Algebra

Problem 24901

12cos(330)+i12sin(330)12 \cos \left(330^{\circ}\right)+i \cdot 12 \sin \left(330^{\circ}\right) A) 12e(510)i12 e^{\left(510^{\circ}\right) i} C) B) 12e(330%)i12 e^{(330 \%) i} D)

See Solution

Problem 24902

10 A B C D E F G I 10ei(4203)3\sqrt[3]{10 e^{i\left(420^{3}\right)}} A) SEIECT ALI APPICA 1012ei(3)10^{\frac{1}{2}} e^{i\left(\frac{\infty}{3}\right)} B) 103[cos(420)+isin(420)]\sqrt[3]{10}\left[\cos \left(420^{\circ}\right)+i \sin \left(420^{\circ}\right)\right] C) D) ei(aP2)e^{i\left(\frac{a P}{2}\right)} 103ei(120)\sqrt[3]{10} e^{i\left(120^{\circ}\right)} E) 103[cos(4203)+isin(4203)]\sqrt[3]{10}\left[\cos \left(\frac{420^{\circ}}{3}\right)+i \sin \left(\frac{420^{\circ}}{3}\right)\right] F) 10[cos(4203)+isin(4203)]10\left[\cos \left(\frac{420^{\circ}}{3}\right)+i \sin \left(\frac{420^{\circ}}{3}\right)\right]

See Solution

Problem 24903

1. On a cold day, Stackhouse measured the outside temperature and discovered it was 13 degrees Fahrenheit. Each hour after that, it was 3 degrees colder than the previous hour's temperature. At this rate, how many hours would it take for the temperature to reach -17 degrees Fahrenheit? (a) 4 hours (b) 9 hours (c) 10 hours (d) 30 hours

See Solution

Problem 24904

Use synthetic division to find the quotient and remainder when 2x4+9x3+5x2+1-2 x^{4}+9 x^{3}+5 x^{2}+1 is divided by x5x-5 by completing the parts below. (a) Complete this synthetic division table. 5)295015) \quad \begin{array}{lllll}-2 & 9 & 5 & 0 & 1\end{array} \square \square \square \square \square \square \square \square \square (b) Write your answer in the following form: Quotient + Remainder x5+\frac{\text { Remainder }}{x-5}. 2x4+9x3+5x2+1x5=+x5\frac{-2 x^{4}+9 x^{3}+5 x^{2}+1}{x-5}=\square+\frac{\square}{x-5} \square Clantinue Submi - 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use 1 Privacy Ce

See Solution

Problem 24905

Critique Reásoning Franco made this graph to show the equation y=xy=-x. Is the graph correct? Explain.

See Solution

Problem 24906

The rate of formation of NO2( g)\mathrm{NO}_{2}(\mathrm{~g}) in the reaction 2 N2O5( g)4NO2( g)+O2( g)2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) is 5.78( molNO2)/L/s5.78\left(\mathrm{~mol} \mathrm{NO}_{2}\right) / \mathrm{L} / \mathrm{s}. What is the rate at which N2O5\mathrm{N}_{2} \mathrm{O}_{5} decomposes?
1. 0.723( mol N2O5)/L/s0.723\left(\mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{5}\right) / \mathrm{L} / \mathrm{s}
2. 5.78( mol N2O5)/L/s5.78\left(\mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{5}\right) / \mathrm{L} / \mathrm{s}
3. 1.45( mol N2O5)/L/s1.45\left(\mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{5}\right) / \mathrm{L} / \mathrm{s}
4. 11.6( mol N2O5)/L/s11.6\left(\mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{5}\right) / \mathrm{L} / \mathrm{s}
5. 2.89( mol N2O5)/L/s2.89\left(\mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{5}\right) / \mathrm{L} / \mathrm{s}

See Solution

Problem 24907

Exponents and Polynomials Polynomial long division: Problem type 1
Divide. (6x2+24x+18)÷(2x+6)\left(6 x^{2}+24 x+18\right) \div(2 x+6)
Your answer should give the quotient and the remainder.
Quotient: \square
Remainder: \square

See Solution

Problem 24908

Begin by graphing f(x)=3xf(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. g(x)=3x4g(x)=3^{x}-4
Which transformation is needed to graph the function g(x)=3x4g(x)=3^{x}-4 ? Choose the correct answer below. A. The graph of f(x)=3xf(x)=3^{x} should be shifted 4 units upward. B. The graph of f(x)=3xf(x)=3^{x} should be shifted 4 units downward. C. The graph of f(x)=3xf(x)=3^{x} should be shifted 4 units to the left. D. The graph of f(x)=3xf(x)=3^{x} should be shifted 4 units to the right.

