Browse Math problems in the Studdy Learning Bank!

Problem 8001

Evaluate the indefinite integral $\int \frac{2 \arccos (7 x)}{\sqrt{1-49 x^{2}}} d x =$ C$

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Problem 8002

Laura has $\frac{5}{7}$ jugs of water and needs $\frac{1}{6}$ jugs per liter of paint. The expression to find the liters of paint she can mix is: $\frac{5}{7} \div \frac{1}{6}$ .

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Problem 8003

Solve the equation $4x - 2 = 10$ using algebra tiles. The solution is $\square$ . (Type the value of $x$ .)

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Problem 8004

Determine if the following polygon pairs are always, sometimes, or never similar: $40.$ two obtuse triangles $41.$ a trapezoid and a parallelogram $42.$ two right triangles $43.$ two isosceles triangles $44.$ a scalene triangle and an isosceles triangle $45.$ two equilateral triangles

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Problem 8005

Résoudre l'équation $x(x+7)=0$ .

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Problem 8006

Evaluate $3x-7$ when $x=6$ . Evaluate $6y-13$ when $y=4$ . Evaluate $\frac{xz}{5}$ when $x=5$ and $z=5$ .

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Problem 8007

Solve the quadratic equation $49 m^{2} - 2 = 79$ for real-valued $m$ .

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Problem 8008

Sketch the region where $y=2$ .

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Problem 8009

Identificar la propiedad mostrada en la ecuación $4+(3+x)=4$ , que implica las propiedades conmutativa, asociativa y distributiva.

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Problem 8010

Find the future cost of a CD after 12 years, given an inflation rate of $4.5 \%$ and a present cost of $\$ 12.95$ . Round the answer to the nearest cent.

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Problem 8011

Find the value of $x$ in the simplified expression $g^{x} + h^{-3} = \frac{1}{g^{6}} + \frac{1}{h^{3}}$ .

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Problem 8012

Find $t$ in simplest radical form. Given: $30, 60, \frac{6}{2}$ (inches).

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Problem 8013

Solve the exponential equation $5^{x}=\frac{1}{625}$ to find the value of $x$ .

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Problem 8014

Solve the inequality $4x - 61 > -85$ for the real number $x$ .

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Problem 8015

Solve for $x$ in the equation $5^{x} = 25$ . Write the answer as an integer or simplified fraction.

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Problem 8016

Multiply $4.3 \times \frac{4}{9}$ and round the answer to the nearest hundredth.

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Problem 8017

Find the value of $f(-2)$ when $f(x) = -\frac{3}{5}x + 2$ .

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Problem 8018

Find the quotient of $\frac{43}{36}$ divided by $\frac{43}{22}$ , reduced to lowest terms.

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Problem 8019

Find the value of $y$ when the line $-904-(-38)x=-14y$ has $x=-3$ . (Round answer to two decimal places)

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Problem 8020

Solve the linear equation $28-\frac{x}{4}=\frac{x}{3}$ and find the solution set.

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Problem 8021

Solve the linear equation $9=5(x-2)-(x-7)$ and select the correct solution set.

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Problem 8022

Solve the linear equation $24-5v=8$ for the variable $v$ .

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Problem 8023

Solve $30kx - 6kx = 8$ for $x$ .

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Problem 8024

Determine the cost in 2018 of an item that cost $100 in 1999 using a line graph and two models:$ C = 1.9x + 120.4 $and$ C = 0.03x^2 + 1.8x + 120.7 $, where$ C $is the cost$ x$ years after 2010.

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Problem 8025

Find the value(s) of $x$ where $5(3x-8)-26=9(x-4)+18$ .

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Problem 8026

Solve for the frequency $f$ given the equation $\frac{480}{f} = 10 \times N$ and $f = \sqrt{50 \times 10}$ .

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Problem 8027

Solve the linear equation $x + 5 = 9$ for the value of $x$ .

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Problem 8028

Identify coefficients and constants in $6y+5+m$ . What error might Sarah make? The coefficients are $6,1$ . The constant is $5$ . Sarah might not include the coefficient $1$ .

