23830

4. Three parallel resistors have a total conductance of 2 mS . If two of the resistors are 1 and $5 \mathrm{k} \Omega$ what is the third resistance? Ans. 1,25 k

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Problem 23831

3. $\begin{aligned} x+y & =8 \\ -x+2 y & =7\end{aligned}$

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Problem 23832

Which of the following is true about the expression $c^{5}+\left(-9 c^{2}\right)+40 c+7 d^{7} e^{3}-5 c^{3}+4 d ?$ The coefficient of the third term is $c$ . The coefficient of the fourth term is 7. The coefficient of the first term is 0 . There are no negative coefficients.

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Problem 23833

Determine algebraically whether the given function is even, odd, or neither. $f(x)=2 x+|-5 x|$
Choose the correct answer. Even Neither

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Problem 23834

$\left(3, \ln (5)^{3} \cdot 3\right)$
10. The graph of $y = f(x)$ shown above, is the graph of a logarithmic function. Which equation below represents the inverse function? \begin{itemize} \item (A) $f^{-1}(x) = e^{x+3} - 2$ \item (B) $f^{-1}(x) = 3e^{x} - 2$ \item (C) $f^{-1}(x) = e^{x+2} - 3$ \item (D) $f^{-1}(x) = e^{x-3} + 2$ \end{itemize} The asymptote is $-2$ .

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Problem 23835

Which expression has the greatest value? $\frac{1}{5}\left(\frac{5^{3}}{5^{2}}\right)^{2}$ $\frac{5^{8}}{\left(5^{2}\right)^{4}}$ $\left(\frac{5^{3}}{5^{4}}\right)^{3}$ $\frac{\left(5^{2}\right)^{3}}{5^{4}}$ sUbmit all

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Problem 23836

THE QUADRATIC FORMULA There once lived a $\qquad$ $x^{2}-5 x+3=0$ near the $\qquad$ $x=\frac{7 \pm \sqrt{29}}{-6}$ $\square$ $\square$ $\frac{-9 \pm \sqrt{73}}{4}$ $x=-3 / 2, x=1 / 3$ suntan \begin{tabular}{c} $x=\frac{1 \pm \sqrt{85}}{10}$ \\ swords \end{tabular} $\quad$ \begin{tabular}{c} $x=-2, x=-1 / 3$ \\ crcus \end{tabular} $\square$ $x=-2, x=-1 / 3$ crcus $\frac{\text { crcus }}{7 \pm \sqrt{73}}$ $\square$ Who thought he'd found $\qquad$ $5 x^{2}+x=3$ i $\square$ $\square$ $x=-5, x=-1 / 2$ tasted $x=\frac{7 \pm \sqrt{73}}{-6}$ He took a $\qquad$ $\square$ $-4 x^{2}+1=9 x$ Use the quadratic formula to solve the equations. Drag the answers on top of the problems to fill in the missing words. $\square$ $\square$ $x=\frac{-1 \pm \sqrt{43}}{10}$ And started to $4 x^{2}-x-5=0$ $\square$ missing words. $\quad x=-3 \pm \sqrt{19}$ $\square$ $x=-5, x=1 / 3$ paraded $\square$ $x=\frac{9 \pm \sqrt{97}}{-8}$ big $\qquad$ $\qquad$ like $\qquad$ $\square$ $x=-1, x=5 / 4$ think

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Problem 23837

Jill is factoring the expression $13 x y-52 y$ . Her work is shown below.
Factors of $13 x y: 1,13, x, y$ Factors of $52 y: 1,2,26,52, y$ GCF: y Factored expression: $y(13 x-52)$
Which best describes the accuracy of Jill's solution? Jill's solution is accurate. Jill omitted a factor pair, which affected the GCF and factored expression. Jill made an error when determining the GCF from her list of factors. Jill made an error when writing the factored expression.

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Problem 23838

Line $m$ passes through the points $(5,1)$ and $(8,6)$ while line $n$ passes through the points $(-4,3)$ and $(-1,8)$ .
Which statement accurately describes the relationship between the two lines? A. Lines $m$ and $n$ have the same slope so they are perpendicular. B. Lines $m$ and $n$ have opposite reciprocal slopes so they are parallel. C. Lines $m$ and $n$ have the same slope so they are parallel. D. Lines $m$ and $n$ have opposite reciprocal slopes so they are perpendicular.

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Problem 23839

If $f(x)=\left\{\begin{array}{ll}3 x-2 & \text { if }-3 \leq x \leq 4 \\ x^{3}-4 & \text { if } 4<x \leq 5\end{array}\right.$ , find: (a) $f(0)$ , (b) $f(1)$ , (c) $f(4)$ , and (d) $f(5)$ .