See Solution

Problem 24909

For the polynomial below, 3 is a zero. f(x)=x3+3x212x18f(x)=x^{3}+3 x^{2}-12 x-18
Express f(x)f(x) as a product of linear factors. f(x)=f(x)=

See Solution

Problem 24910

\#5 Listen
Write a linear function ff with f(9)=10f(-9)=10 and f(1)=2f(-1)=-2. f(x)=f(x)= \square

See Solution

Problem 24911

5. Graph the compound inequality: \qquad L 2(0)+(6)<22y+x<2 and 95\begin{array}{cc} 2(0)+(6)<2 \\ 2 y+x<2 \end{array} \text { and } 9 \geq-5

See Solution

Problem 24912

"The volume of a given mass of a gas varies inversely with the pressure if the absolute temperature is kept constant" is a statement of Charles' law Boyle's law Dalton's law Avagadro's law Next

See Solution

Problem 24913

If f(x)={3x4 if 3x3x33 if 3<x6f(x)=\left\{\begin{array}{ll}3 x-4 & \text { if }-3 \leq x \leq 3 \\ x^{3}-3 & \text { if } 3<x \leq 6\end{array}\right., find: (a) f(0)f(0), (b) f(1)f(1), (c) f(3)f(3), and (d)f(6)(d) f(6).

See Solution

Problem 24914

Given the table of values:\text{Given the table of values:} XY46044280122\begin{array}{|c|c|} \hline X & Y \\ \hline -4 & 6 \\ \hline 0 & 4 \\ \hline 4 & 2 \\ \hline 8 & 0 \\ \hline 12 & -2 \\ \hline \end{array} Find the slope of the line that passes through these points.\text{Find the slope of the line that passes through these points.}

See Solution

Problem 24915

A chemist conducts an experiment in which 2.00 L of hydrogen gas is collected over water at 1.00 atm and 298.15 K .
The phrase "over water" means that the gas was collected by bubbling it into an inverted bottle filled with water, which is sitting in a water bath. The gas is trapped in the bottle, displacing the water into the water bath. However, the gas collected is now saturated with water vapor. The partial pressure of water vapor at 298.15 K is 0.0300 atm .
Using Dalton's Law, calculate the pressure of the hydrogen gas in atm.

See Solution

Problem 24916

Which key feature is different for the two functions? Domain Range End behavior Slope

See Solution

Problem 24917

Express the following as the logarithm of a single quantity. 2loge9+4logeπloge52loge9+4logeπloge5=\begin{array}{r} 2 \log _{e} 9+4 \log _{e} \pi-\log _{e} 5 \\ 2 \log _{e} 9+4 \log _{e} \pi-\log _{e} 5=\square \end{array} \square (Simplify your answer. Type an exact answer, using π\pi as needed. Use integers

See Solution

Problem 24918

Use the properties of logarithms to expand the following expression log(x5(x+6)3)\log \left(\frac{\sqrt{x^{5}}}{(x+6)^{3}}\right)
Your answer should not have radicals or exponents. You may assume that all variables are positive. log(x5(x+6)3)=m\log \left(\frac{\sqrt{x^{5}}}{(x+6)^{3}}\right)=m

See Solution

Problem 24919

Write the expression as a single logarithm. 13logcx+3logcylogcz\frac{1}{3} \log _{c} x+3 \log _{c} y-\log _{c} z

See Solution

Problem 24920

Name: Date: \qquad \qquad Per: Unit 11: Sequences and Series \square Homework 3: Geometric Sequences \qquad This is a 2-page document! **
1. {18,108,648,3888,}\{18,-108,648,-3888, \ldots\}
2. {27,36,48,64,}\{27,36,48,64, \ldots\}
3. {10,4,85,1625,}\left\{10,4, \frac{8}{5}, \frac{16}{25}, \ldots\right\}

Directions: Write a rule for each sequence, then find the indicated term.
4. {3,9,27,81,};a\{-3,-9,-27,-81, \ldots\} ; a,
5. {18,27,812,2434,};a9\left\{-18,27,-\frac{81}{2}, \frac{243}{4}, \ldots\right\} ; a_{9}
6. {140,110,25,85,};a11\left\{\frac{1}{40},-\frac{1}{10}, \frac{2}{5},-\frac{8}{5}, \ldots\right\} ; a_{11}
7. {100,60,36,1085};a8\left\{100,60,36, \frac{108}{5} \ldots\right\} ; a_{8}

See Solution

Problem 24921

192=3x3192=3 x^{3}

See Solution

Problem 24922

an=10(2/5)n1a_{n}=10 \cdot(2 / 5)^{n-1}
5. {18,27,812,2434,};a9\left\{-18,27,-\frac{81}{2}, \frac{243}{4}, \ldots\right\} ; a_{9} {140,110,25,85,};a11\left\{\frac{1}{40},-\frac{1}{10}, \frac{2}{5},-\frac{8}{5}, \ldots\right\} ; a_{11}
7. {100,60,36,1085};a8\left\{100,60,36, \frac{108}{5} \ldots\right\} ; a_{8}

See Solution

Problem 24923

Solve for xx : 42x3=710x9x=\begin{array}{l} 4^{2 x-3}=7^{10 x-9} \\ x=\square \end{array} Calculator