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Problem 8029

Solve the linear equation $5x-7=7x-13$ and select the correct solution.

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Problem 8030

Simplify the expression $\frac{2}{3}\left(\frac{3}{4} x+1 \frac{1}{8}\right)+\frac{4}{5}\left(2 \frac{1}{2} x+15\right)$ .

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Problem 8031

Solve the equation $|3x+2| - 8 = 2x$ for all values of $x$ .

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Problem 8032

Analyze the effect of changing $y=x^{3}$ to $f(x)=(x+1)^{3}$ . Identify the values most affected and describe the impact on the graph.

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Problem 8033

Find the equation of the line of best fit for the data: (4, 3), (6, 4), (8, 9), (11, 12), (13, 17). Round the slope and y-intercept to 3 decimal places.

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Problem 8034

Find the maximum value of the quadratic function $y = -3x^2 + 12x - 9$ . The vertex is at $x_{\text{vertex}} = -b/2a$ , and the maximum value is $y = 3$ .

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Problem 8035

Simplify the expression $(-2)^{3}-12$ and select the correct answer.

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Problem 8036

Graph the quadratic function $f(x) = x^2 - 2x$ .

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Problem 8037

Find the linear function with $f(0)=6$ and slope $f=-9$ .

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Problem 8038

Find the standard form of the rectangular equation given the equations $x=4-2t$ and $y=3-t$ .

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Problem 8039

Determine if the given ordered pairs are solutions to the systems of linear inequalities.
1. $(2,0)$ : $y >$ \$$x-5\$$ and $\$$y \leq 2x+1\$$
2. $(1,4)$: $\$$y < 2x+2\$$ and $\$$y \geq -3x+4\$$

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Problem 8040

Simplify $4x^3 - 6x^2 + 7x - 8 - (7x^3 - 10x^2 - 5x + 4)$ . Find the degree of the resulting polynomial.

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Problem 8041

18. Is the absolute value of -14 equal to 14? True or False.
19. What is the value of $-3+(-14)$ ? a) 11, b) -11, c) -17, d) -42

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Problem 8042

Express a function that multiplies input $x$ by 4, then adds 16.

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Problem 8043

Solve the linear equation $-4x + 8 = 20$ for the value of $x$ .

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Problem 8044

Find the second number that, when multiplied with $\frac{7}{3}$ , results in an irrational product. Options: $\frac{3}{7}$ , $2 \pi$ , 1, $\sqrt{3}$ .

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Problem 8045

Encuentra el máximo común divisor de $9$ y $36$ .

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Problem 8046

Solve for $x$ in the rational equation $\frac{x+1}{3x+6}=\frac{3}{x}+\frac{2x+6}{x(3x+6)}$ using factoring.

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Problem 8047

Determine if each number is prime or composite, and explain your reasoning. $27, 19, 31, 38, 45, 53, 87, 93$

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Problem 8048

Find the lengths of the legs of a right triangle where the first leg is 1 cm longer than the second, and the hypotenuse is 6 cm.
$\text{First Leg: } \sqrt{36 - x^2} + 1 \text{ cm}$ $\text{Second Leg: } \sqrt{36 - x^2} \text{ cm}$

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Problem 8049

Find the probability that 5 out of 10 randomly selected individuals in Kenya use public transportation, given 63% of the population uses public transportation.

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Problem 8050

Solve for the value of $5 \times (-38)$ .

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Problem 8051

Solve for the missing variable in the equation $\frac{x}{6}+4=5$ .

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Problem 8052

Find the value of $x$ where the sum of $\frac{3}{8}$ and $x$ is $\frac{7}{2}$ .

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Problem 8053

Given directly proportional ratios, find the missing variable $y_2$ if $x_1=500$ , $y_1=250$ , and $x_2=370$ .

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Problem 8054

Find the equation of the linear function with $y$ -intercept $(-4)$ and $x$ -intercept $(5,0)$ . $f(x) = \frac{4}{5}x - 4$

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Problem 8055

Find the product of $-9 x(5-2 x)$ .

