Browse Math problems Studdy Solved!

Problem 51801

What is the distance between -52 and $43 ?$ a. 9 b. 52 c. 95 d. 43

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Problem 51802

Evaluate the polynomial function using Synthetic Division $\begin{array}{c} f(x)=5 x^{3}+3 x^{2}-x+7 \\ \text { when } x=2 \end{array}$

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Problem 51803

7. Students measured the diameter of many different plastic rings found in a teacher's classroom. The distribution of their measurements $(M)$ is roughly symmetric, with a mean of 21.3 cm and a standard deviation of 1.88 cm .
The teacher quickly realized that her students were measuring in millimeters and not centimeters. Additionally, they measured from the end of the ruler which was 0.5 centimeters from the mark for zero centimeters. To adjust for these errors, the teacher transforms the distribution using the following expression: $\frac{M}{10}-0.5$

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Problem 51804

The value of a building is currently $£ 251,000 .$
If the value increases by $3.5 \%$ , what will the new value be?

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Problem 51805

Two divers were exploring a new territory. Diver 1 started at 18 * 2 points meters above sea level and was descending at a rate of 3 meters per minute. Diver 2 started 2 meters below sea level and was ascending 2 meters per minute. When will the divers be at the same height? Let $x$ represent minutes and $y$ represent meters traveled.
What equation represents Diver 1? $y=18 x+3$ $y=-3 x+18$ $y=3 x+18$

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Problem 51806

Prove the identity. $\sec ^{4} x \tan ^{6} x=\left(\tan ^{6} x+\tan ^{8} x\right) \sec ^{2} x$
Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button the right of the Rule.
Statement $\sec ^{4} x \tan ^{6} x$ $\square$
Validate This line is incorrect.
Select the Rule
O Algebra Reciprocal Quotient Pythagorean Odd/Even

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Problem 51807

Given that $0 . \dot{6} \dot{3}=\frac{7}{11}$ , what is $0.0 \dot{6} \dot{3}$ as a fraction in its simplest form?

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Problem 51808

What is the $y$ -intercept for the function $y=2(x+3)(x-4)$ ?

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Problem 51809

question 2, refer to Example 2. a) c) e) b) d) f)

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Problem 51810

c) $\log _{2} \sqrt[4]{8}$

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Problem 51811

Work out the value of $u$ when $16^{-6}=4^{u}$

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Problem 51812

Multiply. Simplify the answer and write as a mixed number. $4 \frac{2}{5} \cdot 3 \frac{1}{3}$ 14 $1 \frac{8}{25}$ $14 \frac{2}{3}$ $12 \frac{2}{15}$

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Problem 51813

Jse the information below to write $0.4 \dot{8} \dot{1}$ as a fraction in its simplest form. $\begin{array}{c} 0.4 \dot{8} \dot{i}=0.4+0.0 \dot{8} \dot{1} \\ 0.0 \dot{8} \dot{i}=\frac{9}{110} \end{array}$

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Problem 51814

Fill in each blank to construct an $\epsilon-\delta$ proof showing that $\lim _{x \rightarrow 7} 1-x=-6$
Where it asks for $\delta$ give the largest value that will work. Proof. Let ? $\quad \checkmark>0$ be given. Let $\delta$ be the product $\delta=($ $\square$ ) $(\epsilon)$
If | $x-$ $\square$ $1<?$ $\square$ then after some algebra we arrive at $\mid(1-x)-$ $\square$ $1<$ ? which is what we wanted to prove. Note: You can eam partial credit on this problem.

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Problem 51815

Increase 380 by $143 \%$

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Problem 51816

$f(x)=\frac{3 x^{2}-8 x+6}{x^{2}-4 x+3}$
Use Key Idea 4 (pp.152-3 in APEX Calculus) by applying the principles to the given function.
1. Determine the domain of $f$ . (as an interval) $\square$
2. Find the critical values of $f$ . $\square$ (Separate multiple answers by commas.)
3. Find the possible points of inflection of $f(x$ -values only). Note: Use your graphing calculator to approximate the value to least 4 decimal places. $\square$ (Separate multiple answers by commas.)
4. Find the vertical asymptotes. $x=$ $\square$ (Separate multiple answers by commas.)
5. Find the horizontal aymptotes. $y=$ $\square$ (Separate multiple answers by commas.)
6. Use a number line analysis to complete the following. $f$ is increasing on: $\square$ (as an interval) $f$ is decreasing on: $\square$ (as an interval) $f$ is concave up on: $\square$ (as an interval) $f$ is concave down on: $\square$ (as an interval)
7. Evaluate $f$ at each critical point and possible point of inflection. List all such points below. Each point should be entered as an ordered pair (that is, in the form $(x, y)$ ). $\square$ Note: You can earn partial credit on this problem. (Separate multiple answers by commas.)

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Problem 51817

Factor the following expression completely in order to fill in the $8 x^{2}-32$ $\begin{array}{l} A(B x+C)(D x-E) \\ A= \\ B= \\ C= \\ D= \\ E= \end{array}$
Note: Your answers should be integers.