See Solution

Problem 24924

The equation for h(x)h(x) and the transformed function p(x)p(x) in terms of h(x)h(x) are shown. Describe the transformation(s) performed on h(x)h(x) that produced p(x)p(x). h(x)=x3p(x)=2h(x+3)+6\begin{array}{c} h(x)=x^{3} \\ p(x)=2 h(x+3)+6 \end{array}

See Solution

Problem 24925

3. A bus company has 4000 passengers daily, each paying a fare of $2\$ 2. For each $0.15\$ 0.15 increase in the fare, the company estimates that it will lose 40 passengers. If the company needs to take in (revenue) $10450\$ 10450 per day to stay in business, what fare should be charged?
4. Following its advertising campaign to double its toppings, Zittza Pizza decides to double the area of its 10 cm by 12 cm advertisement in the Woodbridge Times by adding the same length (number of centimeters) to both dimensions of the ad. What length must be added to each side? Give you answer correct to one decimal place? \qquad \qquad \qquad \qquad \qquad \qquad \qquad

See Solution

Problem 24926

In 15-18, tell how many terms each expression has. 15,5,+915,5,+9
16. 3 . 12b\frac{1}{2} b \qquad
17. v3+25\frac{v}{3}+2 \cdot 5
18. 16.2(34)+(14÷2)16.2-(3 \cdot 4)+(14 \div 2)

See Solution

Problem 24927

3) 150\sqrt{-150}

See Solution

Problem 24928

Solve the given linear programming problem. Maximize z=5x+5yz=5 x+5 y subject to x0,y0,x+y1,2x+3y12,3x+2y12x \geq 0, y \geq 0, x+y \geq 1,2 x+3 y \leq 12,3 x+2 y \leq 12
What is the solution? The maximum value of zz is z=z= \square , and it occurs at the point (x,y)=(x, y)= \square . (Type exact answers. Type integers or simplified fractions.)

See Solution

Problem 24929

System C L1: y=x1y=-x-1 L2: y=2x3y=-2 x-3
This system of equations is: - consistent dependent - consistent independent - inconsistent
This means the system has: - a unique solution: - no solution - infinitely many solutions Solution: \qquad ,, )

See Solution

Problem 24930

1. (I) By how much does the gravitational potential energy of a 58kg58-\mathrm{kg} pole vaulter change if her center of mass rises 4.0 m during the jump?

See Solution

Problem 24931

Which description explains how the graph of f(x)=xf(x)=\sqrt{x} could be transformed to form the graph of g(x)=x+7g(x)=\sqrt{x+7} ? vertical stretch by a factor of 7 horizontal shift of 7 units left horizontal shift of 7 units right vertical shift of 7 units down

See Solution

Problem 24932

Find f(a+5)f(a+5). f(x)=x2+5f(a+5)=\begin{array}{c} f(x)=x^{2}+5 \\ f(a+5)=\square \end{array} Tutorial
Additional Materials \square eBook

See Solution

Problem 24933

Solve the system by back substitution {5x3y+3z=282y3z=34z=4x=y=z=\begin{array}{l} \left\{\begin{array}{r} 5 x-3 y+3 z=28 \\ 2 y-3 z=-3 \\ 4 z=4 \end{array}\right. \\ x=\square \\ y=\square \\ z=\square \end{array}

See Solution

Problem 24934

21 Multiple Choice 1 point Factor. 64x312564 x^{3}-125 (4x5)(16x220x+25)(4 x-5)\left(16 x^{2}-20 x+25\right) (4x5)(16x2+20x+25)(4 x-5)\left(16 x^{2}+20 x+25\right) (4x+5)(16x220x+25)(4 x+5)\left(16 x^{2}-20 x+25\right) (4x5)(16x2+25)(4 x-5)\left(16 x^{2}+25\right) Clear my selection
Previous

See Solution

Problem 24935

Write the system of equations as an augmented matrix. {3d+3s6z=123d7s+3z=202d+3s5z=69\left\{\begin{array}{l} 3 d+3 s-6 z=-12 \\ 3 d-7 s+3 z=-20 \\ -2 d+3 s-5 z=-69 \end{array}\right. \square \square \square \square \square \square \square \square \square \square \square \square

See Solution

Problem 24936

12+x2x812+x \leq 2 x-8

See Solution

Problem 24937

You deposit $5000\$ 5000 in a savings account that has a rate of 2%2 \%. The interest is compounded quarterly.
How much money will you have after 10 years? $\$ \square (Simplity your answer. Round to the nearest cent as needed.)

See Solution

Problem 24938

Question 8 (1 point) Graph the function. f(x)=(14)xf(x)=\left(\frac{1}{4}\right) x

See Solution

Problem 24939

Question 8 - of 48 Step 2 of 3
Consider the following equations. 1(4y+3x)=5(xy) and y+3=7+8x1-(4 y+3 x)=5(x-y) \text { and } y+3=7+8 x
Step 2 of 3: Express the second equation in slope-intercept form. Simplify your answer.
Answer 2 Points

See Solution

Problem 24940

๑- learn.hawkeslearning.com/Portal/Test/TestTakeTest\#! Submit Assignment Practice MA111 Fall 24
Question 8 - of 48 Step 3 of 3 Consider the following equations. 1(4y+3x)=5(xy) and y+3=7+8x1-(4 y+3 x)=5(x-y) \text { and } y+3=7+8 x
Step 3 of 3: Determine if the two lines are parallel.
Answer 2 Points Yes No

See Solution

Problem 24941

1-4. "Find f(3)f(3) " means to find the output of function f(x)f(x) for an input of x=3x=3. For the function f(x)=1x2f(x)=\frac{1}{x-2}, find each of the following Homework Help a. Find f(4)f(4). (This means find the output of the function when x=4x=4.) b. Find xx when f(x)=1f(x)=1. (This means find the input that gives an output of 1.)