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Problem 23840

For the quadratic function $f(x)=x^{2}+6 x$ , answer parts $(a)$ through ( $f$ ). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down
The vertex is -3 . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-3$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is $\square$ . (Type an integer or a simplified fraction.) B. There is no y-intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/are $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. Click to enlarge graph (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $\square$ . (Type your answer in interval notation.) The range of $f$ is $\square$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $\square$ .

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Problem 23841

Which expression is equivalent to $(8 a-3 b+7)-(2 a+b-4)$ ? $6 a-2 b+11$ $6 a-4 b+3$ $6 a-2 b+3$ $6 a-4 b+11$

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Problem 23842

For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through ( $f$ ). concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is 0 . $\square$ (Type an integer or a simplified fraction.) B. There is no y-intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/are $0,-6$ . $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function.
Click to enlarge graph (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) The range of $f$ is $[-9, \infty)$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $(-3, \infty)$ . (Type your answer in interval notation.) The function is decreasing on the interval $(-\infty,-3)$ . (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box(es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)<0$ on $\square$ , and $f(x)$ is never positive B. $f(x)>0$ on $\square$ , and $f(x)$ is never negative C. $f(x)>0$ on $\square$ , and $\mathrm{f}(\mathrm{x})<0$ on $\square$

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Problem 23843

Question 16, 1.6-26 points Points: 0 of 1 Save
One maid can clean the house in 4 hours. Another maid can do the job in 6 hours. How long will it take them to do the job working together? A. $\frac{1}{2} \mathrm{hr}$ B. $\frac{1}{10} \mathrm{hr}$ C. $\frac{1}{24} \mathrm{hr}$ D. $\frac{12}{5} \mathrm{hr}$

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Problem 23844

Use point-slope form to write the equation of a line that passes through the point left parenthesis, 18, comma, 20, right parenthesis (with slope minus, start fraction, 3, divided by, 2, end fraction

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Problem 23845

1. Use your calculator to complete the following table. Round the logarithms to four decimal places. \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{\operatorname { l o g } ( \boldsymbol { x } )}$ \\ \hline 1 & 0 \\ \hline 2 & 0.3010 \\ \hline 3 & 0.4771 \\ \hline 4 & 0.6021 \\ \hline 5 & 0.6990 \\ \hline 6 & 0.7782 \\ \hline 7 & 0.8451 \\ \hline 8 & 0.9031 \\ \hline 9 & 0.9542 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline $x$ & $\log (x)$ \\ \hline 10 & 1 \\ \hline 12 & 1.0792 \\ \hline 16 & 1.2091 \\ \hline 18 & 1.2553 \\ \hline 20 & 1.3010 \\ \hline 25 & 1.3979 \\ \hline 30 & 1.4771 \\ \hline 36 & 1.5563 \\ \hline 100 & 2 \\ \hline \end{tabular}
2. Calculate the following values. Do they appear anywhere else in the table? a. $\log (2)+\log (4)$ $\log (8)$ b. $\quad \log (2)+\log (6)$ $\log (12)$ c. $\log (3)+\log (4)$ $\log (12)$ d. $\log (6)+\log (6)$ $\log (36)$ Cailyn Bryant A STORY OF FUNCTIONS Lesson 11 M3 AlgEBRAII
3. What pattern(s) can you see in Exercise 2 and the table from Exercise 1? Write them using logarithmic notation.

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Problem 23846

Name:
Ai $\qquad$ $\qquad$ -
Writing Equations of Lines $\qquad$ Exit Ticket 1) 13 marks] $A$ line passes through the points $(3,2)$ and $(5,-1)$ .
Find the equation of this line in the form $y=m x+b$ . 2) 13 marks/ Find the equation of the line with gradient $\frac{2}{3}$ that passes through the point $(-2,-1)$ in the form $a x+b y+d=0$ .

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Problem 23847

2 $\begin{array}{l} \text { 2.) }-5 x+10=10 \\ -5 x+10-10=10-10 \\ -5 x=0 \end{array}$

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Problem 23848

4. [-/0.32 Points]
DETAILS MY NOTES SCOLALG7 4.4.014. 0/100 Submissions
Use the Laws of Logarithms to evaluate the expression. $-\frac{1}{3} \log _{5}(125)$ $\square$ Need Helo?