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Problem 8056

Solve $-125=w^{3}$ for real number $w$ . Simplify solution(s). If no solution, click "No solution".

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Problem 8057

Find the constant in the equation $y = mx + b$ given the graph points (1,1.5), (2,3), (4,6), (6,9).

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Problem 8058

Determine if the statement is correct: Since $3^{x}=20$ and $3^{x}=243$ are similar, they can be solved the same way.

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Problem 8059

Solve for $x$ in the equation $7 \cdot 8 = x - 4$ .

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Problem 8060

Find the value of $\cosh(3\ln 3) - \sinh(3\ln 3)$ .

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Problem 8061

Exercise 1: Limits 3) Write the reference limits of the function $\ln x$ 4) Using these limits, calculate the limits of the following functions at the bounds of their domain: a) $f(x)=x^{2}-2+\ln x$ b) $g(x)=x^{2}+(2-\ln x)^{2}$ c) $h(x)=\frac{\ln (x+2)}{1+x^{2}}$ d) $l(x)=x(\ln x)^{2}$
Exercise 2: Derivative and sign study of the derivative Calculate the derivative function of the following functions and study the sign of the derivative: 4) $f(x)=-1+(\ln x)^{2}$ 5) $g(x)=\ln \frac{x}{x+1}$ 6) $h(x)=\ln \left|\frac{x-2}{x+4}\right|$
Exercise 3: Complex numbers 3) Solve the equation $z^{2}-2 i z-2=0$ in the set $\mathbb{C}$ of complex numbers 4) Let $z_{1}$ and $z_{2}$ be the solutions of this equation such that $\operatorname{Re}\left(z_{1}\right)>\operatorname{Re}\left(z_{2}\right)$ .

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Problem 8062

Find the largest possible value of $f(15)$ if $f(x)$ is continuous and differentiable on $[6,15]$ , $f(6)=-2$ , and $f'(x) \leq 10$ for all $x \in [6,15]$ .

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Problem 8063

Find the minimum degree of a polynomial with exactly two inflection points.

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Problem 8064

Find the decimal value expressed in thousandths unit: $5.66$ , $10.27$ , $3.478$ , or $100.65$ ?

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Problem 8065

Find the value of $f(81)$ for a continuous function $f$ that satisfies $\int_{0}^{x^{4}} f(t) dt + \int_{0}^{x} f(t^{4}) dt = x$ for all $x$ .

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Problem 8066

Find the limit of the expression $(4^x - 5^x) / (3^x - 4^x)$ as $x$ approaches infinity.

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Problem 8067

Find the solution to the equation $\ln (x-1)=1+\ln (3x+2)$ .

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Problem 8068

Find the solutions to $x-x e^{5 x+2}=0$ . Then find the second derivative of $f(x)$ at $x=1$ , given $f'(x)+5f(x^2)=f^2(x)$ and $f(1)=2$ .

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Problem 8069

Evaluate the definite integral $\int_{-1}^{0} \frac{7 x}{1+x^{4}} d x$ and select the correct answer.

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Problem 8070

Find the linear approximation of $\cos 8$ about $x_0 = \frac{1}{2}$ for the function $f(x) = \cos(2x)$ .

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Problem 8071

Find the value of $2 \sinh (2 \ln x)$ when $x=e$ .

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Problem 8072

Find the inverse of the $2 \times 2$ matrix $A = \begin{bmatrix} 1 & -1 \\ -2 & 1 \end{bmatrix}$ .

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Problem 8073

Find the derivative of $y=\csc^{-1}(\sec x)$ for $0<x<\pi/2$ .

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Problem 8074

Find $c_{12}$ where $C = AB$ and $A = \begin{bmatrix} 1 & -2 & 0 \\ -3 & 4 & -1 \end{bmatrix}, B = \begin{bmatrix} 6 & -5 \\ -2 & 2 \\ 0 & 3 \end{bmatrix}$ .

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Problem 8075

Determine which statement is true for the given universal set $X=\{1,2,3\}$ and set $A=\{1,2\}$ .

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Problem 8076

A manufacturer claims the mean breaking strength of new cables is greater than 1775 lbs. Test this claim using a one-tailed test with $\alpha=0.05$ . The sample mean is 1790 lbs and the population standard deviation is 55 lbs.
(a) $H_0: \mu \leq 1775$ lbs, $H_1: \mu > 1775$ lbs (b) Use a z-test (c) Test statistic $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} = 1.818$ (d) $p$ -value $= 0.035$ (e) Yes, we can support the claim that the mean breaking strength is greater than 1775 lbs.

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Problem 8077

Find the solution of the equation $\frac{y^{2}}{y-1}+\frac{2y-3}{y-1}=1$ .

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Problem 8078

Find the linear approximation of $f(x) = x^{1/4}$ at $x_0 = 2$ . Select the correct answer.

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Problem 8079

Simplify $\frac{2 x}{y^{2}} \cdot \frac{y^{4}}{2 x^{2}}$ and $\frac{1}{01}-\frac{2}{3}$ .

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Problem 8080

Find the value of $z$ given a system of linear equations involving $2 \times 2$ matrices.

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Problem 8081

Find the set difference between the set of odd natural numbers less than or equal to 9 and the set {1, 2, 3, 4}.
$A=\{x: x \text{ is odd natural number } \leq 9\}$ $B=\{1,2,3,4\}$ $A-B=$

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Problem 8082

Find the number of students who do not study Business given that 15 study Mathematics, 30 study Business, and 5 study both.

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Problem 8083

Find the value of $\sqrt{32 x^{5} y}$ .

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Problem 8084

Simplify the expression $(x^{2}+5) \div(x-1)$ and select the correct answer.

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Problem 8085

Find the intersection of the intervals $A=(-\infty, 4] \cap (-3, \infty)$ and $B=(-\infty, 7) \cap [0, \infty)$ .

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Problem 8086

In Polya's problem-solving, which step involves working backward from the desired solution?

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Problem 8087

Find the value of constant $c$ if the given $2 \times 2$ matrix $A$ is singular.

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Problem 8088

Determine which of the given lines $x=-8$ , $y=2x$ , $y=8$ , $y=x+1$ , or $y=x$ is vertical.

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Problem 8089

Find the value of $x$ if $\frac{(3^{x})^{2}}{27}=\frac{1}{9}$ .

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Problem 8090

Estimate relationship between income $x$ and expenditure $y$ using regression equation $\hat{y}=b_{0}+b_{1} x$ . Given 3 observations, find correlation coefficient.

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Problem 8091

Find the positive solution of the equation $3 x^{8/9} + 10 = 129140173$ .

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Problem 8092

Solve for $a$ if $2 a^{2} a^{4} = 128$ . Options: a) 0, b) -1, c) -2, d) None, e) 1, f) 3, g) 2, h) -3.

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Problem 8093

Find the value of $y$ when $x$ is 121, given the equation $y=\sqrt{x}+5$ .

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Problem 8094

Simplify the expression $\frac{42}{55} \times \frac{45}{56} \div \frac{27}{48}$ .

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Problem 8095

Find the largest interval $I$ over which the solution $y(x) = \frac{1}{x^2 + C}$ to the ODE $y' + 2x^6 = 0$ is defined, given $y(4) = \frac{1}{7}$ .

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Problem 8096

Find the zeros of the polynomial function $f(x)=-x^{3}+3x^{2}+13x-15$ and draw its complete graph without a graphing utility.

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Problem 8097

Find the sum of the constants $a, b$ , and $c$ in the equation $ax^{2} + bx + c = 2x^{2} + 16x + 32$ .

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Problem 8098

Given normal calorie burn data with $\mu=310$ and $\sigma=7$ , find probabilities of: (a) >320 calories, (b) <302 calories, (c) 298-330 calories. The probability of (b) is $12.70\%$ , and the probability of (c) is $\square$ .