See Solution

Problem 24942

Find a formula for the inverse of the function f[1](Q)=f(x)=ln(5x+2).f^{[-1]}(Q)=\square \quad f(x)=\ln (5 x+2) .

See Solution

Problem 24943

f(x)={2x+1,x2x27,x>2f(x)=\left\{\begin{array}{ll} 2 x+1, & x \leq-2 \\ x^{2}-7, & x>-2 \end{array}\right. increasing

See Solution

Problem 24944

At a jazz club, the cost of an evening is based on a cover charge of $30\$ 30 plus a beverage charge of $5\$ 5 per drink. (a) Find a formula for t(x)t(x), the total cost for an evening in which xx drinks are consumed. t(x)=5x+30t(x)=5 x+30 (b) If the price of the cover charge is raised by $5\$ 5, express the new total cost function, n(x)n(x), as a transformation of t(x)t(x). n(x)=t(x)+5n(x)=t(x)+5
Note: Do not give an explicit formula. Using function notation, write an expression for n(x)n(x) by performing the necessary transformations to t(x)t(x). For example your answer should be of the form, n(x)=t(x100)+180n(x)=t(x-100)+180 and not of the form n(x)=80x+9n(x)=80 x+9. (c) The management increases the cover charge to $35\$ 35, leaves the price of a drink at $5\$ 5, but includes the first two drinks for free. For x2x \geq 2, express p(x)p(x), the new total cost, as a transformation of t(x)t(x). p(x)=p(x)=\square (see note in (b) above for the correct way to express your answer)

See Solution

Problem 24945

6. 2x2+5x1=02 x^{2}+5 x-1=0 тэгшитгэлийн язгуурууд x1,x2x_{1}, x_{2} бол x1x2=x_{1} \cdot x_{2}= ? A. 5 B. 52-\frac{5}{2} C. 12-\frac{1}{2} D. 12\frac{1}{2} E. -1
7. xx ба yy тооны арифметик дундаж zz нь 30 бол x+y+z=x+y+z= ? A. 10 B. 15 C. 30 D. 60 E. 90

See Solution

Problem 24946

Find the accumulated value of an investment of $10,000\$ 10,000 for 6 years at an interest rate of 1.45%1.45 \% if the money is a. compounded semiannually, b. compounded quarterly, c. compounded monthly d . compounded continuously.
Click the icon to view some finance formulas. a. What is the accumulated value if the money is compounded semiannually? $10,905.54\$ 10,905.54 (Round to the nearest cent as needed) b. What is the accumulated value if the money is compounded quarterly? \ \square$ (Round to the nearest cent as needed.)

See Solution

Problem 24947

Question 22 of 25
Let yy represent the total cost of publishing a book (in dollars). Let xx represent the number of copies of the book printed. Suppose that xx and yy are related by the equation y=15x+1250y=15 x+1250.
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change in the total cost for each book printed? \ \qquadWhatisthecosttogetstarted(beforeanybooksareprinted)?$ What is the cost to get started (before any books are printed)? \$ \qquad$

See Solution

Problem 24948

Problem situation: Amy's cable company charges her a $75\$ 75 installation fee and $89\$ 89 per month for cable services. She has had cable services for 10 months. How much has she paid in total for cable services? Select the equation that represents this situation. The letter cc represents the total cost of cable. CLEAR CHECK 89+10+75=c89×10×75=c89×10+75=c(89+75)×10=c\begin{array}{ll} 89+10+75=c \\ 89 \times 10 \times 75=c \\ 89 \times 10+75=c & (89+75) \times 10=c \end{array}

See Solution

Problem 24949

0x23x=2y52x2+x=y4\begin{array}{l} 0 x^{2}-3 x=2 y-5 \\ 2 x^{2}+x=y-4 \end{array} b) x2+y=8x+19x2y=7x11\begin{array}{l} x^{2}+y=8 x+19 \\ x^{2}-y=7 x-11 \end{array} c) 2p2=4p2m+65m+8=10p+5p2\begin{array}{l} 2 p^{2}=4 p-2 m+6 \\ 5 m+8=10 p+5 p^{2} \end{array} d) 9w2+8k=14w2+k=2\begin{array}{l} 9 w^{2}+8 k=-14 \\ w^{2}+k=-2 \end{array} e) 4h28t=66h29=12t\begin{array}{l} 4 h^{2}-8 t=6 \\ 6 h^{2}-9=12 t \end{array}