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Problem 23849

Given the equation $x / 3=-12$ , the value of $x=-4$ .
A True B False Find the value of $x$ if the answer is false: $\qquad$

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Problem 23850

a. $\quad \log (14)$ b. $\log (35)$

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Problem 23851

Calculate c. $\log (72)$ d. $\log (121)$

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Problem 23852

6.) $7-4 x=x=53$

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Problem 23853

Use the quadratic formula to solve. Express your answer in simplest form. $4 w^{2}+20 w+25=0$

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Problem 23854

6.02 EXAM REVIEW_UNIT 2 XEM OZ6 Q Find une value of X In the equarinn novow. Question o 6/16 $1 / 6(36 x-12)-5 x=10$
A $x=-2$ B $x=8$ C $\mathrm{x}=12$ D $x=22$

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Problem 23855

Use the quadratic formula to solve. Express your answer in simplest form. $4 x^{2}-5 x-6=0$

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Problem 23856

A. Given the equation: $3 \sqrt[4]{m}(5 \sqrt{m})=15 \sqrt[x]{m^{3}}$
Find the value of $x$ .

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Problem 23857

Write the logarithmic expression as a single logarithm with coefficient 1 , and simplify as much as possible. Assume that the variables represent positive real numbers. $\ln y+\ln 3=$

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Problem 23858

Question
Use the properties of exponents to determine the value of $a$ for the equation: $\left(x^{\frac{1}{2}}\right)^{3} \sqrt{x}=x^{a}$

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Problem 23859

Español
For $\log _{5} 28$ , (a) Estimate the value of the logarithm between two consecutive integers. For example, $\log _{2} 7$ is between 2 and 3 because $2^{2}<7<2^{3}$ . (b) Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. (c) Check the result by using the related exponential form.
Part: $0 / 3$
Part 1 of 3 (a) Estimate the value of the logarithm between two consecutive integers. $\square$ $<\log _{5} 28<$ $\square$

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Problem 23860

Part: 1 / 3
Part 2 of 3 (b) Approximate the logarithm to 4 decimal places. If necessary, round intermediate steps to 9 decimal places. $\log _{5} 28 \approx$ $\square$

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Problem 23861

$\underline{\text { Open Ebook section } 7.4}$
Potassium superoxide, $\mathrm{KO}_{2}$ , reacts with carbon dioxide to form potassium carbonate and oxygen: $4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2}$
3rd attempt See Periodic Table
This reaction makes potassium superoxide useful in a self-contained breathing apparatus. How much $\mathrm{O}_{2}$ could be produced from 2.59 g of $\mathrm{KO}_{2}$ and 4.60 g of $\mathrm{CO}_{2}$ ?

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Problem 23862

27. A star-connected load consists of three identical coils each of resistance $30 \Omega$ and inductance 127.3 mH .
If the line current is $5,08 \mathrm{~A}$ , calculate the line voltage if the supply frequency is 50 Hz .

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Problem 23863

Determina la retta comune ai due fasci di equazioni $y=m x-2 m+1$ e $(2-k) x-(k+1) y-3=0$ , e inc $i$ relativi valori di $m$ e $k$ . $[y=2 x-3, m=2, k=$
Considera il triangolo individuato dai centri $A, B, C$ dei tre fasci di rette di equazioni:

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Problem 23864

Subtract. Your answer should be a polynomial in standard form. $\left(d^{2}+6 d+9\right)-\left(d^{3}+6 d+9\right)=$ $\square$

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Problem 23865

Use $\log _{b} 2 \approx 0.393, \log _{b} 3 \approx 0.552$ , and $\log _{b} 5 \approx 0.801$ to approximate the value of the given logarithm to 3 decimal places. Assume that $b>0$ and $b \neq 1$ . $\log _{b} 15 \approx$

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Problem 23866

HW12: Problem 5 Previous Problem Problem List Next Problem much money to lay pipe in the water as it does on land, how far down the shoreline from $P$ should the pipe from the island reach land in order to minimize the total construction costs?
Distance from $P=$ $\square$
Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Page generated at 12/03/2024 at 10:58am EST

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Problem 23867

23. What is the capacitance of a capacitor that draws 150 mA when connected to a $100 \mathrm{~V}, 400 \mathrm{~Hz}$ voltage source?
Ans. 0,597 $\mu \mathrm{F}$ .

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Problem 23868

k. $\left.\begin{array}{rr} +x y=-1 & \left(3 x^{2}+x y=-1\right. \\ x^{2}-3 x y=13 \end{array}\right)$

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Problem 23869

Solve using the quadratic formula. Approximate answers to the nearest tenth. $x^{2}-2 x+1=0$ $\square$ Type your answer, then press Enter. Follow these examples: $\begin{array}{c} x=1 \text { or } 3 \\ x=-5.3 \text { or }-0.1 \end{array}$

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Problem 23870

wledge A mosquito beats its wings at a rate of about 6,000 wing beats per minute. a. What is the frequency in Hertz of the sound wave created by the mosquito's wings? b. Assuming the sound wave moves with a velocity of $350 \mathrm{~m} / \mathrm{s}$ , what is the wavelength of $t$ [4] sound wave generated by the beating wings?