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Problem 51818

4. Identify the GCF of each set of terms. a) $15 a^{2} b$ and $18 a b$ b) $27 m^{2} n^{3}$ and $81 m^{3} n$ c) $8 x^{2} y^{2}$ and $24 x^{3} y^{3}$ d) $12 a^{3} b c^{2}, 28 a^{2} c$ , and $36 a^{2} b^{2} c^{2}$ e) $14 p^{4} q^{5},-24 p^{5} q^{4}$ , and $7 p^{3} q^{3}$
5. State the missing factor represented by each blue box. a) $6 a^{2} b c+9 a b^{2}=\square(2 a c+3 b)$ b) $3 s^{2}-15=3($ c) $3 d^{2}-21 d=3 d$ d) $16 x^{2}-2 x=2 x($ e) $12 x^{2} y^{2}-16 x y=\square(3 x y-4)$
6. Factor each polynomial. a) $5 x+15$ b) $3 y^{2}-5 y$ c) $w^{2} x+w^{2} y-w^{2} z$ d) $6 a^{3} b-18 a b^{2}$ e) $9 x^{3}-12 x^{2}+6 x$
7. Factor each polynomial, if possible. a) $14 x^{2} y+16 x y^{3}$ b) $10 k^{3} m^{2}-6 k^{2} m^{2}$ c) $8 s^{2} y+11 t^{3}$ d) $27 r^{2} s^{2}-18 r^{3} s^{2}-36 r s^{3}$ e) $7 g h+2 m n-13 p q$ f) $4 n^{2} p^{3}+10 n^{4} p^{2}-12 n^{3} p^{2}$
8. Factor each polynomial. a) $3 y(y-2)+4(y-2)$ b) $5 a(a-4)-2(a-4)$ c) $2 c x-8 x+7 c-28$ d) $3 x^{2}-9 x-8 x+24$ e) $2 y^{4}+y^{3}-10 y-5$

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Problem 51819

16. [-/1 Points] DETAILS MY NOTES SPRECALC8 6.2.
Evaluate the expression without using a calculator. $\left(\cos \left(45^{\circ}\right)\right)^{2}-\left(\sin \left(45^{\circ}\right)\right)^{2}$ $\square$

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Problem 51820

$\text{A herd of caribou triples every 10 years. Starting with 200 caribou, how many caribou were there 10 years ago?}$

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Problem 51821

2. Which of the following is closest to the mean of the data set shown? (1) 16.8 (3) 17.7 $11,15,17,19,20,24$ (2) 17.1 (4) 18.2

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Problem 51822

$\frac{10 x+3}{5 x+6}=\frac{1}{2}$

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Problem 51823

The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer Which of the following sentences is true? Use the number line to help you decide. 6.8 is greater than 6.6 6.3 is less than 6.0 . 6.4 is greater than 6.6 . 6.4 is less than 6.2 .

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Problem 51824

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: WI cm Length of the longer leg: $\square$ cm
Length of the hypotenuse: $\square$ cm

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Problem 51825

\begin{align} \text{(b) Write a piecewise defined function to describe the usage rate.} \\ \text{NOTE: Enter the exact answer in dollars, or round to three decimal places.} \\ C(n) = \begin{cases} \square & \text{for } 0 \leq n \leq 16 \\ \square & \text{for } n > 16 \end{cases} \\ \text{(c) What is the cost for 31 kWh?} \\ \text{NOTE: Round your answer to two decimal places.} \\ \text{The cost of 31 kWh is } \$3.35 \\ \text{(d) How many kWh can you burn on a day for } \$4? \\ \text{NOTE: Round your answer to three decimal places.} \\ \text{You can burn } 35.937 \text{ kWh on a day for } \$4. \\ \text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.} \\ \text{Dialogue Transcript:} \\ \text{Assistant:} \\ \text{Hi there! It looks like you're working on a problem related to piecewise functions and cost calculations for electricity usage. However, to help you complete part (b) where a piecewise function needs to be defined, I need more information about the rates for electricity usage for both when } 0 \leq n \leq 16 \text{ and when } n > 16. \\ \text{Could you provide the specific cost rates or any details about the pricing structure?} \\ \text{Once I have that information, I'll be able to assist you further.} \\ \text{User:} \\ \text{kWh: 0, 5, 10, 15, 20, 25, 30, 35, 40 cost in dollars: 0.17, 0.54, 0.93, 1.31, 2.31, 2.96, 3.61, 4.26, 4.91} \end{align}

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Problem 51826

A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 80 miles. The rate of the freight train was 5 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
Rate of the passenger train: $\square$ miles/hour

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Problem 51827

\text{A herd of caribou triples every 10 years starting with 200 caribou. How many caribou were there 10 years ago?}

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Problem 51828

A piece of machinery depreciates $\$ 8000$ the first year, $\$ 7500$ the second year, and $\$ 7000$ the third year. If the rate of depreciation is constant, what is the amount of depreciation of the piece of machinery in the sixth year?
A $\$ 43,500$ B $\$ 6000$ C $\$ 5500$ (D) $\$ 19,500$

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Problem 51829

Identify the bond with the lowest bond length. $\mathrm{N}=\mathrm{O}$ $\mathrm{O}=\mathrm{O}$ $\mathrm{C}=\mathrm{N}$ $\mathrm{C}=\mathrm{C}$ $\mathrm{N}=\mathrm{N}$ Previous Answers Correct

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Problem 51830

Question 1 of 15 Of the writing utensils in a bin, $\frac{5}{8}$ are pens. Of the pens, $\frac{3}{4}$ are black pens. What fraction of the writing utensils are black pens? A. $\frac{15}{32}$ B. $\frac{20}{24}$ C. $\frac{15}{24}$ D. $\frac{1}{8}$

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Problem 51831

Height of a Ball = The height $y$ (in feet) of a punted football is approximated by $y=\frac{-16}{2025} x^{2}+\frac{9}{5} x+\frac{3}{2}$ where $x$ is the horizontal distance (in feet) from where the football is punted. a.) Sketch a graph of this situation. b.) What is the height of the football when the punter punts the ball from the starting point? How do you know? Label on the graph in (a). c.) What is the horizontal distance from the starting point that the football reaches its maximum height? How do you know? Label on the graph in (a). d.) What is the maximum height the football reaches? How do you know? Label on the graph in (a). e.) Use a graphing device to graph the path of the football and determine how far from the punter does the football strike the ground? How do you know? Label on the graph in (a). f.) Graph the path of the football accurately on a piece of graph paper. Label axes appropriately and label key points from b-e above.