See Solution

Problem 24950

Solve the inequality by the test-point method. Write the solution in interval notation. x2+4x+3>0x^{2}+4 x+3>0 (3,1)(-3,-1) None of these answers (1,)(-1, \infty) (,3)(1,)(-\infty,-3) \cup(-1, \infty) (,3)(-\infty,-3)

See Solution

Problem 24951

Identify whether the following equation is an identity. Give your answer as a yes or a no. a+(1+1a1)=a×(1+1a1)a+\left(1+\frac{1}{a-1}\right)=a \times\left(1+\frac{1}{a-1}\right)

See Solution

Problem 24952

omit Assignment Practice MA111 Fall 24
Question 12 - of 48 Step 1 of 1
Solve the following formula for the indicated variable. v2=v02+2ax; solve for a\mathrm{v}^{2}=\mathrm{v}_{0}^{2}+2 \mathrm{ax} ; \text { solve for } a
Answer 2 Points

See Solution

Problem 24953

x=82(4)x=\frac{-8}{2(-4)}

See Solution

Problem 24954

You are asked to show that 1x+1+1x1=2xx21\frac{1}{x+1}+\frac{1}{x-1}=\frac{2 x}{x^{2}-1}. Which of the following would be an appropriate first step?
1 Subtract 1x1\frac{1}{x-1} from both sides. (2) Substitute in several values of xx to see if it is true.
3 Multiply both sides by x21x^{2}-1 to clear the denominators.
4 Find a common denominator on the LHS to combine the two rational expressions (i.e., fractions) into one.

See Solution

Problem 24955

(a) Let g(x)g(x) be some function whose graph passes through the point (3,6)(3,-6). Let h(x)=g(x)+7h(x)=g(x)+7. Based on this information, what point do you know must be on the graph of hh ? (b) Let g(x)g(x) be some function whose domain is the interval [1,2][1,2] and whose image is the interval [1,1][-1,1]. Let h(x)=g(15x)h(x)=g\left(\frac{1}{5} x\right). What are the domain and image of h(x)h(x) ?

See Solution

Problem 24956

(1 point) Find the following expressions using the graph below of vectors u,v\mathbf{u}, \mathbf{v}, and w\mathbf{w}.
1. u+v=\mathbf{u}+\mathbf{v}= i+4j
2. 2u+w=2 u+w= \square
3. 3v6w=3 \mathbf{v}-6 \mathbf{w}= \square
4. w=|w|= \square

See Solution

Problem 24957

Prob. 4 On the right, the graph of the function f(x)f(x) is shown.
On the below plots, perform the six steps detailed on the previous page in order to transform this graph into that of: 3f(12(x+2))+1-3 f\left(\frac{1}{2}(x+2)\right)+1
1. First, rescale vertically by a factor of \qquad
2. Second, reflect vertically (across the xx-axis) if appropriate; otherwise, leave the graph the same.
3. Third, shift vertically \qquad unit(s) in the \qquad direction.
4. Fourth, rescale horizontally by a factor of \qquad
5. Fifth, reflect horizontally (across the yy-axis) if appropriate; otherwise, leave the graph the same.
6. Finally, shift horizontally \qquad unit(s) in the \qquad direction. You did it!

See Solution

Problem 24958

Problem Situation: Gabi buys tickets to the movies. She buys 1 adult ticket for $14\$ 14 and 3 youth tickets. She pays a total of $35\$ 35. What is the cost of each youth ticket?
Complete the equation to represent this situation. The letter tt represents the cost of a youth ticket.

See Solution

Problem 24959

10. Rod says that he is thinking of two functions that have the following characteristics: a. One is rational, and has a yy-intercept at -2 b. One is trigonometric, and does not include the cosine function c. One contains the digit " 3 " and the other does not. d. Both have an instantaneous rate of change of 1.23 (rounded to two decimal places) at x=2x=2 e. The two functions intersect at x=2x=2
Provide one example of a pair of functions that meet Rod's criteria. Explain your thought process in making the functions, a screenshot, and calculations to verify each criterion. [7 marks]

See Solution

Problem 24960

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse. f(x)=8x72f(x)=8 x-72 f1(x)=8x+72f^{-1}(x)=8 x+72 None of these answers f1(x)=19x+8f^{-1}(x)=\frac{1}{9} x+8 f1(x)=18x+9f^{-1}(x)=\frac{1}{8} x+9 Function is not one-to-one

See Solution

Problem 24961

(1 point) Suppose that 8x(14+x)=n=0cnxn\frac{8 x}{(14+x)}=\sum_{n=0}^{\infty} c_{n} x^{n}. Find the first few coefficients. c0=c1=c2=c3=c4=\begin{array}{l} c_{0}= \\ c_{1}= \\ c_{2}= \\ c_{3}= \\ c_{4}= \end{array}
Find the radius of convergence RR of the power series. R=R= \square

See Solution

Problem 24962

(a) Let g(x)g(x) be some function whose graph passes through the point (2,8)(2,8). Let h(x)=54g(13(x+1))2h(x)=\frac{5}{4} g\left(\frac{1}{3}(x+1)\right)-2. Based on this information, what point do you know must be on the graph of hh ? (b) Let g(x)g(x) be some function whose graph passes through the point (4,6)(4,6). Let h(x)=12g(2x6)+7h(x)=-\frac{1}{2} g(2 x-6)+7. Based on this information, what point do you know must be on the graph of hh ?