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Problem 23871

The function $f(x)=\frac{x+24}{x-6}$ is one-to-one. For the function, a. Find an equation for $f^{-1}(x)$ , the inverse function. b. Verify that your equation is correct by showing that $f\left(f^{-1}(x)\right)=x$ and $f^{-1}(f(x))=x$ . a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression.) A. $f^{-1}(x)=$ $\square$ , for $\mathrm{x} \neq$ $\square$ B. $f^{-1}(x)=$ $\square$ , for $x \leq$ $\square$ C. $f^{-1}(x)=$ $\square$ , for $x \geq$ $\square$ D. $f^{-1}(x)=$ $\square$ , for all $x$

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Problem 23872

Determine each feature of the graph of the given function. $f(x)=\frac{4 x-16}{x^{2}-x-12}$
Answer Attempt 1 out of 2
Horizontal Asymptote: $y=$ $\square$ No horizontal asymptote
Vertical Asymptote: $x=$ $\square$ No vertical asymptote $x$ -Intercept: $\square$ ,0) No $x$ -intercept $\square$ $y$ -Intercept: (0, $\square$ No $y$ -intercept $\qquad$
Hole: $\square$ $\square$ , ) No hole

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Problem 23873

Find the vertical asymptotes, if any, and the values of $x$ corresponding to holes, if any, of the graph of the rational function. $f(x)=\frac{x}{x+7}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an equation. Use commas to separate answers as needed.) A. There are no vertical asymptotes but there is(are) hole(s) corresponding to $\square$ . B. The vertical asymptote(s) is(are) $\square$ . There are no holes. C. The vertical asymptote(s) is(are) $\square$ and hole(s) corresponding to $\square$ . D. There are no discontinuities.

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Problem 23874

Simplify: $-4 w(4 t)$ $\square$
Submit Question

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Problem 23875

What is the solution to the following system of equations? $\begin{array}{l} y=5 x-1 \\ x=-4-4 y \end{array}$
Enter your answer by filling in the boxes. $\square$ $\square$

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Problem 23876

Simplify. Assume all variables represent positive real numbers. $\sqrt[3]{-27 x^{6}}$

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Problem 23877

Find the vertical asymptotes, if any, and the values of $x$ corresponding to holes, if any, of the graph of the rational function. $f(x)=\frac{x}{x^{2}+12}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a fraction. Use a comma to separate answers as needed.) A. The vertical asymptote(s) is (are) $x=$ $\square$ and hole(s) corresponding to $x=$ $\square$ . B. There are no vertical asymptotes but there is (are) hole(s) corresponding to $x=$ $\square$ . C. The vertical asymptote(s) is (are) $x=$ $\square$ . There are no holes. D. There are no discontinuities.

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Problem 23878

Find the horizontal asymptote, if any, of the graph of the rational function. $f(x)=\frac{17 x}{7 x^{2}+5}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is $\square$ . (Type an equation.) B. There is no horizontal asymptote.

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Problem 23879

Use the properties of logarithms to expand $\log \frac{z^{4}}{y}$ . Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. $\log \frac{z^{4}}{y}=$ $\log$ $\square$

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Problem 23880

Solve: $\frac{2}{3} t=6$ $\mathrm{t}=$

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Problem 23881

From the video, how do the graphs of the form $f(x)=(x-h)^{2}$ differ from $y=x^{2}$ ? Consider the location of the vertex $(h, 0)$ on these graphs of the form $f(x)=(x-h)^{2}$ . By what other name is this point $(h, 0)$ called on a graph?
How do the graphs of the form $f(x)=(x-h)^{2}$ differ from $y=x^{2} ?$ If $h$ is positive, the graph of $f(x)=(x-h)^{2}$ is the graph of $y=x^{2}$ shifted $\square$ $h$ units. If $h$ is negative, the graph of $f(x)=(x-h)^{2}$ is the graph of $y=x^{2}$ shifted $\square$ $|h|$ units.
Consider the location of the vertex $(h, 0)$ on these graphs of the form $f(x)=(x-h)^{2}$ . By what other name is this point $(h, 0)$ called on a graph?

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Problem 23882

In certain deep parts of oceans, the pressure of sea water, $P$ , in pounds per square foot, at a depth of $d$ feet below the surface, is given by the following equation: $P=12+\frac{8 d}{13}$
If a scientific team uses special equipment to measures the pressure under water and finds it to be 596 pounds per square foot, at what depth is the team making their measurements?
Answer: The team is are measuring at $\square$ feet below the surface. Submit Question

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Problem 23883

Find the principal $P$ that will generate the given future value $A$ , where $A=\$ 14,000$ at $7 \%$ compounded daily for 9 years.
The principal P will be approximately $\$$ $\square$ (Round to two decimal places as needed.)

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Problem 23884

Find the unknown number in the proportion $\frac{3}{9}=\frac{2}{x}$ $\square$ Submit Question

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Problem 23885

Begin by graphing $f(x)=3^{x}$ . Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. $h(x)=3^{x-1}-2$ shifted 1 unit to the right and vertically shifted 2 units upward. D. The graph of $f(x)=3^{x}$ should be horizontally shifted 1 unit to the left and vertically shifted 2 units upward.
Graph $h(x)=3^{x-1}-2$ and its asymptote. Graph the asymptote as a dashed line. Use the graphing tool to graph the function.
4 Find the equation of the asymptote for $h(x)=3^{x-1}-2$ using the graph. $\square$ (Type an equation.)

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Problem 23886

(a) Graph the equations in the system. (b) Solve the system by using the substitution method. $\begin{array}{l} x^{2}+y^{2}=25 \\ x+y=-1 \end{array}$
Part: $0 / 2$

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Problem 23887

Solve $36 x^{2}-1764=0$ by factoring. a) Factor $36 x^{2}-1764=0$ to rewrite the equation. $\square$ $=0$ b) The solution set is: $\{$ $\square$ \}

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Problem 23888

11
Un objeto sigue una trayectoria como la que muestra la figura. (Este problema debe incluir procedimiento claro con unidades o no se tomará en cuenta.) Toma en cuenta los datos que aparecen en la imagen y calcula: * (4 puntos) $\omega$ en $\frac{\mathrm{rad}}{\mathrm{s}}$ Gira a razón de $\mathbf{2 5 0 0}$ vueltas por minuto

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Problem 23889

3 Multiple Choice 1 point The least common multiple of two rational expressions is $x^{2}+7 x+12$ . Given the original fraction below, find the value of the numerator that would form an equivalent fraction with a denominator of $x^{2}+7 x+12$ . $\frac{x-2}{x+4}=\frac{?}{x^{2}+7 x+12}$ $(x-2)(x+4)$ $(x-2)(x+3)$ $x+3$ $x-2$ Clear my selection

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Problem 23890

Prehistoric cave paintings were discovered in a cave in France. The paint contained $29 \%$ of the original carbon-14. Use the exponential decay model for carbon-14, $A=A_{0} e^{-0.000121 t}$ , to estimate the age of the paintings.
The paintings are approximately $\square$ years old. (Round to the nearest integer.)

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Problem 23891

[a.] The equation of line $j$ is $y=\frac{-3}{4} x+\frac{3}{8}$ . Line $k$ is perpendicular to $j$ . What is the slop of line $k$ ?
Simplify your answer and write it as a proper fraction, improper fraction, or integer $\square$ Submit Work it out Not feeling ready yet? These can help: Reciprocals Slope-intercept form: find the slo

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Problem 23892

$\text{For each sequence below, use the general formula to find the term indicated.}$ $15, 13, 21, \ldots u_{9}$ $240, 32, 24, \ldots u_{11}$ $\text{The formula is } U_n = U_1 + (n-1)d$

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Problem 23893

$x-14 \leq 5$

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Problem 23894

Video the slope of line $d$ ?
媇, Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out Not feeling ready yet? These can help: Reciprocals Slope-intercept form: find the slope and $y$ -intercept

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Problem 23895

Vid ( $\frac{1}{4}$ . The equation of line $a$ is $y=\frac{52}{67} x-24$ . Line $b$ is parallel to line $a$ . What is the slope of line $b$ ? (x) Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out Not feeling ready yet? These can help: Reciprocals Slope-intercept form: find the slope and $y$ -interce

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Problem 23896

(3) Line $g$ has a slope of $\frac{40}{77}$ . Line $h$ is perpendicular to $g$ . What is the slope of line $h$ ? $\square$ Submit If Work it out Not feeling ready yet? These can help:

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Problem 23897

for Unit 4 Question 12, 4.3.28
Use synthetic division to find the function values. Then ch $f(x)=x^{3}-12 x^{2}+47 x-60 ;$ find $f(3), f(-4)$ , and $f(5)$ . $\qquad$ $\square$ $f(3)=x^{2}-9 x+20$ (Simplify your answer.) $f(-4)=x^{2}-16 x+111-\frac{504}{x-4}$ (Simplify your answer.) $\square$ $\square$ $f(5)=x^{2}-7 x+12-\frac{10}{x+5}$ (Simplify your answer.) Iiew an example Get more help

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Problem 23898

31) $\frac{x}{\sqrt{x-4}}$ A) $\{x \mid x \geq 4\}$ B) all real numbers C) $\{x \mid x \neq 4\}$ D) $\{x \mid x>4\}$

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Problem 23899

The equation of line $t$ is $y=\frac{-9}{37} x-61$ . Line $u$ is perpendicular to $t$ . What is the slope of line $u$ ? (3), Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out

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Problem 23900

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. $\begin{array}{l} 6+4(x+3 y)=7 y+6 \\ 4 x+9=9-3 y \end{array}$ Español The system has one solution. The solution set is $\square$ \}. The system has no solution, $\}$ . The system is inconsistent. The equations are dependent. The system has infinitely many solutions. The solution set is $\square$ $\{x$ is any real number $\}$ . The system is inconsistent. The equations are dependent.

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Algebra

Problem 23801

Упростите выражение: 2log⁡4k−3log⁡462 \log _{4} k-3 \log _{4} 62log4​k−3log4​6

Problem 23802

Problem 23803

Problem 23804

Find the domain of the function f(x)=1−x+x−1 f(x) = \sqrt{1-x} + \sqrt{x-1} f(x)=1−x​+x−1​.

Problem 23805

3. x+5=14xx+5=\frac{14}{x}x+5=x14​5. x+4xx−3=12x−3x+\frac{4 x}{x-3}=\frac{12}{x-3}x+x−34x​=x−312​

Problem 23806

10. 11k+2=2411 k+2=2411k+2=24

Problem 23807

10. x+6x=−7x+\frac{6}{x}=-7x+x6​=−712. 2−3x+4=12x2+4x2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}2−x+43​=x2+4x12​

Problem 23808

6. Find the positive value of xxx that solves the following equation: x60=∑k=030(30k)2030−kx^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}x60=k=0∑30​(k30​)2030−kANS:

Problem 23809

Factor the expression: 3c3+243c^3 + 243c3+24.

Problem 23810

1. Let an=−n2+18n−56a_{n}=-n^{2}+18 n-56an​=−n2+18n−56 where n∈Nn \in \mathbb{N}n∈N. What is the smallest n0∈Nn_{0} \in \mathbb{N}n0​∈N such that ana_{n}an​ is decreasing for all n⩾n0n \geqslant n_{0}n⩾n0​.ANS:

Problem 23811

3. If S(N)=∑k=1NkS(N)=\sum_{k=1}^{N} kS(N)=∑k=1N​k then which value of NNN solves the following equation? ∑n=1S(N)4n=43(455−1).\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .n=1∑S(N)​4n=34​(455−1).ANS: \qquad

Problem 23812

5. If a savings account offers a nominal interest rate of 3%3 \%3% per year, compounded every four months, then how many years will it take for a deposit to double in value?ANS:

Problem 23813

Identify the coefficient and degree of the term: −10x4b4-10 x^{4} b^{4}−10x4b4 The coefficient is □\square□ and the degree is □\square□ Question Help: Video Written Example

Problem 23814

Problem 23815

ANS: x∈(1,5)∪18;+x \in(1,5) \cup 18 ;+x∈(1,5)∪18;+3. If S(N)=∑k=1NkS(N)=\sum_{k=1}^{N} kS(N)=∑k=1N​k then which value of NNN solves the following equation? ∑n=1S(N)4n=43(455−1)\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)n=1∑S(N)​4n=34​(455−1)ANS: N=10N=10N=10

Problem 23816

Problem 23817

5) Complete the table using the function y=3x−4y=3 x-4y=3x−4.

Problem 23818

(iii) Evaluate the following without using log tables: 2log⁡5+log⁡3+3log⁡2−12log⁡36−2log⁡102 \log 5+\log 3+3 \log 2-\frac{1}{2} \log 36-2 \log 102log5+log3+3log2−21​log36−2log10

Problem 23819

Problem 23820

2. 4. What is the conductance of a 39Ω39 \Omega39Ω resistor? Ans. 25,6 mS.

Problem 23821

Problem 23822

8. 11. The conductance of a wire is 2,5 S2,5 \mathrm{~S}2,5 S. Another wire of the same material and at the same temperature has a diameter one-forth as great and the length twice as great. Find the conductance of the second wire. Ans. 78,1mS78,1 \mathrm{mS}78,1mS.

Problem 23823

14. 17. Find the temperature coefficient of resistance of iron at 20∘C20^{\circ} \mathrm{C}20∘C, if iron has an inferred zero resistance temperature −162∘C-162^{\circ} \mathrm{C}−162∘C ? Ans 0,00551/∘C−0,00551 /{ }^{\circ} \mathrm{C}-0,00551/∘C−

Problem 23824

Graph each equation. 5) y=x2−2x−3y=x^{2}-2 x-3y=x2−2x−3Identify the min⁡/max⁡\min / \maxmin/max value of each. Th

Problem 23825

Problem 8. An e.m.f. of 250 V is connected across a resistance and the current flowing through the resistance is 4 A . What is the power developed? Ans. 1 kW.

Problem 23826

Write the function whose graph is the graph of y=xy=\sqrt{x}y=x​ but is shifted down 3 units.

Problem 23827

31. The sum of two numbers is 37 . One number is 5 more than the other. Find the numbers.

Problem 23828

19. Use voltage division twice to find the voltage UUU in the circuit given below. Ans. 36V.

Problem 23829

Problem 23830

4. Three parallel resistors have a total conductance of 2 mS . If two of the resistors are 1 and 5kΩ5 \mathrm{k} \Omega5kΩ what is the third resistance? Ans. 1,25 k

Problem 23831

3. x+y=8−x+2y=7\begin{aligned} x+y & =8 \\ -x+2 y & =7\end{aligned}x+y−x+2y​=8=7​

Problem 23832

Problem 23833

Determine algebraically whether the given function is even, odd, or neither. f(x)=2x+∣−5x∣f(x)=2 x+|-5 x|f(x)=2x+∣−5x∣Choose the correct answer. Even Neither

Problem 23834

Problem 23835

Which expression has the greatest value? 15(5352)2\frac{1}{5}\left(\frac{5^{3}}{5^{2}}\right)^{2}51​(5253​)2 58(52)4\frac{5^{8}}{\left(5^{2}\right)^{4}}(52)458​ (5354)3\left(\frac{5^{3}}{5^{4}}\right)^{3}(5453​)3 (52)354\frac{\left(5^{2}\right)^{3}}{5^{4}}54(52)3​ sUbmit all

Problem 23836

Problem 23837

Problem 23838

Problem 23839

Problem 23840

Problem 23841

Which expression is equivalent to (8a−3b+7)−(2a+b−4)(8 a-3 b+7)-(2 a+b-4)(8a−3b+7)−(2a+b−4) ? 6a−2b+116 a-2 b+116a−2b+11 6a−4b+36 a-4 b+36a−4b+3 6a−2b+36 a-2 b+36a−2b+3 6a−4b+116 a-4 b+116a−4b+11

Problem 23842

Problem 23843

Problem 23844

Use point-slope form to write the equation of a line that passes through the point left parenthesis, 18, comma, 20, right parenthesis (with slope minus, start fraction, 3, divided by, 2, end fraction

Problem 23845

Problem 23846

Problem 23847

2 2.) −5x+10=10−5x+10−10=10−10−5x=0\begin{array}{l} \text { 2.) }-5 x+10=10 \\ -5 x+10-10=10-10 \\ -5 x=0 \end{array} 2.) −5x+10=10−5x+10−10=10−10−5x=0​

Problem 23848

4. [-/0.32 Points]DETAILS MY NOTES SCOLALG7 4.4.014. 0/100 SubmissionsUse the Laws of Logarithms to evaluate the expression. −13log⁡5(125)-\frac{1}{3} \log _{5}(125)−31​log5​(125) □\square□ Need Helo?

Problem 23849

Упростите выражение: $2 \log _{4} k-3 \log _{4} 6$

Find the domain of the function $f(x) = \sqrt{1-x} + \sqrt{x-1}$ .

3. $x+5=\frac{14}{x}$
5. $x+\frac{4 x}{x-3}=\frac{12}{x-3}$

10. $11 k+2=24$

10. $x+\frac{6}{x}=-7$
12. $2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}$

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS:

Factor the expression: $3c^3 + 24$ .

1. Let $a_{n}=-n^{2}+18 n-56$ where $n \in \mathbb{N}$ . What is the smallest $n_{0} \in \mathbb{N}$ such that $a_{n}$ is decreasing for all $n \geqslant n_{0}$ .
ANS:

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$
ANS: $\qquad$

5. If a savings account offers a nominal interest rate of $3 \%$ per year, compounded every four months, then how many years will it take for a deposit to double in value?
ANS:

Identify the coefficient and degree of the term: $-10 x^{4} b^{4}$ The coefficient is $\square$ and the degree is $\square$ Question Help: Video Written Example

ANS: $x \in(1,5) \cup 18 ;+$
3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS: $N=10$

5) Complete the table using the function $y=3 x-4$ .

(iii) Evaluate the following without using log tables: $2 \log 5+\log 3+3 \log 2-\frac{1}{2} \log 36-2 \log 10$

2. 4. What is the conductance of a $39 \Omega$ resistor? Ans. 25,6 mS.

8. 11. The conductance of a wire is $2,5 \mathrm{~S}$ . Another wire of the same material and at the same temperature has a diameter one-forth as great and the length twice as great. Find the conductance of the second wire. Ans. $78,1 \mathrm{mS}$ .

14. 17. Find the temperature coefficient of resistance of iron at $20^{\circ} \mathrm{C}$ , if iron has an inferred zero resistance temperature $-162^{\circ} \mathrm{C}$ ? Ans $0,00551 /{ }^{\circ} \mathrm{C}-$

Graph each equation. 5) $y=x^{2}-2 x-3$
Identify the $\min / \max$ value of each. Th

Write the function whose graph is the graph of $y=\sqrt{x}$ but is shifted down 3 units.

19. Use voltage division twice to find the voltage $U$ in the circuit given below. Ans. 36V.

4. Three parallel resistors have a total conductance of 2 mS . If two of the resistors are 1 and $5 \mathrm{k} \Omega$ what is the third resistance? Ans. 1,25 k

3. $\begin{aligned} x+y & =8 \\ -x+2 y & =7\end{aligned}$

Determine algebraically whether the given function is even, odd, or neither. $f(x)=2 x+|-5 x|$
Choose the correct answer. Even Neither

Which expression has the greatest value? $\frac{1}{5}\left(\frac{5^{3}}{5^{2}}\right)^{2}$ $\frac{5^{8}}{\left(5^{2}\right)^{4}}$ $\left(\frac{5^{3}}{5^{4}}\right)^{3}$ $\frac{\left(5^{2}\right)^{3}}{5^{4}}$ sUbmit all

Which expression is equivalent to $(8 a-3 b+7)-(2 a+b-4)$ ? $6 a-2 b+11$ $6 a-4 b+3$ $6 a-2 b+3$ $6 a-4 b+11$

2 $\begin{array}{l} \text { 2.) }-5 x+10=10 \\ -5 x+10-10=10-10 \\ -5 x=0 \end{array}$

4. [-/0.32 Points]
DETAILS MY NOTES SCOLALG7 4.4.014. 0/100 Submissions
Use the Laws of Logarithms to evaluate the expression. $-\frac{1}{3} \log _{5}(125)$ $\square$ Need Helo?

Given the equation $x / 3=-12$ , the value of $x=-4$ .
A True B False Find the value of $x$ if the answer is false: $\qquad$

a. $\quad \log (14)$ b. $\log (35)$

Calculate c. $\log (72)$ d. $\log (121)$

6.) $7-4 x=x=53$

Use the quadratic formula to solve. Express your answer in simplest form. $4 w^{2}+20 w+25=0$

6.02 EXAM REVIEW_UNIT 2 XEM OZ6 Q Find une value of X In the equarinn novow. Question o 6/16 $1 / 6(36 x-12)-5 x=10$
A $x=-2$ B $x=8$ C $\mathrm{x}=12$ D $x=22$

Use the quadratic formula to solve. Express your answer in simplest form. $4 x^{2}-5 x-6=0$

A. Given the equation: $3 \sqrt[4]{m}(5 \sqrt{m})=15 \sqrt[x]{m^{3}}$
Find the value of $x$ .

Write the logarithmic expression as a single logarithm with coefficient 1 , and simplify as much as possible. Assume that the variables represent positive real numbers. $\ln y+\ln 3=$

Question
Use the properties of exponents to determine the value of $a$ for the equation: $\left(x^{\frac{1}{2}}\right)^{3} \sqrt{x}=x^{a}$

Part: 1 / 3
Part 2 of 3 (b) Approximate the logarithm to 4 decimal places. If necessary, round intermediate steps to 9 decimal places. $\log _{5} 28 \approx$ $\square$

27. A star-connected load consists of three identical coils each of resistance $30 \Omega$ and inductance 127.3 mH .
If the line current is $5,08 \mathrm{~A}$ , calculate the line voltage if the supply frequency is 50 Hz .

Subtract. Your answer should be a polynomial in standard form. $\left(d^{2}+6 d+9\right)-\left(d^{3}+6 d+9\right)=$ $\square$

23. What is the capacitance of a capacitor that draws 150 mA when connected to a $100 \mathrm{~V}, 400 \mathrm{~Hz}$ voltage source?
Ans. 0,597 $\mu \mathrm{F}$ .

k. $\left.\begin{array}{rr} +x y=-1 & \left(3 x^{2}+x y=-1\right. \\ x^{2}-3 x y=13 \end{array}\right)$

Simplify: $-4 w(4 t)$ $\square$
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