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Problem 51832

Find the $y$ -intercept(s) and $x$ -intercept(s) of the graph of the following. $25 x^{2}+81 y^{2}=1$

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Problem 51833

If $a_{7}=\frac{704}{81}$ and $r=-\frac{2}{3}$ , find $a_{11}$

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Problem 51834

```latex \text{Given the function } f(x) = \frac{2}{x^2 + 2}, \text{ perform the following tasks:}
\text{a) Find the first and second derivatives.}
f'(x) = \square
f''(x) = \square
\text{b) Identify the graph that displays } f \text{ in blue and } f'' \text{ in red.} \square
\text{A.}
\text{B.}
\text{C.}
\text{D.}
\text{c) Using the graphs of } f \text{ and } f'', \text{ indicate where } f \text{ is concave up and concave down. Give your answer in the form of an interval.}
\text{NOTE: When using interval notation in WeBWorK, remember that:}
\text{You use 'INF' for } \infty \text{ and '-INF' for } -\infty.
\text{And use ' U ' for the union symbol.}
\text{Enter DNE if an answer does not exist.}
f \text{ is concave up on } \square
f \text{ is concave down on } \square
\text{Note: You can earn partial credit on this problem.} ```

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Problem 51835

You flip two coins and roll a die. How many outcomes are possible? $\square$
Save answer

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Problem 51836

Simplify the expression without using a calculator. $\log _{\sqrt{6}} 1=$ $\square$ $\square$

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Problem 51837

Give the equation of the circle centered at the origin and passing through the point $(0,-9)$ .

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Problem 51838

15. Divide the complex numbers. Write the answer in the form $a+b i$ . $\frac{1-9 i}{2-8 i}$

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Problem 51839

$=1$ $=2$ $=3$ 4 5 6 7 8 9
Write the domain in Interval notation. $g(x)=\log (3-x)$
The domain is $\square$ .

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Problem 51840

Find an equation of the circle whose diameter has endpoints $(-5,-4)$ and $(5,6)$ . $\square$

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Problem 51841

6. What are the two numbers that have a difference of 10 and have the minimum product?

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Problem 51842

Part 1 of 2 Begin by graphing the absolute value function, $f(x)=|x|$ . Then use transformations of this graph to graph the given function. $h(x)=|x|+7$
What transformations are needed in order to obtain the graph of $h(x)$ from the graph of $f(x)$ ? Select all that apply. A. Reflection about the $x$ -axis B. Reflection about the $y$ -axis C. Horizontal translation D. Vertical stretch/shrink E. Horizontal stretch/shrink F. Vertical translation

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Problem 51843

7. The hypotenuse of a right triangle is 15 cm . If the 2 other sides differ by 3 cm , what are their lengths?

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Problem 51844

Write the following expression as a logarithm of a single expression. $\log 55+\log \frac{1}{11}$
Write a logarithm of a single expression that is equivalent to $\log 55+\log \frac{1}{11}$ . $\square$ (Simplify your answer. Type an exact answer.)

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Problem 51845

Solve $\log _{2}(x+2)=2-\log _{2}(x-5)$

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Problem 51846

4. Simplify the expression. $|28.1-7.03|-|3.5 \cdot 4.1|+|-9|$

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Problem 51847

4. From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring $30^{\circ}$ . Find the distance between the tree and the tower.

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Problem 51848

6. A ladder is leaning against a vertical wall makes an angle of $50^{\circ}$ with the ground. The foot of the ladder is 3 ft from the wall. Find the length of ladder.

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Problem 51849

Use the image to answer the question.
For the given box plot, which measure of centermean or median-best represents the shape of the distribution? Enter 1 for median or 2 for mean. (1 point) $\square$

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Problem 51850

roblem. Then, divide Xavier has 29 baseball cards he'd like to share with his 3 best friends. Each friend gets an equal number of cards. How many baseball cards will be left over?

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Problem 51851

For the right triangles below, find the exact values of the side lengths $d$ and $c$ . If necessary, wite your responses in simplified radical form.

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Problem 51852

Let $f(x)=6 x+5$ and $g(x)=2 x-7$ . Find $(f+g)(x),(f-g)(x),(f g)(x),\left(\frac{f}{g}\right)(x),(f \circ g)(x)$ , and $(g \circ f)(x)$ . Give the domain of each. $(f+g)(x)=8 x-2$ (Simplify your answer.) The domain of $f+g$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) $(\mathrm{f}-\mathrm{g})(\mathrm{x})=\square$ (Simplify your answer.)

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Problem 51853

Use the table to answer the question. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Group 1 & 20 & 22 & 14 & 25 & 18 & 33 & 28 & 35 & 43 & 18 \\ \hline Group 2 & 16 & 24 & 30 & 26 & 28 & 32 & 34 & 23 & 25 & 33 \\ \hline \end{tabular}
The math scores of the two groups of students are summarized in the table. Which group of scores is more dispersed than the other? (1 point)
Group $\square$

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Problem 51854

Example: Graph $y=2 \sin \left[3\left(x-\frac{\pi}{4}\right)\right]-1$ a) for one cycle

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Problem 51855

Find the measures of center-mean, median, and mode-for the given dataset. $10,17,11,24,12,7,15,17,20,5,11,21,16,17$ (2 points) mean: $\square$ ; median: $\square$ ; mode: $\square$
Check answer Remaining Attempts : 3

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Problem 51856

$(\csc x-\cot x)^{2}=\frac{1-\cos x}{1+\cos x}$

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Problem 51857

$\frac{1}{4}+2$

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Problem 51858

Summarize the dataset by finding its measures of center-mean, median, and mode. $\begin{array}{l} 20,30,32,16,31,32,13,20,28,32,15,18,20, \\ 21,32 \end{array}$ (1 point) mean: 21; median: 24; mode: 32 mean: 22.5; median: 21; mode: 20 mean: 24; median: 24.5; mode: 20 mean: 24; median: 21; mode: 32

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Problem 51859

17. $\log (4 x+3)+\log (5)=2$
18. $\ln (4 x-1)-1=\ln (3)$
19. $\ln \left(x^{2}+3\right)=\ln (x+2)+\ln 4$
20. $\log (x+28)-\log (x+3)=\log (x+4)$

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Problem 51860

$\frac{7}{3} \cdot 0$

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Problem 51861

Exact Angles Worksheet
1. Find the exact value of the following. Include a sketch. a) $\operatorname{Cos} 120$ b) $\operatorname{Sin} 315$ c) $\operatorname{Tan} 210$ d) $\operatorname{Cot} 225$ e) $\operatorname{Csc} 315$ f) $\operatorname{Sec} 210$
2. Find the values for $\theta$ . Include a sketch a) $\cos \theta=\frac{\sqrt{3}}{2}$ b) $\sin \theta=-\frac{1}{2}$ c) $\csc \theta=-\sqrt{2}$ d) $\tan \theta=1$ e) $\sec \theta=2$ f) $\cot \theta=\frac{1}{\sqrt{3}}$

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Problem 51862

25. Let $\varphi: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}, \psi: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ be linear mapping fulfilling $\varphi((1,1,1))=(3,7), \varphi((1,1,0))=$ $(2,5), \varphi((1,0,0))=(1,6)$ and $\psi((2,2,1))=(3,3), \psi((2,1,0))=(5,0), \psi((2,1,1))=$ $(4,2)$ . Find a formula for $\varphi+\psi$ .

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Problem 51863

Use the image to answer the question.
For the given box plot, which measure of variability -range or IQR-best represents the shape of the distribution? (1 point) IQR, the shape of the distribution is skewed to the right. Range, the shape of the distribution is skewed to the right. Range; the shape of the distribution is symmetrical, or close to it. IQR, the shape of the distribution is symmetrical, or close to it.

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Problem 51864

Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below. \begin{tabular}{lcccccccc} \hline Male & 15,890 & 25,564 & 1408 & 7950 & 18,542 & 15,146 & 14,229 & 25,967 \\ \hline Female & 24,647 & 13,482 & 18,166 & 17,593 & 12,701 & 17,094 & 16,460 & 18,587 \\ \hline \end{tabular}
In this example, $\mu_{d}$ is the mean value of the ditferences a tor the population of all pairs of data, where each individual difference $d$ is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test? $H_{0}: \mu_{d}=0$ word(s) $H_{1}: \mu_{d}<0$ word(s) (Type integers or decimals. Do not round.) Identify the test statistic. $\mathrm{t}=$ $\square$ (Round to two decimal places as needed.)

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Problem 51865

26. Consider a linear mapping $\varphi: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ given by the formula $\varphi\left(\left(x_{1}, x_{2}, x_{3}\right)\right)=$ $\left(x_{1}-x_{2}+4 x_{3},-3 x_{1}+8 x_{3}\right)$ . Let $\mathcal{A}=\{(3,4,1),(2,3,1),(5,1,1)\}, \mathcal{B}=\{(3,1),(2,1)\}$ . Find $M(\varphi)_{\mathcal{A}}^{\mathcal{B}}$ and $M(\varphi)_{\mathrm{st}}^{\mathrm{st}}$ (matrices of $\varphi$ in the bases $\mathcal{A}, \mathcal{B}$ and in the standard bases

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Problem 51866

2. Find a second order homogenous linear ODE in standard form for which a basis of the solution is $\cos 5 x, \sin 5 x$
Show linear independence by the Wronskian. Solve the initial value problem with initial conditions $y(0)=3, y^{\prime}(0)=-5 .$

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Problem 51867

Remainder, Factor, and Rational Root Theorems
1. Use the Remainder Theorem to find the remainder when $f(x)=x^{3}-6 x^{2}+11 x-6$ is divided by $x-2$

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Problem 51868

ii. $\lim _{x \rightarrow 0^{+}}(1+4 x)^{\cot x}$

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Problem 51869

What is the $y$ -intercept of the function $f(x)=-4 x+5$ ? * B) 5 D) 4 A) -4 C) -5

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Problem 51870

Factor the trinomial. $x^{2}+10 x+21$
Select the correct choice below and fill in any answer boxes within your choice. A. $x^{2}+10 x+21=$ $\square$ (Simplify your answer. Factor completely.) B. The trinomial is not factorable.

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Problem 51871

Graph the function. $f(x)=\sqrt[3]{x}-6$
Plot five points on the graph of tliz function, as follows. - Plot the first point using the $x$ -value that satisfies $\sqrt[3]{x}=0$ . - Plot two points to the left and two points to the right of the first point.
Then click on the graph-a-function button.

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Problem 51872

2.020 Ein Kreditgeber verzinst eingelegte Geldbeträge mit $i=3,5 \%$ und verlangt für verliehene Beträge $i^{\prime}=6 \%$ . Berechnen Sie jenen Zinsgewinn, den er dadurch bei einem Betrag von € $100.000,00$ in 20 Jahren hat.

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Problem 51873

Determine the domain and range of the function. Domain: $(-\infty, \infty)$ ; Range ( $-\infty,-2]$ Domain: $(-\infty,-2] ;$ Range $[3, \infty)$ Domain: $(-\infty, \infty)$ ; Range $(-\infty, \infty)$ Domain: $(-\infty,-2] ;$ Range $(-\infty, \infty)$

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Problem 51874

A particle is moving with the given data. Find the position function of the particle. $v(t)=\sin t-\cos t, \quad s(0)=3$

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Problem 51875

49) Write equation of a line which passes through $(27,12)$ and parallel to $y=2016$ .

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Problem 51876

When the nuclide uranium-238 undergoes alpha decay: (1) The name of the product nuclide is $\square$ (2) The symbol for the product nuclide is $\square$

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Problem 51877

Find the slope of the line passing through the points $(-2,3)$ and $(5,4)$ .

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Problem 51878

Question 2
Factor $15 w^{6}+5 w^{4}$ .

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Problem 51879

Write a balanced nuclear equation for the following: The nuclide bismuth-214 undergoes alpha emission. Not submitted

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Problem 51880

$\text{Find the slope of the line passing through the points } (-5, -6) \text{ and } (4, -2).$

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Problem 51881

50) Write equation of a line which passes through $(2,5)$ and perpendicular to $y=x$

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Problem 51882

30. Let $\mathcal{A}=\{(1,2,3),(2,1,0),(4,5,0)\}, \mathcal{B}=\{(2,1,2),(3,1,2),(2,1,3)\}$ . Find a matrix $C \in M_{3 \times 3}(\mathbb{R})$ , fulfilling the following condition. For a given vector $\alpha \in \mathbb{R}^{3}$ : if the coordinates of $\alpha$ in the basis $\mathcal{A}$ are $x_{1}, x_{2}, x_{3}$ and the coordinates of $\alpha$ in the basis $\mathcal{B}$ are $y_{1}, y_{2}, y_{3}$ , then $C \cdot\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]=\left[\begin{array}{l} y_{1} \\ y_{2} \\ y_{3} \end{array}\right] .$

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Problem 51883

52) Write equation of a line which passes through $(5,3)$ and perpendicular to $x=\frac{1}{3} y$ .

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Problem 51884

The graph shows $g(x)$ , which is a translation of $f(x)=x^{2}$ . Write the function rule for $g(x)$
Write your answer in the form $\mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k}$ , where $\mathrm{a}, \mathrm{h}$ , and k are integers or simplified fractions.

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Problem 51885

Simplify the following expression completely. $\frac{x^{2}-9 x+14}{x^{2}+2 x-8}$

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Problem 51886

Listen
The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval. $v(t)=10 t-10,0 \leq t \leq 5$

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Problem 51887

15) Given a parabola has a vertex at $(-2,16)$ and a point at $(3,-9)$ a) Write the equation in vertex form b) Write the equation in standard form c) Write the equation in intercept form

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Problem 51888

Questions 9 - 12 are for the ellipse having foci located at $(3,1)$ and $(7,1)$ and a major axis of length 10 .
9. What are the coordinates of the vertices?
10. What is the length of the minor axis?
11. Find the eccentricity of the ellipse.

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Problem 51889

Find $\sin (2 x), \cos (2 x)$ , and $\tan (2 x)$ from the given information. $\begin{array}{l} \cos (x)=\frac{15}{17}, \quad \csc (x)<0 \\ \sin (2 x)=\square \\ \cos (2 x)=\square \\ \tan (2 x)=\square \end{array}$

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Problem 51890

Question Watch Video Show Exar
Solve for $x$ , rounding to the nearest hundredth. $12 \cdot 10^{\frac{x}{4}}=43$
Answer Attempt 1 out of 2 $x=$ $\square$ Submit Answer Sign out Dec 4 $D \cong$ ㄴ

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Problem 51891

$A D$ bisects $\angle C A B$ . Find $x$ .
Enter the correct number in the box.
Show Hints $x=$ $\square$

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Problem 51892

Given that $\log x=2, \log y=7$ , and $\log 4 \approx 0.6$ , evaluate the following expression without using a calculator. $\log \left(4 x^{2} y\right)$ $\log \left(4 x^{2} y\right) \approx$ $\square$ (Type an integer or a decimal.)

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Problem 51893

Express each using a positive exponent. (Example 2)
5. $3^{-2}=$
6. $5^{-3}=$ $\qquad$
8. $w^{-7}=$ $\qquad$

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Problem 51894

Solve the compound inequality $2 y-3 \leq 7$ or $-3 y \leq-18$ . Then graph the solution set.

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Problem 51895

Express each using a positive exponent.
5. $3^{-2}=$ $\qquad$
7. $m^{-5}=$ $\qquad$
Express each fraction using a negative ex
9. $\frac{1}{d^{3}}=$ $\qquad$
11. $\frac{1}{r^{8}}=$ $\qquad$

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Problem 51896

Name:
Part A: Knowledge and Understanding
1. [1] Which of the following is true about $y=-2(x+3)^{2}-7$ in its transformation from $y=x^{2}$ . a. a vertical stretch of $-1 / 2$ b. a horizontal c. a vertical d. a reflection about translation of 3 translation of 7 the $y$ -axis units left unit up
2. [2] What is the equation in factored form of the graph of the parabola (A) below? $\qquad$ $\qquad$ $\qquad$ $\qquad$ [2] What is the equation in vertex form of the graph of the parabola (B) at right? $\qquad$ $\qquad$ $\qquad$ $\qquad$
3. [1] The roots of the equation $-3(x+4)(x-1)=0$ are: a. $(-4,0)(1,0)$ b. $(0,-4)(0,-1)$ c. $(0,-4)(0,1)$ d. $(4,0)(-1,0)$
4. [1] What are the number of roots for the equation $-5 x^{2}+20 x-14=0$ : a. 0 b. 1 c. 2 d. 3
5. [1] The parabola $x^{2}-4 x+7$ has a. Real roots b. No real roots c. Branches not roots
6. [1] Completing the square allows you to find the maximum or minimum point of a quadratic relation of the form $y=a x^{2}+b x+c$ algebraically. a. True b. False

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Problem 51897

The road outside of Butch's house, when seen from above, takes on the shape the graph of $y=x^{5}$ where both $x$ and $y$ are measured in feet. The end of Butch's driveway (where he gets onto the road) is at the origin which we will call the point $H$ (for home)
One day Butch goes for a drive on this road, leaving home sometime in the mid-afernoon when the traffic is virtually nonexistent Butch's position on the road can be thought of as the point B with coordinates $(x, y)$ where both $x$ and $y$ are differentiable functions of time, say $x(t)$ and $y(t)$ . At some time, not long after leaving home, Butch passes through the point where $x=4$ . At that instant his $x$ -coordinate is increasing at a rate of 2 feet per second. a) What is the rate of change of Butch's $y$ -coordinate at this instant? \begin{tabular}{|l|l|} \hline Number & Units \\ \hline \end{tabular}

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Problem 51898

8. $w^{-7}=$ $\qquad$ tive exponent. (Example 3)
10. $\frac{1}{12^{2}}=$ $\qquad$
12. $\frac{1}{6^{4}}=$ $\qquad$

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Problem 51899

14 Kegelstumpf: Ein Kegelstumpf entsteht durch Abtrennen eines Kegels parallel zur Grundfläche des Ausgangskegels. a) Zeige, dass für das Volumen eines Kegelstumpfs gilt: $V=\frac{\pi}{3} \cdot h \cdot\left(r_{2}^{2}+r_{2} \cdot r_{1}+r_{1}^{2}\right)$ b) Berechne das Volumen eines Kegelstumpfs mit $\mathrm{r}_{1}=44 \mathrm{~mm}, \mathrm{r}_{2}=28 \mathrm{~mm}$ und $\mathrm{h}=32 \mathrm{~mm}$ .

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Problem 51900

For what value of $x$ does $625=5^{6-2 \times}$ ? 1 2 4 5

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Math

Problem 51801

What is the distance between -52 and 43?43 ?43? a. 9 b. 52 c. 95 d. 43

Problem 51802

Evaluate the polynomial function using Synthetic Division f(x)=5x3+3x2−x+7 when x=2\begin{array}{c} f(x)=5 x^{3}+3 x^{2}-x+7 \\ \text { when } x=2 \end{array}f(x)=5x3+3x2−x+7 when x=2​

Problem 51803

Problem 51804

The value of a building is currently £251,000.£ 251,000 .£251,000.If the value increases by 3.5%3.5 \%3.5%, what will the new value be?

Problem 51805

Problem 51806

Problem 51807

Given that 0.6˙3˙=7110 . \dot{6} \dot{3}=\frac{7}{11}0.6˙3˙=117​, what is 0.06˙3˙0.0 \dot{6} \dot{3}0.06˙3˙ as a fraction in its simplest form?

Problem 51808

What is the yyy-intercept for the function y=2(x+3)(x−4)y=2(x+3)(x-4)y=2(x+3)(x−4) ?

Problem 51809

question 2, refer to Example 2. a) c) e) b) d) f)

Problem 51810

c) log⁡284\log _{2} \sqrt[4]{8}log2​48​

Problem 51811

Work out the value of uuu when 16−6=4u16^{-6}=4^{u}16−6=4u

Problem 51812

Multiply. Simplify the answer and write as a mixed number. 425⋅3134 \frac{2}{5} \cdot 3 \frac{1}{3}452​⋅331​ 14 18251 \frac{8}{25}1258​ 142314 \frac{2}{3}1432​ 1221512 \frac{2}{15}12152​

Problem 51813

Jse the information below to write 0.48˙1˙0.4 \dot{8} \dot{1}0.48˙1˙ as a fraction in its simplest form. 0.48˙i˙=0.4+0.08˙1˙0.08˙i˙=9110\begin{array}{c} 0.4 \dot{8} \dot{i}=0.4+0.0 \dot{8} \dot{1} \\ 0.0 \dot{8} \dot{i}=\frac{9}{110} \end{array}0.48˙i˙=0.4+0.08˙1˙0.08˙i˙=1109​​

Problem 51814

Problem 51815

Increase 380 by 143%143 \%143%

Problem 51816

Problem 51817

Factor the following expression completely in order to fill in the 8x2−328 x^{2}-328x2−32 A(Bx+C)(Dx−E)A=B=C=D=E=\begin{array}{l} A(B x+C)(D x-E) \\ A= \\ B= \\ C= \\ D= \\ E= \end{array}A(Bx+C)(Dx−E)A=B=C=D=E=​Note: Your answers should be integers.

Problem 51818

Problem 51819

16. [-/1 Points] DETAILS MY NOTES SPRECALC8 6.2.Evaluate the expression without using a calculator. (cos⁡(45∘))2−(sin⁡(45∘))2\left(\cos \left(45^{\circ}\right)\right)^{2}-\left(\sin \left(45^{\circ}\right)\right)^{2}(cos(45∘))2−(sin(45∘))2 □\square□

Problem 51820

Problem 51821

2. Which of the following is closest to the mean of the data set shown? (1) 16.8 (3) 17.7 11,15,17,19,20,2411,15,17,19,20,2411,15,17,19,20,24 (2) 17.1 (4) 18.2

Problem 51822

10x+35x+6=12\frac{10 x+3}{5 x+6}=\frac{1}{2}5x+610x+3​=21​

Problem 51823

Problem 51824

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle.Length of the shorter leg: WI cm Length of the longer leg: □\square□ cmLength of the hypotenuse: □\square□ cm

Problem 51825

Problem 51826

A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 80 miles. The rate of the freight train was 5 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.Rate of the passenger train: □\square□ miles/hour

Problem 51827

\text{A herd of caribou triples every 10 years starting with 200 caribou. How many caribou were there 10 years ago?}

Problem 51828

Problem 51829

Identify the bond with the lowest bond length. N=O\mathrm{N}=\mathrm{O}N=O O=O\mathrm{O}=\mathrm{O}O=O C=N\mathrm{C}=\mathrm{N}C=N C=C\mathrm{C}=\mathrm{C}C=C N=N\mathrm{N}=\mathrm{N}N=N Previous Answers Correct

Problem 51830

Question 1 of 15 Of the writing utensils in a bin, 58\frac{5}{8}85​ are pens. Of the pens, 34\frac{3}{4}43​ are black pens. What fraction of the writing utensils are black pens? A. 1532\frac{15}{32}3215​ B. 2024\frac{20}{24}2420​ C. 1524\frac{15}{24}2415​ D. 18\frac{1}{8}81​

Problem 51831

Problem 51832

Find the yyy-intercept(s) and xxx-intercept(s) of the graph of the following. 25x2+81y2=125 x^{2}+81 y^{2}=125x2+81y2=1

Problem 51833

If a7=70481a_{7}=\frac{704}{81}a7​=81704​ and r=−23r=-\frac{2}{3}r=−32​, find a11a_{11}a11​

Problem 51834

Problem 51835

You flip two coins and roll a die. How many outcomes are possible? □\square□Save answer

Problem 51836

Simplify the expression without using a calculator. log⁡61=\log _{\sqrt{6}} 1=log6​​1= □\square□ □\square□

Problem 51837

Give the equation of the circle centered at the origin and passing through the point (0,−9)(0,-9)(0,−9).

Problem 51838

15. Divide the complex numbers. Write the answer in the form a+bia+b ia+bi. 1−9i2−8i\frac{1-9 i}{2-8 i}2−8i1−9i​

Problem 51839

=1=1=1 =2=2=2 =3=3=3 4 5 6 7 8 9Write the domain in Interval notation. g(x)=log⁡(3−x)g(x)=\log (3-x)g(x)=log(3−x)The domain is □\square□ .

Problem 51840

Find an equation of the circle whose diameter has endpoints (−5,−4)(-5,-4)(−5,−4) and (5,6)(5,6)(5,6). □\square□

Problem 51841

6. What are the two numbers that have a difference of 10 and have the minimum product?

Problem 51842

Problem 51843

7. The hypotenuse of a right triangle is 15 cm . If the 2 other sides differ by 3 cm , what are their lengths?

Problem 51844

Problem 51845

Solve log⁡2(x+2)=2−log⁡2(x−5)\log _{2}(x+2)=2-\log _{2}(x-5)log2​(x+2)=2−log2​(x−5)

Problem 51846

4. Simplify the expression. ∣28.1−7.03∣−∣3.5⋅4.1∣+∣−9∣|28.1-7.03|-|3.5 \cdot 4.1|+|-9|∣28.1−7.03∣−∣3.5⋅4.1∣+∣−9∣

Problem 51847

What is the distance between -52 and $43 ?$ a. 9 b. 52 c. 95 d. 43

Evaluate the polynomial function using Synthetic Division $\begin{array}{c} f(x)=5 x^{3}+3 x^{2}-x+7 \\ \text { when } x=2 \end{array}$

The value of a building is currently $£ 251,000 .$
If the value increases by $3.5 \%$ , what will the new value be?

Given that $0 . \dot{6} \dot{3}=\frac{7}{11}$ , what is $0.0 \dot{6} \dot{3}$ as a fraction in its simplest form?

What is the $y$ -intercept for the function $y=2(x+3)(x-4)$ ?

c) $\log _{2} \sqrt[4]{8}$

Work out the value of $u$ when $16^{-6}=4^{u}$

Multiply. Simplify the answer and write as a mixed number. $4 \frac{2}{5} \cdot 3 \frac{1}{3}$ 14 $1 \frac{8}{25}$ $14 \frac{2}{3}$ $12 \frac{2}{15}$

Jse the information below to write $0.4 \dot{8} \dot{1}$ as a fraction in its simplest form. $\begin{array}{c} 0.4 \dot{8} \dot{i}=0.4+0.0 \dot{8} \dot{1} \\ 0.0 \dot{8} \dot{i}=\frac{9}{110} \end{array}$

Increase 380 by $143 \%$

Factor the following expression completely in order to fill in the $8 x^{2}-32$ $\begin{array}{l} A(B x+C)(D x-E) \\ A= \\ B= \\ C= \\ D= \\ E= \end{array}$
Note: Your answers should be integers.

16. [-/1 Points] DETAILS MY NOTES SPRECALC8 6.2.
Evaluate the expression without using a calculator. $\left(\cos \left(45^{\circ}\right)\right)^{2}-\left(\sin \left(45^{\circ}\right)\right)^{2}$ $\square$

2. Which of the following is closest to the mean of the data set shown? (1) 16.8 (3) 17.7 $11,15,17,19,20,24$ (2) 17.1 (4) 18.2

$\frac{10 x+3}{5 x+6}=\frac{1}{2}$

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: WI cm Length of the longer leg: $\square$ cm
Length of the hypotenuse: $\square$ cm

A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 80 miles. The rate of the freight train was 5 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
Rate of the passenger train: $\square$ miles/hour

Identify the bond with the lowest bond length. $\mathrm{N}=\mathrm{O}$ $\mathrm{O}=\mathrm{O}$ $\mathrm{C}=\mathrm{N}$ $\mathrm{C}=\mathrm{C}$ $\mathrm{N}=\mathrm{N}$ Previous Answers Correct

Question 1 of 15 Of the writing utensils in a bin, $\frac{5}{8}$ are pens. Of the pens, $\frac{3}{4}$ are black pens. What fraction of the writing utensils are black pens? A. $\frac{15}{32}$ B. $\frac{20}{24}$ C. $\frac{15}{24}$ D. $\frac{1}{8}$

Find the $y$ -intercept(s) and $x$ -intercept(s) of the graph of the following. $25 x^{2}+81 y^{2}=1$

If $a_{7}=\frac{704}{81}$ and $r=-\frac{2}{3}$ , find $a_{11}$

You flip two coins and roll a die. How many outcomes are possible? $\square$
Save answer

Simplify the expression without using a calculator. $\log _{\sqrt{6}} 1=$ $\square$ $\square$

Give the equation of the circle centered at the origin and passing through the point $(0,-9)$ .

15. Divide the complex numbers. Write the answer in the form $a+b i$ . $\frac{1-9 i}{2-8 i}$

$=1$ $=2$ $=3$ 4 5 6 7 8 9
Write the domain in Interval notation. $g(x)=\log (3-x)$
The domain is $\square$ .

Find an equation of the circle whose diameter has endpoints $(-5,-4)$ and $(5,6)$ . $\square$

Solve $\log _{2}(x+2)=2-\log _{2}(x-5)$

4. Simplify the expression. $|28.1-7.03|-|3.5 \cdot 4.1|+|-9|$

4. From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring $30^{\circ}$ . Find the distance between the tree and the tower.

6. A ladder is leaning against a vertical wall makes an angle of $50^{\circ}$ with the ground. The foot of the ladder is 3 ft from the wall. Find the length of ladder.

Use the image to answer the question.
For the given box plot, which measure of centermean or median-best represents the shape of the distribution? Enter 1 for median or 2 for mean. (1 point) $\square$

For the right triangles below, find the exact values of the side lengths $d$ and $c$ . If necessary, wite your responses in simplified radical form.

Example: Graph $y=2 \sin \left[3\left(x-\frac{\pi}{4}\right)\right]-1$ a) for one cycle

$(\csc x-\cot x)^{2}=\frac{1-\cos x}{1+\cos x}$

$\frac{1}{4}+2$

$\frac{7}{3} \cdot 0$

Remainder, Factor, and Rational Root Theorems
1. Use the Remainder Theorem to find the remainder when $f(x)=x^{3}-6 x^{2}+11 x-6$ is divided by $x-2$

ii. $\lim _{x \rightarrow 0^{+}}(1+4 x)^{\cot x}$

What is the $y$ -intercept of the function $f(x)=-4 x+5$ ? * B) 5 D) 4 A) -4 C) -5

Factor the trinomial. $x^{2}+10 x+21$
Select the correct choice below and fill in any answer boxes within your choice. A. $x^{2}+10 x+21=$ $\square$ (Simplify your answer. Factor completely.) B. The trinomial is not factorable.

2.020 Ein Kreditgeber verzinst eingelegte Geldbeträge mit $i=3,5 \%$ und verlangt für verliehene Beträge $i^{\prime}=6 \%$ . Berechnen Sie jenen Zinsgewinn, den er dadurch bei einem Betrag von € $100.000,00$ in 20 Jahren hat.

A particle is moving with the given data. Find the position function of the particle. $v(t)=\sin t-\cos t, \quad s(0)=3$