See Solution

Problem 24963

Find the partial fraction decomposition for the rational expression. 3x25x49(x3)(x2+4)\frac{-3 x^{2}-5 x-49}{(x-3)\left(x^{2}+4\right)} 4x+7x2+4+7x3\frac{4 x+7}{x^{2}+4}+\frac{7}{x-3} 7x+4x2+47x3\frac{7 x+4}{x^{2}+4}-\frac{7}{x-3} 4x+8x2+47x3\frac{4 x+8}{x^{2}+4}-\frac{7}{x-3} 4x+7x2+47x3\frac{4 x+7}{x^{2}+4}-\frac{7}{x-3} None of these answers

See Solution

Problem 24964

Parents wish to have $110,000\$ 110,000 available for a child's education. If the child is now 8 years old, how much money must be set aside at 7%7 \% compounded semiannually to meet their financial goal when the child is 18?18 ? Click the icon to view some finance formulas.
The amount that should be set aside is $\$ \square (Round up to the nearest dollar.)

See Solution

Problem 24965

A student takes out two loans totaling $13,000\$ 13,000 to help pay for college expenses. One loan is at 7%7 \% simple interest, and the other is at 8%8 \% simple interest. The first-year interest is $950\$ 950. Find the amount of the loan at 8%8 \%. None of these answers \630630 \9000 9000 \320320 \4000 4000

See Solution

Problem 24966

9x+79 \mid x+7 기 +8. g(x)=9x+67g(x)=9|x+6|-7 g(x)=9x+6+23g(x)=9|x+6|+23 g(x)=9x+8+23g(x)=9|x+8|+23 g(x)=9x+87g(x)=9|x+8|-7

See Solution

Problem 24967

An account has a rate of 2.6%2.6 \%. Find the effective annual yield if the interest is compounded semiannually. (1) Click the icon to view some finance formulas.
The effective annual yield is \square \%. (Round to the nearest hundredth as needed.)

See Solution

Problem 24968

Substitute the value of a to find the equation of the given graph. f(x)=(x+4)2+3f(x)=-(x+4)^{2}+3

See Solution

Problem 24969

Submit Assignment Practice MA111 Fall 24 BRYCE GUILLORY Question 20 - of 48 Step 1 of 1 00:39:27
Use polynomial long division to rewrite the following fraction in the form q(x)+r(x)d(x)\mathrm{q}(\mathrm{x})+\frac{\mathrm{r}(\mathrm{x})}{\mathrm{d}(\mathrm{x})}, where d(x)\mathrm{d}(\mathrm{x}) is the denominator of the original fraction, q(x)\mathrm{q}(\mathrm{x}) is the quotient, and r(x)\mathrm{r}(\mathrm{x}) is the remainder. 8x410x3+10x2+4x+22x2+1\frac{8 x^{4}-10 x^{3}+10 x^{2}+4 x+2}{2 x^{2}+1}
Answer 2 Points Keypad Keyboard Shortcuts

See Solution

Problem 24970

Part 11 of 11
For the quadratic function f(x)=x2+2x+1f(x)=x^{2}+2 x+1, answer parts (a) through ( ff ). (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 yy-intercept and the xx-intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The xx-intercept(s) is/are -1 . \square : (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no xx-intercepts.
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 1. \square (Type an integer or a simplified fraction.) B. There is no yy-intercept. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. \square (d) Find the domain and the range of the quadratic function.
The domain of ff is (,)(-\infty, \infty). (Type your answer in interval notation.) The range of ff is [0,)[0, \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 (1,)(-1, \infty). (Type your answer in interval notation.) The function is decreasing on the interval (,1)(-\infty,-1). (Type your answer in interval notation.) (f) Determine where f(x)>0f(x)>0 and where f(x)<0f(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)>0f(x)>0 on and f(x)<0f(x)<0 on \square B. f(x)<0f(x)<0 on and f(x)f(x) is never positive \square C. f(x)>0f(x)>0 on (,1)(1,)(-\infty,-1) \cup(-1, \infty) and f(x)f(x) is never negative ctbook Ask my instructor

See Solution

Problem 24971

Prob. 5 The function f(x)=x2f(x)=x^{2} is not invertible, as it is possible for two different numbers to have the same square. (For instance, 22=42^{2}=4 and (2)2=4(-2)^{2}=4.) However, in spite of this, we still like to talk about the square root function g(x)=xg(x)=\sqrt{x}. (a) What is 9\sqrt{9} ? Is this the only number whose square is 9 ? (b) For which values of xx is it true that x2=x\sqrt{x^{2}}=x ?