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Problem 8099

Determine the number of shares issued given that 100,000 shares are authorized, 60,000 were originally issued, and 10,000 were reacquired.

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Problem 8100

Solve for $a$ in $y=\frac{ab}{2c}$ when $b \neq 0, c \neq 0$ .

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Math

Problem 8001

Evaluate the indefinite integral ∫2arccos⁡(7x)1−49x2dx=\int \frac{2 \arccos (7 x)}{\sqrt{1-49 x^{2}}} d x = ∫1−49x2​2arccos(7x)​dx=C$

Problem 8002

Laura has 57\frac{5}{7}75​ jugs of water and needs 16\frac{1}{6}61​ jugs per liter of paint. The expression to find the liters of paint she can mix is: 57÷16\frac{5}{7} \div \frac{1}{6}75​÷61​.

Problem 8003

Solve the equation 4x−2=104x - 2 = 104x−2=10 using algebra tiles. The solution is □\square□. (Type the value of xxx.)

Problem 8004

Problem 8005

Résoudre l'équation x(x+7)=0x(x+7)=0x(x+7)=0.

Problem 8006

Evaluate 3x−73x-73x−7 when x=6x=6x=6. Evaluate 6y−136y-136y−13 when y=4y=4y=4. Evaluate xz5\frac{xz}{5}5xz​ when x=5x=5x=5 and z=5z=5z=5.

Problem 8007

Solve the quadratic equation 49m2−2=7949 m^{2} - 2 = 7949m2−2=79 for real-valued mmm.

Problem 8008

Sketch the region where y=2y=2y=2.

Problem 8009

Identificar la propiedad mostrada en la ecuación 4+(3+x)=44+(3+x)=44+(3+x)=4, que implica las propiedades conmutativa, asociativa y distributiva.

Problem 8010

Find the future cost of a CD after 12 years, given an inflation rate of 4.5%4.5 \%4.5% and a present cost of $12.95\$ 12.95$12.95. Round the answer to the nearest cent.

Problem 8011

Find the value of xxx in the simplified expression gx+h−3=1g6+1h3g^{x} + h^{-3} = \frac{1}{g^{6}} + \frac{1}{h^{3}}gx+h−3=g61​+h31​.

Problem 8012

Find ttt in simplest radical form. Given: 30,60,6230, 60, \frac{6}{2}30,60,26​ (inches).

Problem 8013

Solve the exponential equation 5x=16255^{x}=\frac{1}{625}5x=6251​ to find the value of xxx.

Problem 8014

Solve the inequality 4x−61>−854x - 61 > -854x−61>−85 for the real number xxx.

Problem 8015

Solve for xxx in the equation 5x=255^{x} = 255x=25. Write the answer as an integer or simplified fraction.

Problem 8016

Multiply 4.3×494.3 \times \frac{4}{9}4.3×94​ and round the answer to the nearest hundredth.

Problem 8017

Find the value of f(−2)f(-2)f(−2) when f(x)=−35x+2f(x) = -\frac{3}{5}x + 2f(x)=−53​x+2.

Problem 8018

Find the quotient of 4336\frac{43}{36}3643​ divided by 4322\frac{43}{22}2243​, reduced to lowest terms.

Problem 8019

Find the value of yyy when the line −904−(−38)x=−14y-904-(-38)x=-14y−904−(−38)x=−14y has x=−3x=-3x=−3. (Round answer to two decimal places)

Problem 8020

Solve the linear equation 28−x4=x328-\frac{x}{4}=\frac{x}{3}28−4x​=3x​ and find the solution set.

Problem 8021

Solve the linear equation 9=5(x−2)−(x−7)9=5(x-2)-(x-7)9=5(x−2)−(x−7) and select the correct solution set.

Problem 8022

Solve the linear equation 24−5v=824-5v=824−5v=8 for the variable vvv.

Problem 8023

Solve 30kx−6kx=830kx - 6kx = 830kx−6kx=8 for xxx.

Problem 8024

Determine the cost in 2018 of an item that cost 100in1999usingalinegraphandtwomodels:100 in 1999 using a line graph and two models: 100in1999usingalinegraphandtwomodels:C = 1.9x + 120.4and and andC = 0.03x^2 + 1.8x + 120.7,where, where ,whereCisthecost is the cost isthecostx$ years after 2010.

Problem 8025

Find the value(s) of xxx where 5(3x−8)−26=9(x−4)+185(3x-8)-26=9(x-4)+185(3x−8)−26=9(x−4)+18.

Problem 8026

Solve for the frequency fff given the equation 480f=10×N\frac{480}{f} = 10 \times Nf480​=10×N and f=50×10f = \sqrt{50 \times 10}f=50×10​.

Problem 8027

Solve the linear equation x+5=9x + 5 = 9x+5=9 for the value of xxx.

Problem 8028

Identify coefficients and constants in 6y+5+m6y+5+m6y+5+m. What error might Sarah make? The coefficients are 6,16,16,1. The constant is 555. Sarah might not include the coefficient 111.

Problem 8029

Solve the linear equation 5x−7=7x−135x-7=7x-135x−7=7x−13 and select the correct solution.

Problem 8030

Simplify the expression 23(34x+118)+45(212x+15)\frac{2}{3}\left(\frac{3}{4} x+1 \frac{1}{8}\right)+\frac{4}{5}\left(2 \frac{1}{2} x+15\right)32​(43​x+181​)+54​(221​x+15).

Problem 8031

Solve the equation ∣3x+2∣−8=2x|3x+2| - 8 = 2x∣3x+2∣−8=2x for all values of xxx.

Problem 8032

Analyze the effect of changing y=x3y=x^{3}y=x3 to f(x)=(x+1)3f(x)=(x+1)^{3}f(x)=(x+1)3. Identify the values most affected and describe the impact on the graph.

Problem 8033

Find the equation of the line of best fit for the data: (4, 3), (6, 4), (8, 9), (11, 12), (13, 17). Round the slope and y-intercept to 3 decimal places.

Problem 8034

Find the maximum value of the quadratic function y=−3x2+12x−9y = -3x^2 + 12x - 9y=−3x2+12x−9. The vertex is at xvertex=−b/2ax_{\text{vertex}} = -b/2axvertex​=−b/2a, and the maximum value is y=3y = 3y=3.

Problem 8035

Simplify the expression (−2)3−12(-2)^{3}-12(−2)3−12 and select the correct answer.

Problem 8036

Graph the quadratic function f(x)=x2−2xf(x) = x^2 - 2xf(x)=x2−2x.

Problem 8037

Find the linear function with f(0)=6f(0)=6f(0)=6 and slope f=−9f=-9f=−9.

Problem 8038

Find the standard form of the rectangular equation given the equations x=4−2tx=4-2tx=4−2t and y=3−ty=3-ty=3−t.

Problem 8039

Determine if the given ordered pairs are solutions to the systems of linear inequalities.1. (2,0)(2,0)(2,0): y>y > y>\$$x-5\$$ and $\$$y \leq 2x+1\$$2. $(1,4)$: $\$$y < 2x+2\$$ and $\$$y \geq -3x+4\$$

Problem 8040

Simplify 4x3−6x2+7x−8−(7x3−10x2−5x+4)4x^3 - 6x^2 + 7x - 8 - (7x^3 - 10x^2 - 5x + 4)4x3−6x2+7x−8−(7x3−10x2−5x+4). Find the degree of the resulting polynomial.

Evaluate the indefinite integral $\int \frac{2 \arccos (7 x)}{\sqrt{1-49 x^{2}}} d x =$ C$

Laura has $\frac{5}{7}$ jugs of water and needs $\frac{1}{6}$ jugs per liter of paint. The expression to find the liters of paint she can mix is: $\frac{5}{7} \div \frac{1}{6}$ .

Solve the equation $4x - 2 = 10$ using algebra tiles. The solution is $\square$ . (Type the value of $x$ .)

Résoudre l'équation $x(x+7)=0$ .

Evaluate $3x-7$ when $x=6$ . Evaluate $6y-13$ when $y=4$ . Evaluate $\frac{xz}{5}$ when $x=5$ and $z=5$ .

Solve the quadratic equation $49 m^{2} - 2 = 79$ for real-valued $m$ .

Sketch the region where $y=2$ .

Identificar la propiedad mostrada en la ecuación $4+(3+x)=4$ , que implica las propiedades conmutativa, asociativa y distributiva.

Find the future cost of a CD after 12 years, given an inflation rate of $4.5 \%$ and a present cost of $\$ 12.95$ . Round the answer to the nearest cent.

Find the value of $x$ in the simplified expression $g^{x} + h^{-3} = \frac{1}{g^{6}} + \frac{1}{h^{3}}$ .

Find $t$ in simplest radical form. Given: $30, 60, \frac{6}{2}$ (inches).

Solve the exponential equation $5^{x}=\frac{1}{625}$ to find the value of $x$ .

Solve the inequality $4x - 61 > -85$ for the real number $x$ .

Solve for $x$ in the equation $5^{x} = 25$ . Write the answer as an integer or simplified fraction.

Multiply $4.3 \times \frac{4}{9}$ and round the answer to the nearest hundredth.

Find the value of $f(-2)$ when $f(x) = -\frac{3}{5}x + 2$ .

Find the quotient of $\frac{43}{36}$ divided by $\frac{43}{22}$ , reduced to lowest terms.

Find the value of $y$ when the line $-904-(-38)x=-14y$ has $x=-3$ . (Round answer to two decimal places)

Solve the linear equation $28-\frac{x}{4}=\frac{x}{3}$ and find the solution set.

Solve the linear equation $9=5(x-2)-(x-7)$ and select the correct solution set.

Solve the linear equation $24-5v=8$ for the variable $v$ .

Solve $30kx - 6kx = 8$ for $x$ .

Determine the cost in 2018 of an item that cost $100 in 1999 using a line graph and two models:$ C = 1.9x + 120.4 $and$ C = 0.03x^2 + 1.8x + 120.7 $, where$ C $is the cost$ x$ years after 2010.

Find the value(s) of $x$ where $5(3x-8)-26=9(x-4)+18$ .

Solve for the frequency $f$ given the equation $\frac{480}{f} = 10 \times N$ and $f = \sqrt{50 \times 10}$ .

Solve the linear equation $x + 5 = 9$ for the value of $x$ .

Identify coefficients and constants in $6y+5+m$ . What error might Sarah make? The coefficients are $6,1$ . The constant is $5$ . Sarah might not include the coefficient $1$ .

Solve the linear equation $5x-7=7x-13$ and select the correct solution.

Simplify the expression $\frac{2}{3}\left(\frac{3}{4} x+1 \frac{1}{8}\right)+\frac{4}{5}\left(2 \frac{1}{2} x+15\right)$ .

Solve the equation $|3x+2| - 8 = 2x$ for all values of $x$ .

Analyze the effect of changing $y=x^{3}$ to $f(x)=(x+1)^{3}$ . Identify the values most affected and describe the impact on the graph.

Find the maximum value of the quadratic function $y = -3x^2 + 12x - 9$ . The vertex is at $x_{\text{vertex}} = -b/2a$ , and the maximum value is $y = 3$ .

Simplify the expression $(-2)^{3}-12$ and select the correct answer.

Graph the quadratic function $f(x) = x^2 - 2x$ .

Find the linear function with $f(0)=6$ and slope $f=-9$ .

Find the standard form of the rectangular equation given the equations $x=4-2t$ and $y=3-t$ .

Determine if the given ordered pairs are solutions to the systems of linear inequalities.
1. $(2,0)$ : $y >$ \$$x-5\$$ and $\$$y \leq 2x+1\$$
2. $(1,4)$: $\$$y < 2x+2\$$ and $\$$y \geq -3x+4\$$

Simplify $4x^3 - 6x^2 + 7x - 8 - (7x^3 - 10x^2 - 5x + 4)$ . Find the degree of the resulting polynomial.

18. Is the absolute value of -14 equal to 14? True or False.
19. What is the value of $-3+(-14)$ ? a) 11, b) -11, c) -17, d) -42

Express a function that multiplies input $x$ by 4, then adds 16.

Solve the linear equation $-4x + 8 = 20$ for the value of $x$ .

Find the second number that, when multiplied with $\frac{7}{3}$ , results in an irrational product. Options: $\frac{3}{7}$ , $2 \pi$ , 1, $\sqrt{3}$ .

Encuentra el máximo común divisor de $9$ y $36$ .

Solve for $x$ in the rational equation $\frac{x+1}{3x+6}=\frac{3}{x}+\frac{2x+6}{x(3x+6)}$ using factoring.

Determine if each number is prime or composite, and explain your reasoning. $27, 19, 31, 38, 45, 53, 87, 93$

Solve for the value of $5 \times (-38)$ .

Solve for the missing variable in the equation $\frac{x}{6}+4=5$ .

Find the value of $x$ where the sum of $\frac{3}{8}$ and $x$ is $\frac{7}{2}$ .

Given directly proportional ratios, find the missing variable $y_2$ if $x_1=500$ , $y_1=250$ , and $x_2=370$ .

Find the equation of the linear function with $y$ -intercept $(-4)$ and $x$ -intercept $(5,0)$ . $f(x) = \frac{4}{5}x - 4$

Find the product of $-9 x(5-2 x)$ .

Solve $-125=w^{3}$ for real number $w$ . Simplify solution(s). If no solution, click "No solution".

Find the constant in the equation $y = mx + b$ given the graph points (1,1.5), (2,3), (4,6), (6,9).

Determine if the statement is correct: Since $3^{x}=20$ and $3^{x}=243$ are similar, they can be solved the same way.

Solve for $x$ in the equation $7 \cdot 8 = x - 4$ .

Find the value of $\cosh(3\ln 3) - \sinh(3\ln 3)$ .

Find the largest possible value of $f(15)$ if $f(x)$ is continuous and differentiable on $[6,15]$ , $f(6)=-2$ , and $f'(x) \leq 10$ for all $x \in [6,15]$ .

Find the decimal value expressed in thousandths unit: $5.66$ , $10.27$ , $3.478$ , or $100.65$ ?

Find the value of $f(81)$ for a continuous function $f$ that satisfies $\int_{0}^{x^{4}} f(t) dt + \int_{0}^{x} f(t^{4}) dt = x$ for all $x$ .

Find the limit of the expression $(4^x - 5^x) / (3^x - 4^x)$ as $x$ approaches infinity.

Find the solution to the equation $\ln (x-1)=1+\ln (3x+2)$ .

Find the solutions to $x-x e^{5 x+2}=0$ . Then find the second derivative of $f(x)$ at $x=1$ , given $f'(x)+5f(x^2)=f^2(x)$ and $f(1)=2$ .

Evaluate the definite integral $\int_{-1}^{0} \frac{7 x}{1+x^{4}} d x$ and select the correct answer.

Find the linear approximation of $\cos 8$ about $x_0 = \frac{1}{2}$ for the function $f(x) = \cos(2x)$ .

Find the value of $2 \sinh (2 \ln x)$ when $x=e$ .

Find the inverse of the $2 \times 2$ matrix $A = \begin{bmatrix} 1 & -1 \\ -2 & 1 \end{bmatrix}$ .

Find the derivative of $y=\csc^{-1}(\sec x)$ for $0<x<\pi/2$ .

Find $c_{12}$ where $C = AB$ and $A = \begin{bmatrix} 1 & -2 & 0 \\ -3 & 4 & -1 \end{bmatrix}, B = \begin{bmatrix} 6 & -5 \\ -2 & 2 \\ 0 & 3 \end{bmatrix}$ .