Browse Algebra problems Studdy Solved!

Problem 24001

$\frac{\frac{x}{x+3}}{1+\frac{1}{x+3}}$

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Problem 24002

Question Watch Video Show Examples
A new car is purchased for 20300 dollars. The value of the car depreciates at $8.75 \%$ per year. What will the value of the car be, to the nearest cent, after 12 years?
Answer $\square$ Submit Answer You have up to 8 questions left to raise your score. Still Stuck?

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Problem 24003

SECTION 3.4 Exercises perercises 1-12, assuming $x$ and $y$ are positive, use properties of 1 /nulup les of logarithms.
1. $\ln 8 x$
2. $\ln 9 y$
3. $10 \frac{3}{x}$
4. $\log \frac{2}{y}$
5. $\log _{2} y^{5}$
6. $\log _{2} x^{-2}$
7. $\log x^{3} y^{2}$
8. $\log x y^{3}$
9. $\ln \frac{x^{2}}{y^{3}}$
10. $\log 1000 x^{4}$
11. $\log \sqrt[4]{\frac{x}{y}}$
12. $\ln \frac{\sqrt[3]{x}}{\sqrt[3]{y}}$

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Problem 24004

Use the definition of a one-to-one function to determine if the function is one-to-one. $k(x)=|x-1|$ The function is one-to-one. The function is not one-to-one.

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Problem 24005

Jada was solving the equation $\sqrt{6-x}=-16$ . She was about to square each side, but then she realized she could give an answer without doing any algebra. What did she realize?

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Problem 24006

Question 6 of 9, Step 1 of 1 $4 / 11$ Correct 1
The function $\mathrm{C}(\mathrm{t})=\mathrm{C}_{0}(1+\mathrm{r})^{t}$ models the rise in the cost of a product that has a cost of $\mathrm{C}_{0}$ today, subject to an average yearly inflation rate of $r$ for $t$ years. If the average annual rate of inflation over the next 11 years is assumed to be $3.5 \%$ , what will the inflation-adjusted cost of a $\$ 18,100$ car be in 11 years? Round to two decimal places.

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Problem 24007

There are 35 nickels on one pan of a pan balance and 26 nickels on the other. To make the pans balance, Levi thinks 5 nickels should be added to the higher pan, Isaac thinks 8 nickels should be added, and Miranda thinks 9 nickels should be added. Use the equation $35=26+n$ to determine who is correct. $\square$ is correct because the value $\square$ makes the equation $\square$

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Problem 24008

Consider the following EQUATIONS, make a table, plot the points, and
1. $f(x)=\sqrt{x}$
2. $f(x)=2 \sqrt{x}$ \begin{tabular}{c|c} $x$ & $y$ \\ \hline-4 & \\ -1 & \\ 0 & \\ 1 & \\ 2 & \\ 3 & \\ 4 & \\ \hline \end{tabular} \begin{tabular}{c|c} $x$ & $y$ \\ \hline-4 & \\ -1 & \\ 0 & \\ 1 & \\ 2 & \\ 3 & \\ 4 & \end{tabular} 3.

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Problem 24009

Math and Physics Power and quotient rules with positive exponents
Simplify. $\frac{\left(3 b^{2}\right)^{2}}{\left(2 b^{3}\right)^{3}}$
Write your answer using only positive exponents.

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Problem 24010

The price of a jumper is reduced by $17 \%$ in a sale. The sale price is $£ 62.25$
What was the original price of the jumper?

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Problem 24011

Make $x$ the subject of $x-9=r$

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Problem 24012

Make $x$ the subject of $5 x=r$

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Problem 24013

Rearrange $g=f r$ to make $f$ the subject.

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Problem 24014

Use the function below to answer the following questions. $n(x)=-e^{x}+3$ (a) Use transformations of the graph of $y=e^{x}$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.
Part: $0 / 3$
Part 1 of 3

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Problem 24015

Rearrange $k=d w$ to make $d$ the subject.

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Problem 24016

Rearrange $a k-y=c$ to make $k$ the subject.

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Problem 24017

Use the function below to answer the following questions. $m(x)=5^{x+4}$ (a) Use transformations of the graph of $y=5^{x}$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.
Part: $0 / 3$

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Problem 24018

Make $k$ the subject of $d=\frac{k+m}{2}$

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Problem 24019

Which of the following is equivalent to $i^{26}$ ? -1 $-i$ 1 i

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Problem 24020

Directions: Solve, graph, and write the solution to each inequality in interval notation.
1. $|b+3| \geq 7$
Interval Notation:
3. $|5 k+4| \geq 36$
Interval Notation:
5. $\left|\frac{n}{7}\right|-6>-5$
Interval Notation:
2. $|-2 v-4|<8$
Interval Notation:
4. $|3-9 y| \leq 33$
Interval Notation:
6. $\frac{|5+3 w|}{-2} \leq-1$
Interval Notation: Gina Wilson (All Things Algebra), 201

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Problem 24021

$x^{2}-2 x-8 \leq 0$

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Problem 24022

$5 x+3 y=15$

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Problem 24023

Factor the expression completely. $-60 x^{4}+54 x$

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Problem 24024

Solve by completing the square. $-3 v^{2}+48 v-75=0$
言A Write your answers as integers, proper or improper fractions in simplest form, or cimals rounded to the nearest hundredth. ) [ix $\left.\dot{x}_{A}\right]=$ $\square$ or $v=$ $\square$

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Problem 24025

Solve the system by using the addition method. $\begin{aligned} 4 x^{2}+y^{2} & =37 \\ 6 x^{2}-4 y^{2} & =50 \end{aligned}$ There are infinitely many solutions. The solution set is the empty set, $\}$ . The solution set is a finite set. The solution set is $\square$ \}

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Problem 24026

3. The population of the People's Republic of China has been doubling approximately every sixty years. The population in 1975 was about 824000000 . If the current growth rate continues, what will the population be in $2215 ?$

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Problem 24027

1. $(04.02 \mathrm{LC})$
Solve the following system of equations: (1 point) $\begin{array}{l} x-2 y=14 \\ x+3 y=9 \end{array}$ $(1,12)$ $(-1,-12)$ $(12,-1)$ $(12,1)$

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Problem 24028

Solve the following equation: $\frac{3}{4} x=60$

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Problem 24029

6. (04.02 MC)
A gym offers regular memberships for $\$ 80$ per month and off-peak memberships for $\$ 60$ per month. Last month, the gym sold a total of 420 memberships for a total of $\$ 31,100$ . The following system of equations models this scenario: $\begin{array}{l} 80 x+60 y=31,100 \\ x+y=420 \end{array}$
How many of the memberships sold were regular memberships? (1 point) 125 140 235 295

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Problem 24030

Find the number of solutions by graphing the system of equations. Select "None" if applicable. (Hint: Rewrite the system of equations into familiar forms to graph.) $\begin{array}{l} \ln 7=2 \ln x-\ln y \\ x^{2}+y^{2}-6 y+8=0 \end{array}$
Number of solutions: $\square$ None

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Problem 24031

Quadratic and Exponential Functions Graphing a parabola of the form $y=\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}$ : Integer coefficier aph the parabola. $y=3 x^{2}-30 x+69$
Plot five points on the parabola: the vertex, two points to the le button.

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Problem 24032

e graph of a rational function $f$ is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary.
Vertical asymptote(s): $x=-1$
Horizontal asymptote(s): $\square$ (b) Find all $x$ -intercepts and $y$ -intercepts. Check all that apply. $x$ -intercept(s): $\square$ $-1$ $-3$ $\square$ - 6 $\square$ None $y$ -intercept(s): $\square$ $-6$ $\square$ $-2$ $\square$ $-3$ None (c) Find the domain and range of $f$ .
Write each answer as an interval or union of intervals. Domain: $\square$ Range: $\square$

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Problem 24033

4) Let $f(x)=3 x+2, g(x)=x^{2}+2 x+1$ , and $h(x)=\frac{2 x+1}{x-1}$ a) Find and simplify $(g \circ f)(x),(f \circ g)(x),(f \circ f)(x)$ . b) Find $f^{-1}$ and show that the function you found is indeed the inverse of $f(x)$ c) $h(x), x \neq 1$ is one-to-one. Find its inverse and check the result.

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Problem 24034

Find an equation of the form $y=a x^{2}+b$ for a parabola that passes through the points $(-1,1)$ and $(-2,7)$ . $y=$

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Problem 24035

$\mathrm{V}_{2} \mathrm{O}_{5}+\ldots \mathrm{HCl} \rightarrow \ldots \mathrm{VOCl}_{3}+\ldots \mathrm{H}_{2} \mathrm{O}$

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Problem 24036

Solve the equation. Simplify the answer as much as possible. $27^{x+5}=9^{2 x+2}$
The solution set is $\square$ \}.

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Problem 24037

hmic Functions Question 11, 5.4.67
Solve the equation. Use the change of base formula when appropriate. $e^{-x}=18$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=$ $\square$ (Type an integer or decimal rounded to the nearest hundredth as needed.) B. There is no solution.

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Problem 24038

Using Descartes' Rule of Signs, what can be said about the following polynomial: $x^{3}-4 x^{2}+7 x-10$ ? Since there are two negatives and one positive, there will be only two negative roots. Since there are an even amount of positive and negative signs, there is no solution. Since there is only one variable ( $x$ ), there will be fewer than three answers. There are three sign changes, meaning this polynomial has up to three positive roots.

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Problem 24039

unctions Question 13, 5.4.71
Solve the equation. $10^{5 x}=10000$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $x=$ $\square$ . (Type an integer or a fraction.) B. There is no solution.

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Problem 24040

14. This year, a rancher counted 225 horses on the range. This count is 22 fewer than last year. How many horses did the rancher count last year? Let $h$ be the number of horses counted last year. Solve $h-22=225$ to find the number of horses counted last year.

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Problem 24041

Equations Points: 0 of 1
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1 , and roots of $2-\sqrt{6}, 2+\sqrt{6}$ , and $7-i$ .
The polynomial function is $\mathrm{P}(\mathrm{x})=$ $\square$ (Simplify your answer.) View an example Get more help

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Problem 24042

Part 3 of 3 Points: 0.67 of 1
For the function shown below, complete the following. $f(x)=x^{3}-2 x^{2}-9 x+18$ a. List all possible zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. a. List all possible rational zeros. $\pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18$ (Use a comma to separate answers as needed.) b. Use synthetic division to test the possible rational zeros and find an actual zero.
One of the actual rational zeros is 2 . c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. Then write all of the zeros of the function.
The solution of $f(x)=x^{3}-2 x^{2}-9 x+18$ is $\square$ (Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) example Calculator

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Problem 24043

$\begin{array}{l}\frac{c}{3}=-5 m-\frac{8}{3} \\ -\frac{m}{7}+\frac{3 c}{4}=-6\end{array}$

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Problem 24044

Feng invests money in an account paying simple interest. He invests $\$ 70$ and no money is added or removed from the investment. After one year, he has $\$ 70.70$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

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Problem 24045

6. Form a polynomial $f(x)$ with real coefficients having the given degree and zeros.
Degree 4 ; zeros: 4 , multiplicity $2 ; 6 i$ Enter the polynomial. Let a represent the leading coefficient. $f(x)=a($ ]) $\square$ (Type an expression using $x$ as the variable. Use integers or fractions for any numbers in the

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Problem 24046

Amelia invests money in an account paying simple interest. She invests $\$ 100$ and no money is added or removed from the investment. After one year, she has $\$ 101$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

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Problem 24047

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 16 miles per hour slower than the eastbound train. If the two trains are 540 miles apart after 3 hours, what is the rate of the westbound train?
Do not do any rounding. $\square$ 7 miles \$er hour

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Problem 24048

$\begin{array}{l}x-6 y=\frac{56}{17} \\ y=3 x-\frac{47}{34}\end{array}$

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Problem 24049

$\begin{array}{l}-7 r+10 p=-\frac{137}{9} \\ 2 r+6 p=\frac{16}{3}\end{array}$

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Problem 24050

2. Luke, Obi-Wan and Yoda are collecting light sabers for their collections. Together, they have 11 light sabers. The number of light sabers Luke has combined with 2 times the number Obi-Wan has equals three less than three times the number Yoda has. Four times the number Obi-Wan has combined with three times the number Yoda has is the same as four times as many as Luke. How many light sabers does each person have?
Luke: $\qquad$ light sabers
Obi-wan: $\qquad$ light sabers
Yoda: $\qquad$ light sabers

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Problem 24051

$61=-9 c+7$

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Problem 24052

Use the Binomial Theorem to expand the binomial: $\left(x^{8}+\sqrt{x}\right)^{3}$

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Problem 24053

Listen
Evaluate the function for the given value of $x$ . $\begin{array}{l} y=-9(3)^{x} ; x=-1 \\ y=\square \quad 0_{\varphi} \end{array}$ $\square$

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Problem 24054

Given the equation $q=Q_{0} e^{-t / R C}$ , rearrange the equation to solve for $t$ .

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Problem 24055

Perform the operation. Write the answer in standard form. $(4+i)(2-i)$ $\square$

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Problem 24056

$d(z-8)+5(z-8)=$

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Problem 24057

Video
A line has a slope of $\frac{7}{2}$ and includes the points $(5, k)$ and $(3,-3)$ . What is the value of $k$ ? $k=$ $\square$ Submit

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Problem 24058

Solve the following equation and check your solution. $-14 y+12(-14 y-11)=4418$ $y=$ $\square$ (Simplify your answer.)

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Problem 24059

Question 2, 10.6.10
HW Score: $0 \%, 0$ of 10 points Points: 0 of 1
Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if $\$ 80$ is invested semiannually for 35 year $6.5 \%$ compounded semiannually.

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Problem 24060

Divide. Express your answer in lowest terms. $\frac{30 x^{2}+11 x y-30 y^{2}}{48 x^{2}-46 x y+5 y^{2}} \div \frac{25 x^{2}-60 x y+36 y^{2}}{40 x^{2}-53 x y+6 y^{2}}$

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Problem 24061

Divide. Express your answer in lowest terms. $\frac{30 x^{2}+11 x y-30 y^{2}}{48 x^{2}-46 x y+5 y^{2}} \div \frac{25 x^{2}-60 x y+36 y^{2}}{40 x^{2}-53 x y+6 y^{2}}$

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Problem 24062

Find a possible formula for the function graphed below. The $x$ -intercepts are marked with points located at $(5,0)$ and $(-4,0)$ , while the $y$ -intercept is marked with a point located at $\left(0,-\frac{5}{3}\right)$ . The asymptotes are $y=-1, x=-3$ , and $x=4$ . Give your formula as a reduced rational function. $f(x)=$ $\square$ help (formulas) (Click on graph to enlarge)

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Problem 24063

Which of the formulas below could be a polynomial with all of the following properties: its only zeros are $x=-6,-3,2$ , it has $y$ -intercept $y=3$ , and its long-run behavior is $y \rightarrow-\infty$ as $x \rightarrow \pm \infty$ ? Select every formula that has all of these properties. A. $y=-\frac{3}{108}(x+6)(x+3)^{2}(x-2)$ B. $y=-\frac{3}{972}(x+6)(x+3)^{4}(x-2)$ (i) C. $y=-\frac{3}{36}(x+6)(x+3)(x-2)$ D. $y=-3 x(x+6)(x+3)(x-2)$ E. $y=\frac{3}{72}(x+6)(x+3)(x-2)^{2}$ F. $y=-\frac{3}{72}(x+6)(x+3)(x-2)^{2}$ G. $y=-\frac{3}{216}(x+6)^{2}(x+3)(x-2)$

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Problem 24064

A small bicycle manufacturer has daily fixed costs of $\$ 1992$ and each bicycle costs $\$ 76$ to manufacture. Let $x$ represent the number of bicycles manufactured and $\mathrm{C}(\mathrm{x})$ represents the cost of manufacturing. Complete parts (a) through (c). (a) Write a linear function that models this situation. $C(x)=$ $\square$

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Problem 24065

Solve the inequality for $w$ . $8 w-11>6 w-5$
Simplify your answer as much as possible.

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Problem 24066

The graph of the equation representing compound interest is that of: A. linear function. B. quadratic function. C. exponential function. D. None of the above

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Problem 24067

A package of silicone straws costs $\$ 6$ . This is $\$ 7$ less than the cost of a package of metal straws. Select the equations that could be used to find the cost c of th package of metal straws. A) $7=c \div 6$ B) $c-7=6$ C) $c \times 7=6$ D) $6+7=c$ E) $-6+7=c$

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Problem 24068

Which of the following is true about the base $b$ of a logarithmic function? $b=0$ and $b=1$ $b>0$ and $b=1$ $b<0$ and $b=1$ b : 0 ando b

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Problem 24069

In 2010, a laptop computer was purchased for $\$ 2050$ . Each year since, the resale value has decreased by $24 \%$ . Let $t$ be the number of years since 2010. Let $y$ be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between $y$ and $t$ . $\square$ O 2024 McGraw Hill LLC. All Rights Rese (1) 397 Sunny Search

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Problem 24070

What is the solution to the equation $y+7=-21 ?$ A) $y=24$ B) $y=14$ C) $y=-14$ D) $y=-28$

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Problem 24071

Simplify. $\left(x^{3}-7 x^{2}+13 x-15\right) \div(x-5)$
Put your answer in standard form. (no

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Problem 24072

Solve the system. $\begin{array}{c} x^{2}+8 x+y+7=2 \\ y=-2 x+4 \end{array}$

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Problem 24073

Bookwork code: 5C Calculator allowed
A bowling alley can be hired for a party. The formula below shows the cost. A party cost $£ 316$ . How many people were at the party?

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Problem 24074

A cereal company is developing a new granola bar. It follows a recipe based on the graph shown below.
1. What is the constant of proportionality?
2. Explain what the constant of proportionality means for this example. Your response should mention "nuts" and "fruit".
3. How many cups of nuts would be needed for 10 cups of fruit? Show or explain how you know.
4. How many cups of fruit would be needed for 9 cups of nuts? Show or explain how you know.
5. Make a table of the graph above. Include at least five pairs of values.

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Problem 24075

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $\begin{array}{l} \sqrt[3]{\frac{7 x}{81 y^{12}}} \\ \sqrt[3]{\frac{7 x}{81 y^{12}}}= \end{array}$ $\square$ (Type an exact answer, using radicals as needed. Simplify your answer.)

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Problem 24076

A hot dog stand sells hot dogs for $\$ 3$ each. a. Write a linear equation to represent the total income, I, the stand makes based on the number of hot dogs sold, $h$ . b. What is the income if 150 hotdogs are sold? c. How many hotdogs to earn $\$ 2200$ .

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Problem 24077

Jse the parent function $f(x)=|x|$ to graph $g(x)=-|x-4|$ .

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Problem 24078

1 Numeric 1 point What is $p(4)$ for $p(x)=4 x^{2}-5 x-20$

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Problem 24079

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of $8 \%$ per hour. Suppose that a sample culture has an initial population of 522 bacteria. Find the population predicted after six hours, according to the model.
Do not round any intermediate computations, and round your answer to the nearest tenth. $\square$ bacteria

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Problem 24080

Use the information below to find the value of $r$ . $\begin{array}{c} r=f(4 f+m) \\ f=-2 \\ m=14 \end{array}$

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Problem 24081

Evaluate the function $d(x)=-2 x+9$ when $x=5$ .

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Problem 24082

Check here for instructional material to complete this problem. Let a be the length of a snowboard, and let b be length of the bag needed to hold it. Identify the independent variable and the dependent variab
For the variables b and a , identify the independent variable and the dependent variable. A. The variable a is the independent variable and variable b is the dependent variable. B. The variable $a$ is the dependent variable and variable $b$ is the independent variable.

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Problem 24083

Express as a single logarithm and simplify, if possible. $\frac{1}{3} \log _{b} x+5 \log _{b} y-2 \log _{b} x$

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Problem 24084

9) Perform the following transformations of $h(x)=\frac{1}{x^{2}}$ (write your resulting equation in every step below): a) Shift $h(x)$ up 3 units. b) Shift the result of a) left 2 units. c) Reflect the result of b) about the $x$ -axis. d) Reflect the result of c) about the $y$ -axis. 10) Perform the transformations of Problem 9 applied to the functions $f(x)=e^{2 x}$ and $g(x)=\ln x$ . Sketch the resulting graphs.

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Problem 24085

Identify the property that justifies the statement $z(2 w+y)=(2 w+y) z$ . A associative property of multiplication B commutative property of multiplication C multiplication property of equality D symmetric property of equality

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Problem 24086

6. Describe the number and type of solutions to the equation. $2 x^{2}-6 x+8=0$

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Problem 24087

3) Which answer choice best describes the end behavior of the graph of $y=3\left(\frac{1}{3}\right)^{x}+2$ ? You need to sketch the graph to answer. (1) $\quad x \rightarrow \infty, f(x) \rightarrow 0$ (3) $\quad x \rightarrow \infty, f(x) \rightarrow 2$ $x \rightarrow-\infty, f(x) \rightarrow \infty$ $x \rightarrow-\infty, f(x) \rightarrow \infty$ (2) $x \rightarrow \infty, f(x) \rightarrow-\infty$ (4) $\quad x \rightarrow \infty, f(x) \rightarrow \infty$ $x \rightarrow-\infty, f(x) \rightarrow 0$ $x \rightarrow-\infty, f(x) \rightarrow 2$

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Problem 24088

Show that the given functions are inverse functions of each other. Then display the graphs of each function and the line $y=x$ on a graphing calculator and note that each is the mirror image of the other across $y=x$ . $y=10^{x / 2} \text { and } y=2 \log _{10} x$
Transform the function $y=10^{x / 2}$ to show that it is the inverse of $y=2 \log _{10} x$ . $y=10^{x / 2} \rightarrow \square$ $\square$

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Problem 24089

Rationalize the denominator of $\sqrt[4]{\frac{81}{8}}$ .

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Problem 24090

Given the sequential instructions below. Identify the instructions suitable for parallelism and those that are not suitable. i. $\quad \mathrm{e}=\mathrm{a}+\mathrm{b}$ ii. $p=f+c$ iii. $\quad f=c+d$ iv. $g=e * f$

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Problem 24091

$90 \%$ of the stores at a shopping mall sell clothing. If 63 of the stores sell clothing, how many total stores are at the mall?
Pick the model that represents the problem. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline $0 \%$ & $10 \%$ & $20 \%$ & $30 \%$ & $40 \%$ & $50 \%$ & $60 \%$ & $70 \%$ & $80 \%$ & $90 \%$ & $100 \%$ \\ \hline & & & & & & & & & & & & \\ \hline \\ \hline 0 & & & & & & & & & & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline $0 \%$ & $10 \%$ & $20 \%$ & $30 \%$ & $40 \%$ & $50 \%$ & $60 \%$ & $70 \%$ & $80 \%$ & $90 \%$ & $100 \%$ \\ \hline & & & & & & & & & & & & \\ \hline \\ \hline 0 & & & & & & & & & & & & \\ \hline \end{tabular}
How many total stores are at the mall? $\square$ stores

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Problem 24092

71 Soit $S_{n}$ la somme définie pour tout $n \in \mathbb{N}$ par $S_{n}=1+5+5^{2}+5^{3}+\ldots+5^{n}$ .
1. Exprimer $S_{n}$ en fonction de $n$ .
2. Déterminer limite de $S_{n}$ quand $n$ tend vers $+\infty$ en justifiant.

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Problem 24093

Rationalize the denominator of $4 \sqrt{\frac{16}{27}}$ .

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Problem 24094

(3.) The equation $p(h)=5,000 \cdot 2^{h}$ represents a bacteria population as a function of time in hours. Here is a graph of the function $P$ , (4.) Use the graph to determine when the population will reach 100,000 D. Explain why $\log _{2} 20$ also tells us when the population will reach 100,000 ,
4. Solve $9 \cdot 10^{(0.2 t)}=900$ . Show your reasoning.

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Problem 24095

Rationalize the denominator. $\frac{4 \sqrt{5}+\sqrt{10}}{8 \sqrt{5}-\sqrt{10}}$

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Problem 24096

12. A patient weighs 16.5 kg and is prescribed a medication for $0.4 \mathrm{mg} / \mathrm{kg} /$ dose. The stock strength is $20 \mathrm{mg} / 5 \mathrm{~mL}$ . What volume will you give the patient?

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Problem 24097

5 Honors Question 1, $\mathbf{6 . 0 . 6 0}$ Points: 0 of 1
Determine the smallest number both the numerator and denominator should be multiplied by to rationalize the denominator of the radical expression. $\frac{2}{\sqrt[3]{3}}$

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Problem 24098

Given $f(x)=-x^{2}+4 x+10$ , find $f(-6)$
Answer Attempt 1 out of 2

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Problem 24099

at is the value of the expression below when $y=2$ ? $8 y-8$ Attempt 1 out of 2

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Problem 24100

4. Given the line whose equation is $2 y-6 x=10$ , for every one unit of increase in $x$ , which of the following is true about $y$ ? (Hint, rearrange into $y=m x+b$ form first.) (1) $y$ decreases by 6 (2) $y$ increases by 3 (3) $y$ increases by 2 (4) $y$ decreases by 10

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Algebra

Problem 24001

xx+31+1x+3\frac{\frac{x}{x+3}}{1+\frac{1}{x+3}}1+x+31​x+3x​​

Problem 24002

Problem 24003

Problem 24004

Use the definition of a one-to-one function to determine if the function is one-to-one. k(x)=∣x−1∣k(x)=|x-1|k(x)=∣x−1∣ The function is one-to-one. The function is not one-to-one.

Problem 24005

Jada was solving the equation 6−x=−16\sqrt{6-x}=-166−x​=−16. She was about to square each side, but then she realized she could give an answer without doing any algebra. What did she realize?

Problem 24006

Problem 24007

Problem 24008

Problem 24009

Math and Physics Power and quotient rules with positive exponentsSimplify. (3b2)2(2b3)3\frac{\left(3 b^{2}\right)^{2}}{\left(2 b^{3}\right)^{3}}(2b3)3(3b2)2​Write your answer using only positive exponents.

Problem 24010

The price of a jumper is reduced by 17%17 \%17% in a sale. The sale price is £62.25£ 62.25£62.25What was the original price of the jumper?

Problem 24011

Make xxx the subject of x−9=rx-9=rx−9=r

Problem 24012

Make xxx the subject of 5x=r5 x=r5x=r

Problem 24013

Rearrange g=frg=f rg=fr to make fff the subject.

Problem 24014

Problem 24015

Rearrange k=dwk=d wk=dw to make ddd the subject.

Problem 24016

Rearrange ak−y=ca k-y=cak−y=c to make kkk the subject.

Problem 24017

Use the function below to answer the following questions. m(x)=5x+4m(x)=5^{x+4}m(x)=5x+4 (a) Use transformations of the graph of y=5xy=5^{x}y=5x to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.Part: 0/30 / 30/3

Problem 24018

Make kkk the subject of d=k+m2d=\frac{k+m}{2}d=2k+m​

Problem 24019

Which of the following is equivalent to i26i^{26}i26 ? -1 −i-i−i 1 i

Problem 24020

Problem 24021

x2−2x−8≤0x^{2}-2 x-8 \leq 0x2−2x−8≤0

Problem 24022

5x+3y=155 x+3 y=155x+3y=15

Problem 24023

Factor the expression completely. −60x4+54x-60 x^{4}+54 x−60x4+54x

Problem 24024

Solve by completing the square. −3v2+48v−75=0-3 v^{2}+48 v-75=0−3v2+48v−75=0言A Write your answers as integers, proper or improper fractions in simplest form, or cimals rounded to the nearest hundredth. ) [ix x˙A]=\left.\dot{x}_{A}\right]=x˙A​]= □\square□ or v=v=v= □\square□

Problem 24025

Problem 24026

3. The population of the People's Republic of China has been doubling approximately every sixty years. The population in 1975 was about 824000000 . If the current growth rate continues, what will the population be in 2215?2215 ?2215?

Problem 24027

1. (04.02LC)(04.02 \mathrm{LC})(04.02LC)Solve the following system of equations: (1 point) x−2y=14x+3y=9\begin{array}{l} x-2 y=14 \\ x+3 y=9 \end{array}x−2y=14x+3y=9​ (1,12)(1,12)(1,12) (−1,−12)(-1,-12)(−1,−12) (12,−1)(12,-1)(12,−1) (12,1)(12,1)(12,1)

Problem 24028

Solve the following equation: 34x=60\frac{3}{4} x=6043​x=60

Problem 24029

Problem 24030

Problem 24031

Quadratic and Exponential Functions Graphing a parabola of the form y=ax2+bx+cy=\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}y=ax2+bx+c : Integer coefficier aph the parabola. y=3x2−30x+69y=3 x^{2}-30 x+69y=3x2−30x+69Plot five points on the parabola: the vertex, two points to the le button.

Problem 24032

Problem 24033

Problem 24034

Find an equation of the form y=ax2+by=a x^{2}+by=ax2+b for a parabola that passes through the points (−1,1)(-1,1)(−1,1) and (−2,7)(-2,7)(−2,7). y=y=y=

Problem 24035

V2O5+…HCl→…VOCl3+…H2O\mathrm{V}_{2} \mathrm{O}_{5}+\ldots \mathrm{HCl} \rightarrow \ldots \mathrm{VOCl}_{3}+\ldots \mathrm{H}_{2} \mathrm{O}V2​O5​+…HCl→…VOCl3​+…H2​O

Problem 24036

Solve the equation. Simplify the answer as much as possible. 27x+5=92x+227^{x+5}=9^{2 x+2}27x+5=92x+2The solution set is □\square□ \}.

Problem 24037

Problem 24038

Problem 24039

unctions Question 13, 5.4.71Solve the equation. 105x=1000010^{5 x}=10000105x=10000Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is x=x=x= □\square□ . (Type an integer or a fraction.) B. There is no solution.

Problem 24040

14. This year, a rancher counted 225 horses on the range. This count is 22 fewer than last year. How many horses did the rancher count last year? Let hhh be the number of horses counted last year. Solve h−22=225h-22=225h−22=225 to find the number of horses counted last year.

Problem 24041

Problem 24042

Problem 24043

c3=−5m−83−m7+3c4=−6\begin{array}{l}\frac{c}{3}=-5 m-\frac{8}{3} \\ -\frac{m}{7}+\frac{3 c}{4}=-6\end{array}3c​=−5m−38​−7m​+43c​=−6​

Problem 24044

Feng invests money in an account paying simple interest. He invests $70\$ 70$70 and no money is added or removed from the investment. After one year, he has $70.70\$ 70.70$70.70. What is the simple percent interest per year?Answer □\square□ \% Submit Answer

Problem 24045

Problem 24046

Amelia invests money in an account paying simple interest. She invests $100\$ 100$100 and no money is added or removed from the investment. After one year, she has $101\$ 101$101. What is the simple percent interest per year?Answer □\square□ \% Submit Answer

Problem 24047

Problem 24048

x−6y=5617y=3x−4734\begin{array}{l}x-6 y=\frac{56}{17} \\ y=3 x-\frac{47}{34}\end{array}x−6y=1756​y=3x−3447​​

Problem 24049

$\frac{\frac{x}{x+3}}{1+\frac{1}{x+3}}$

Use the definition of a one-to-one function to determine if the function is one-to-one. $k(x)=|x-1|$ The function is one-to-one. The function is not one-to-one.

Jada was solving the equation $\sqrt{6-x}=-16$ . She was about to square each side, but then she realized she could give an answer without doing any algebra. What did she realize?

Math and Physics Power and quotient rules with positive exponents
Simplify. $\frac{\left(3 b^{2}\right)^{2}}{\left(2 b^{3}\right)^{3}}$
Write your answer using only positive exponents.

The price of a jumper is reduced by $17 \%$ in a sale. The sale price is $£ 62.25$
What was the original price of the jumper?

Make $x$ the subject of $x-9=r$

Make $x$ the subject of $5 x=r$

Rearrange $g=f r$ to make $f$ the subject.

Rearrange $k=d w$ to make $d$ the subject.

Rearrange $a k-y=c$ to make $k$ the subject.

Use the function below to answer the following questions. $m(x)=5^{x+4}$ (a) Use transformations of the graph of $y=5^{x}$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.
Part: $0 / 3$

Make $k$ the subject of $d=\frac{k+m}{2}$

Which of the following is equivalent to $i^{26}$ ? -1 $-i$ 1 i

$x^{2}-2 x-8 \leq 0$

$5 x+3 y=15$

Factor the expression completely. $-60 x^{4}+54 x$

Solve by completing the square. $-3 v^{2}+48 v-75=0$
言A Write your answers as integers, proper or improper fractions in simplest form, or cimals rounded to the nearest hundredth. ) [ix $\left.\dot{x}_{A}\right]=$ $\square$ or $v=$ $\square$

3. The population of the People's Republic of China has been doubling approximately every sixty years. The population in 1975 was about 824000000 . If the current growth rate continues, what will the population be in $2215 ?$

1. $(04.02 \mathrm{LC})$
Solve the following system of equations: (1 point) $\begin{array}{l} x-2 y=14 \\ x+3 y=9 \end{array}$ $(1,12)$ $(-1,-12)$ $(12,-1)$ $(12,1)$

Solve the following equation: $\frac{3}{4} x=60$

Quadratic and Exponential Functions Graphing a parabola of the form $y=\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}$ : Integer coefficier aph the parabola. $y=3 x^{2}-30 x+69$
Plot five points on the parabola: the vertex, two points to the le button.

Find an equation of the form $y=a x^{2}+b$ for a parabola that passes through the points $(-1,1)$ and $(-2,7)$ . $y=$

$\mathrm{V}_{2} \mathrm{O}_{5}+\ldots \mathrm{HCl} \rightarrow \ldots \mathrm{VOCl}_{3}+\ldots \mathrm{H}_{2} \mathrm{O}$

Solve the equation. Simplify the answer as much as possible. $27^{x+5}=9^{2 x+2}$
The solution set is $\square$ \}.

unctions Question 13, 5.4.71
Solve the equation. $10^{5 x}=10000$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $x=$ $\square$ . (Type an integer or a fraction.) B. There is no solution.

14. This year, a rancher counted 225 horses on the range. This count is 22 fewer than last year. How many horses did the rancher count last year? Let $h$ be the number of horses counted last year. Solve $h-22=225$ to find the number of horses counted last year.

$\begin{array}{l}\frac{c}{3}=-5 m-\frac{8}{3} \\ -\frac{m}{7}+\frac{3 c}{4}=-6\end{array}$

Feng invests money in an account paying simple interest. He invests $\$ 70$ and no money is added or removed from the investment. After one year, he has $\$ 70.70$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

Amelia invests money in an account paying simple interest. She invests $\$ 100$ and no money is added or removed from the investment. After one year, she has $\$ 101$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

$\begin{array}{l}x-6 y=\frac{56}{17} \\ y=3 x-\frac{47}{34}\end{array}$

$\begin{array}{l}-7 r+10 p=-\frac{137}{9} \\ 2 r+6 p=\frac{16}{3}\end{array}$

$61=-9 c+7$

Use the Binomial Theorem to expand the binomial: $\left(x^{8}+\sqrt{x}\right)^{3}$

Listen
Evaluate the function for the given value of $x$ . $\begin{array}{l} y=-9(3)^{x} ; x=-1 \\ y=\square \quad 0_{\varphi} \end{array}$ $\square$

Given the equation $q=Q_{0} e^{-t / R C}$ , rearrange the equation to solve for $t$ .

Perform the operation. Write the answer in standard form. $(4+i)(2-i)$ $\square$

$d(z-8)+5(z-8)=$

Video
A line has a slope of $\frac{7}{2}$ and includes the points $(5, k)$ and $(3,-3)$ . What is the value of $k$ ? $k=$ $\square$ Submit

Solve the following equation and check your solution. $-14 y+12(-14 y-11)=4418$ $y=$ $\square$ (Simplify your answer.)

Question 2, 10.6.10
HW Score: $0 \%, 0$ of 10 points Points: 0 of 1
Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if $\$ 80$ is invested semiannually for 35 year $6.5 \%$ compounded semiannually.

Divide. Express your answer in lowest terms. $\frac{30 x^{2}+11 x y-30 y^{2}}{48 x^{2}-46 x y+5 y^{2}} \div \frac{25 x^{2}-60 x y+36 y^{2}}{40 x^{2}-53 x y+6 y^{2}}$

Divide. Express your answer in lowest terms. $\frac{30 x^{2}+11 x y-30 y^{2}}{48 x^{2}-46 x y+5 y^{2}} \div \frac{25 x^{2}-60 x y+36 y^{2}}{40 x^{2}-53 x y+6 y^{2}}$

Solve the inequality for $w$ . $8 w-11>6 w-5$
Simplify your answer as much as possible.

Which of the following is true about the base $b$ of a logarithmic function? $b=0$ and $b=1$ $b>0$ and $b=1$ $b<0$ and $b=1$ b : 0 ando b

What is the solution to the equation $y+7=-21 ?$ A) $y=24$ B) $y=14$ C) $y=-14$ D) $y=-28$

Simplify. $\left(x^{3}-7 x^{2}+13 x-15\right) \div(x-5)$
Put your answer in standard form. (no

Solve the system. $\begin{array}{c} x^{2}+8 x+y+7=2 \\ y=-2 x+4 \end{array}$

Bookwork code: 5C Calculator allowed
A bowling alley can be hired for a party. The formula below shows the cost. A party cost $£ 316$ . How many people were at the party?