See Solution

Problem 24972

Question 21 - of 48 Step 1 of 1 00:18:27
Two trucks leave a warehouse at the same time. One travels due east at an average speed of 62 miles per hour, and the other travels due west at an average speed of 47 miles per hour. After how many hours will the two trucks be 763 miles apart?
Answer How to enter your answer (opens in new window) 2 Points Keypad Keyboard Shortcu \square hours

See Solution

Problem 24973

Question 22 - of 48 Step 1 of 1 Write the following logarithmic equation as an exponential equation. Do not simplify your answer. 2x=logc( V)2 \mathrm{x}=\log _{\mathrm{c}}(\mathrm{~V})
Answer 2 Points

See Solution

Problem 24974

8. A contestant on a game show spins a wheel that is located ona plane perpendicular to the floor. He grabs the only red peg ons the circumference of the wheel, which is 1.5 m above the floor, and pushes it downward. The red peg reaches a minimum height of 0.25 m above the floor and a maximum height of 2.75 m above the floor. Sketch two cycles of the graph that represents the height of the red peg above the floor, as a function of the total distance it moved. Then determine the equation of the sine function that describes the graph.

See Solution

Problem 24975

12. 18x+12y=243x+2y=6\begin{array}{l} 18 x+12 y=24 \\ 3 x+2 y=6 \end{array}

See Solution

Problem 24976

Convert the following equation to polar coordinates. y=4x2y=4 x^{2}
The polar form of y=4x2y=4 x^{2} is \square (Type an exact answer.)

See Solution

Problem 24977

Solve the inequality: 2(x+2)<14-2(x+2)<14 x<5x<-5 x<9x<-9 x>5x>-5 x>9x>-9

See Solution

Problem 24978

Is there a mistake on the equation solved? If so where was the mistake made? 3(2x5)=46x6x15=46x15=4\begin{array}{c} 3(2 x-5)=4-6 x \\ 6 x-15=4-6 x \\ -15=4 \end{array} no solution The mistake was made on the second step of moving the variable The mistake was made on the first step of doing the distributive property 15=4-15=4 should not be interpreted as "no solution" This equation is solved correctly

See Solution

Problem 24979

For a given geometric sequence, the 10th 10^{\text {th }} term, a10a_{10}, is equal to 1916\frac{19}{16}, and the 13th 13^{\text {th }} term, a13a_{13}, is equal to -76 . Find the value of the 17th 17^{\text {th }} term, a171fa_{17} \cdot 1 f applicable, write your answer as a fraction. a17=a_{17}= \square

See Solution

Problem 24980

9. pp2+2=8p24\frac{p}{p-2}+2=\frac{8}{p^{2}-4}
10. 133w31w1=w9\frac{13}{3 w-3}-\frac{1}{w-1}=\frac{w}{9}
11. x+6x+3=25x+12x+3\frac{x+6}{x+3}=2-\frac{5 x+12}{x+3}
12. 3c2c24c=cc41\frac{3 c-2}{c^{2}-4 c}=\frac{c}{c-4}-1

See Solution

Problem 24981

System A Line 1: y=12x52y=-\frac{1}{2} x-\frac{5}{2}
Line 2: y=x1y=x-1
This system of equations is: inconsistent consistent independent consistent dependent This means the system has: a unique solution Solution: \square \square no solution infinitely many solutions
System B Line 1: y=12x+3y=\frac{1}{2} x+3 Line 2: y=12x1y=\frac{1}{2} x-1
This system of equations is: inconsistent consistent independent consistent dependent This means the system has: a unique solution Solution: \square \square no solution infinitely many solutions
System C Line 1: y=52x+3y=-\frac{5}{2} x+3
Line 2: 5x+2y=65 x+2 y=6
This system of equations is: inconsistent consistent independent consistent dependent This means the system has: a unique solution Solution: \square D no solution infinitely many solutions Explanation Check

See Solution

Problem 24982

Solve this system of equations by using graphing. {y=12x+1y=x2\left\{\begin{array}{l} y=\frac{1}{2} x+1 \\ y=-x-2 \end{array}\right. ([?], \square Enter

See Solution

Problem 24983

How many real zeros does the following quadratic function have? y=5x2+2x+4y=5 x^{2}+2 x+4
Use the Discriminant: b² - 4ac no real zeros two real zeros one real zero

See Solution

Problem 24984

Solve the equation. 3w2+2w8+3w2+w6=5w2+7w+12\frac{3}{w^{2}+2 w-8}+\frac{3}{w^{2}+w-6}=\frac{5}{w^{2}+7 w+12}

See Solution

Problem 24985

Evaluate the expression for the given value of the variable. x4+3 for x=68\sqrt{x-4}+3 \text { for } x=68

See Solution

Problem 24986

The expression log(x10y7z10)\log \left(\frac{x^{10} y^{7}}{z^{10}}\right) can be written in the form Alog(x)+Blog(y)+Clog(z)A \log (x)+B \log (y)+C \log (z) where A=A= \square B=B= \square σ\sigma^{\infty}, and C=C= \square Question Help: Video Read
Message instructor Submit Question

See Solution

Problem 24987

Simplify. Enter the result as a single logarithm with a coefficient of 1. log7(6x6)log7(7x7)\log _{7}\left(6 x^{6}\right)-\log _{7}\left(7 x^{7}\right) \square Question Help: Video Message instructor Submit Question

See Solution

Problem 24988

Given MM, find M1\mathrm{M}^{-1} and show that M1M=I\mathrm{M}^{-1} \mathrm{M}=\mathrm{I}. M=[120013114]M=\left[\begin{array}{rrr} 1 & 2 & 0 \\ 0 & 1 & 3 \\ -1 & -1 & 4 \end{array}\right]
Find the value in the first row and first column of the product M1MM^{-1} M using matrix multiplication. Select the correct expression below and fill in the answer box to complete your selection. A. (31)+(40)+(31)=(-3 \cdot 1)+(4 \cdot 0)+(-3 \cdot-1)= \square (Simplify your answer.) B. (71)+(80)+(61)=(7 \cdot 1)+(-8 \cdot 0)+(6 \cdot-1)= \square (Simplify your answer.) C. (70)+(83)+(64)=(7 \cdot 0)+(-8 \cdot 3)+(6 \cdot 4)= \square (Simplify your answer.) D. (72)+(81)+(61)=(7 \cdot 2)+(-8 \cdot 1)+(6 \cdot-1)= \square (Simplify your answer.)

See Solution

Problem 24989

Section 4.4 Score: 9.5/12 Answered: 10/12
Question 3
Simplify. Enter the result as a sing Next log8(4x7)log8(5x4)=\begin{array}{l} \log _{8}\left(4 x^{7}\right)-\log _{8}\left(5 x^{4}\right) \\ = \end{array} Question Help: Video Message instructor

See Solution

Problem 24990

Question 3
Find the domain of y=log(3+3x)y=\log (3+3 x). The domain is: \square Question Help: Video Message instructor Submit Question

See Solution

Problem 24991

Question 4
Write an equation for the transformed logarithm shown below, that passes through (2,0)(2,0) and (1(1, f(x)=f(x)= \square Question Help: Video 1 Video 2 Video 3 Message instructor Submit Question

See Solution

Problem 24992

Solve this system of equations by using elimination. {3x+5y=2x+2y=8([?]\begin{array}{c} \left\{\begin{array}{l} 3 x+5 y=-2 \\ -x+2 y=8 \end{array}\right. \\ ([?] \end{array} Enter

See Solution

Problem 24993

x111=21\sqrt{x-111}=-21

See Solution

Problem 24994

3. f(x)=x44x2f(x)=x^{4}-4 x^{2}

See Solution

Problem 24995

Use the definition of a one-to-one function to determine if the function is one-to-one. f(x)=x21f(x)=x^{2}-1
Part 1 of 5
To show a function ff is a one-to-one function using the definition, it must be shown that if f(a)=f(b)f(a)=f(b), then a=ba=b .
Part: 1/51 / 5
Part 2 of 5
For the given function f(x)=x21f(x)=x^{2}-1, we begin by assuming that (Choose one) \nabla.

See Solution

Problem 24996

Describe and correct the error in solving the equation. x2+10x+74=0x=10±1024(1)(74)2(1)=10±1962=10±142\begin{aligned} x^{2} & +10 x+74=0 \\ x & =\frac{-10 \pm \sqrt{10^{2}-4(1)(74)}}{2(1)} \\ & =\frac{-10 \pm \sqrt{-196}}{2} \\ & =\frac{-10 \pm 14}{2} \end{aligned}

See Solution

Problem 24997

Find the zeros of m(x)=5x2+50x135m(x)=-5 x^{2}+50 x-135

See Solution

Problem 24998

A TYT/Temel Matematik
13. Bir babanın yaşı, oğlunun yaşının 3 katıdır. Oğul, babasının bugünkü yaşına geldiğinde yaşlarının toplamı 72 olacaktır. Buna göre baba bugün kaç yaşındadır? A) 20 B) 25 C) 27 D) 35 E) 40

See Solution

Problem 24999

12. If the graph of f(x)f(x) has a horizontal asymptote at y=1y=1 and a vertical asymptote at x=2\boldsymbol{x}=-\mathbf{2}, then the horizontal \& vertical asymptotes of g(x)=f(x1)+5g(x)=\boldsymbol{f}(\boldsymbol{x}-1)+5 are A. y=2,x=1y=-2, x=1 B. y=1,x=2y=-1, x=-2 C. y=5,x=3y=5, x=-3 D. y=6,x=1y=6, x=-1

See Solution

Problem 25000

2. Which one of these functions might have the given graph? A. f(x)=x(x1)(x2)f(x)=-x(x-1)(x-2) B. f(x)=x(x1)(x2)f(x)=x(x-1)(x-2) C. f(x)=x2(x1)(x2)f(x)=x^{2}(x-1)(x-2) D. f(x)=x2(x1)(x2)f(x)=-x^{2}(x-1)(x-2)

See Solution
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord