Browse Math problems in the Studdy Learning Bank!

Problem 2001

Find $(f \cdot g)(x)$ and $(f \cdot g)(1)$ for $f(x)=-7x+3$ and $g(x)=3x^2-4x-1$ .

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Problem 2002

Determine the function describing a toy rocket's height, its maximum height and time, the time interval it's above 268 feet, and when it hits the ground, given an initial velocity of $180$ feet/second from a $145$ -foot building.

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Problem 2003

Solve the system of linear and quadratic equations $x-6y=10, 3y^2=4x+1$ . Show that $3y^2-24y-41=0$ .

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Problem 2004

Find equations of horizontal and vertical lines through point $(-2,-8)$ .

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Problem 2005

Solve the linear equation $2(x+1)=10$ for the variable $x$ .

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Problem 2006

Evaluate the expression $8^{-2}$ and write the answer as a fraction or whole number without exponents.

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Problem 2007

Find a function $f$ such that $a_{n}=f(n)$ for recurrence relations: $a_{n+2}=a_{n+1}+a_{n}+n^{2}, a_{1}=1, a_{2}=2$ or $a_{n+2}=4 a_{n+1}+4 a_{n}, a_{1}=1, a_{2}=2$ .

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Problem 2008

Find the time $t$ when the velocity $v(t)$ is equal to 3, given the velocity function $v(t)=-10t+11$ .

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Problem 2009

Find the result of adding $13.2$ and $0.9$ , then dividing the sum by $0.6$ .

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Problem 2010

Find the value of $p$ that satisfies the inequality $-31p + 79 > -59p + 81$ . Express the solution in simplest form.

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Problem 2011

Find the degree and leading coefficient of $f(x)=5x-4$ , and state the end behavior of its graph.

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Problem 2012

Solve the linear equation $\frac{g}{3} - 2 = 1$ for the variable $g$ .

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Problem 2013

Find the solution set for the absolute value inequality $|5x - 6| < 12$ .

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Problem 2014

Simplify $\frac{27}{30}$ to its simplest form using the Greatest Common Factor (GCF).

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Problem 2015

Expand the equation $f(x)=(3x+2)^3(x+1)$ . What is the first term and the constant term?

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Problem 2016

Determine which statements are true: $\sqrt{4}$ is rational and integer, $\sqrt{3}$ is rational, 0 is neither rational nor irrational, $-6.1\overline{33}$ is irrational.

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Problem 2017

Use the distributive property to solve $\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}$ .

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Problem 2018

Solve the equation $-3(x+4)=2x+8$ to find the value of $x$ .

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Problem 2019

Probability that a randomly selected teacher in Connecticut makes less than $54,500 per year.$ $P(X < 54,500) = \Phi \left( \frac{54,500 - 57,337}{7,500} \right) \approx \square$ $

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Problem 2020

Deshaun estimates $7 \times 74$ by computing $7 \times 70$ . What is his estimate?

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Problem 2021

Solve the equation $9v - 1(2u + 4) = 0$ for variable $v$ .

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Problem 2022

Evaluate $g(2)$ for the function $g(x) = 9x^2 + 4x - 21$ .

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Problem 2023

Solve for $x$ if $4(2x + 3x) = 30$ . Options: A) 1.50, B) 1.75, C) 2.00, D) 2.50.

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Problem 2024

Rewrite $\cosh 6x - \sinh 6x$ in terms of exponentials and simplify.

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Problem 2025

Find the value of $q$ given the equation $k=4pq^2$ .

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Problem 2026

Which expression equals -4? A) $-8 \div-2$ B) $-2 \times-2$ C) $-7-11$ D) $7+-11$

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Problem 2027

Find the solution to the inequality $3x < 3x + 5$ .

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Problem 2028

Find the exact value of $y$ where $y = \arcsin(1/2)$ without using a calculator.

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Problem 2029

Solve the linear equation $u - 3 = 2$ for the unknown variable $u$ .

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Problem 2030

Solve the linear equation $-x+7=-6$ for the unknown variable $x$ .

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Problem 2031

Solve the equation $-5+B=h$ for the variable $B$ , accounting for capitalization.

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Problem 2032

Which statement best describes $f(6)=12$ ? The input is 6 and the output is 12.

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Problem 2033

Find a positive or negative integer representing the altitude (in feet) of a commercial airplane climbing to 37,500 feet.

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Problem 2034

Determine if the statement $-3^{3}=27$ is true or false. If false, provide the correct statement.

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Problem 2035

Find the inverse function $h^{-1}(x)$ of $h(x)=\frac{7x}{x-4}$ and its domain and range in interval notation.

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Problem 2036

Find the distance between the points $L=(1,0)$ and $N=(-5,3)$ in the coordinate plane, giving the exact answer.

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Problem 2037

Find an integer that has remainders of 2, 2, and 3 when divided by 3, 7, and 5 respectively, as described by Sun Zi's Chinese Remainder Theorem.

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Problem 2038

Solve the system of linear equations $y=-2.89x+7.07, y=1.56x-7.26$ and select the correct solution.

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Problem 2039

Find the complement of $\angle A$ given that $B$ is the midpoint of $AC$ and $AB = BC = 6x - 3 = 4x + 9$ .

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Problem 2040

Écrivez une fonction polynomiale satisfaisant les conditions: a) $x$ dans les quadrants III-IV, 1 point d'inflexion, $y$ -int: 2. b) $x$ dans les quadrants III-I, 3 abscisses à l'origine. c) croissante, degré 1, $y$ -int: -3. d) 2 points d'inflexion, $y$ -int: 5. e) $y \leq 2$ , $y$ -int: 2.

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Problem 2041

Combine like terms in expressions with variables and coefficients. $-7c + 2c - 3c - 5c =$ $3w + 4w^3 + 7w + w^2 - w^3 =$ $3a + 5b + a - (-2)b =$ $\frac{1}{2}v - \frac{2}{3}v + v =$

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Problem 2042

Simplify the fraction $\frac{2 q^{8} r}{6 q^{4}}$ .

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Problem 2043

Write a system of equations to find the cost of pens and pencils, where $x$ is the number of pens and $y$ is the number of pencils. Gabby bought $4$ pens and $5$ pencils for $\$ 6.71$ , and Sydney bought $5$ pens and $3$ pencils for $\$ 7.12$ .

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Problem 2044

Find the number of students who chose Drama, Other, or Historical genres from a college with 15,000 students, given the percentages: $27\%$ Drama, $23\%$ Other, and $20\%$ Historical.

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Problem 2045

Calculate the given fractions. Show your work. (4 marks) a) $-\frac{3}{4} \times\left(-\frac{1}{9}\right)$ b) $\frac{7}{9}\left(-\frac{6}{11}\right)$ c) $-\frac{3}{8} \div \frac{7}{10}$ d) $-2 \frac{1}{8} \div 1 \frac{1}{4}$

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Problem 2046

Multiply $6 \times \frac{5}{9}$ and write the answer as a simplified fraction.

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Problem 2047

Find the critical value(s) for the left-tailed $t$ -test with $\alpha=0.025$ and $n=27$ . The critical value(s) is/are $t_{\alpha, n-1}$ .

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Problem 2048

Explain: Think of an even number. Multiply it by $5$ . What is the last digit of the $5x$ product? Explain why the last digit is always $0$ or $5$ .

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Problem 2049

Find the expression that represents $-30+9k$ as a product with -3 as one of the factors.

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Problem 2050

Solve the linear equation $4x + 6 = 17$ for the value of $x$ .

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Problem 2051

Solve for $x$ in the equation $\sqrt{x-8}+2=7$ . The solutions are $x=1, 13, 17, 33$ .

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Problem 2052

Solve the linear equation $21+2f=9f$ for the unknown variable $f$ .

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Problem 2053

Solve the equation $10b = 50$ for $b$ .

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Problem 2054

Find the number of jumpers in Jacob's wardrobe given the ratio of T-shirts to jumpers is $8: 7$ and there are 24 T-shirts.

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Problem 2055

Solve for $h$ in the equation $2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h$ .

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Problem 2056

Solve the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ to find the possible values of $m$ .

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Problem 2057

Solve the equation $2(x+1)=12$ for $x$ .

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Problem 2058

Construct a 99% confidence interval for the mean body temperature of 105 healthy adults with $\bar{x}=98.7^{\circ}F$ and $s=0.64^{\circ}F$ . Does the interval suggest the use of $98.6^{\circ}F$ as the mean body temperature?
A. The interval suggests the mean could be $98.6^{\circ}F$ . B. The interval suggests the mean is higher than $98.6^{\circ}F$ . C. The interval suggests the mean is lower than $98.6^{\circ}F$ .

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Problem 2059

Find the true statement about the opposite and absolute value of 45 and -45.
The opposite of -45 is equal to the absolute value of -45.

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Problem 2060

Find the number of elements in the set $A = \{1, 3, 5, \ldots, 31\}$ .

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Problem 2061

Find the value of $\frac{2}{8}$ .

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Problem 2062

Find the values of the constant $c$ and the $y$ -intercept in the linear equation $y=\frac{1}{\sqrt{1}}x+0$ .

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Problem 2063

Elijah's town voted on a new speed limit. $\frac{36}{60}$ of the votes were in favor. What is the percentage of votes in favor?

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Problem 2064

Find the proportion of steel rods with length less than $24.9 \mathrm{cm}$ , given the rods have a mean length of $25 \mathrm{cm}$ and standard deviation of $0.07 \mathrm{cm}$ .

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Problem 2065

Solve the linear equation $10x + 8(10x - 6) = 0$ for $x$ .

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Problem 2066

Find the solutions to the equation $\sqrt{2x-1}-2=0$ .

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Problem 2067

Find the equation of a line given the slope $m=-4$ and a point $(1,8)$ on the line.

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Problem 2068

Simplify the expression $\left(16 b^{\frac{1}{3}}\right)^{\frac{3}{2}}$ as a power of $b$ .

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Problem 2069

Convert $135^{\circ}$ to radian measure.

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Problem 2070

Determine the possible number of positive and negative real zeros for $f(x) = -4x^4 + 3x^3 - 9x^2 + 6x - 9$ using Descartes' Rule of Signs.

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Problem 2071

Determine how the graph of $y=-\frac{1}{3}x+3$ changes when it is modified to $y=-\frac{1}{3}x-1$ .

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Problem 2072

Solve the equation $\frac{1}{2}(x-9)+\frac{1}{3}(x+5)=-2$ for $x$ .

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Problem 2073

Find the value of $3 \sqrt[3]{x+y}-\sqrt{x}$ when $x=4$ and $y=-12$ .

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Problem 2074

Find the number of adult tickets sold for a school play where 752 total tickets were sold, with 52 more student tickets than adult tickets.
Let $x$ be the number of adult tickets and $y$ be the number of student tickets. Then, $x + y = 752$ and $y = x + 52$ .

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Problem 2075

Find the value of $s$ given the equation $P=q+6+s$ .

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Problem 2076

Determine if the linear equation $y = -2x + 3$ represents a linear function. Explain your reasoning.

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Problem 2077

Find the mapping rule for the function $y=2 \sqrt{-(x+3)}-4$ .

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Problem 2078

Solve the linear equation $13x - 5y = 35$ for $x$ and $y$ .

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Problem 2079

Solve for the variable $\boldsymbol{e}$ in the equation $e+7=41$ .

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Problem 2080

Solve the linear equation $y + 5(2y - 7) = 9$ for the variable $y$ .

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Problem 2081

Is $c = \pm 50$ or $c = \pm 20$ the solution to the equation $15 = c - 35$ ?

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Problem 2082

Geben Sie Zahlen an, die: a) ganze, aber keine rationalen Zahlen sind. $/(v) ?$ b) Brüche und negative Zahlen sind. $-\frac{2 y}{4},-\frac{1}{2}$ c) reell, aber nicht rational sind. d) irrationale Zahlen sind, deren Quadrat natürliche Zahlen sind.

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Problem 2083

Find the cost of carpet for a rectangular living room floor with length 16 ft and width 14 ft, if carpet costs $\$ 12$ per square foot.

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Problem 2084

Graph $y=2 \cos^{2}(x)$ and $y=2 e^{-x}+2 x-2$ on $[0, 2\pi)$ . Find the intersection points and their coordinates to 4 decimal places. If no solution, enter "NO SOLUTION".

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Problem 2085

Find the value of $x$ that satisfies the equation $2x+12=6x-14$ .

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Problem 2086

Clothing business finds linear relationship between number of shirts $n$ and price $p$ per shirt. Given: 5000 shirts sold at $\$71$ , 6000 shirts sold at $\$65$ . Find linear equation $p=mn+b$ for price $p$ of $n$ shirts.

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Problem 2087

Solve for $x$ the equation $2(2)^{x}=\frac{1}{8}$ .

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Problem 2088

Solve for $f$ where $-5(f-7)<5$ .

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Problem 2089

Find the values of $s$ , $t$ , and $r$ in the given $2\times 2$ matrix equation.

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Problem 2090

Solve $-6 x^{\frac{3}{2}}+5=-2,053$ for $x$ . Options: A) $x=49$ , B) $x=28$ , C) $x=14$ , D) $x=7$ .

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Problem 2091

Kayak rental cost ( $C$ ) vs. hours ( $x$ ) data. Find equation that best models the data: A. $C \equiv x^{2}=8 x+41.9$ , B. $C \equiv 55.8=2 x^{2}$ , C. $C \equiv 14.9 x+20$ , D. $C \equiv 12.9 x+22$ .

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Problem 2092

Use properties of integer exponents to explain the meaning of $2^{\frac{1}{5}}$ .

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Problem 2093

Find the value of $c$ in the equation $8g + c - 6 = 0$ . Select the correct solution: $c = 2gc$ or $c = 8gc + 6$ .

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Problem 2094

Describe a flour machine's flour amount vs. time graph. (a) What is the initial flour amount $x$ grams? (b) As time $t$ increases, does flour amount (i) decrease at rate $y$ g/min or (ii) increase at rate $z$ g/min?

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Problem 2095

Determine if the lines $y=\frac{-5}{6}x+\frac{9}{4}$ and $y=\frac{6}{5}x+\frac{5}{2}$ are parallel, perpendicular, or neither.

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Problem 2096

Choose the correct integers $y \geq -1$ for the set $\{y: y \text{ is an integer and } y \geq -1\}$ . Choose 1 option, 5 points.

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Problem 2097

Find the equivalent function to $f(x)=2(5)^{2x}$ : $f(x)=50^{x}$ , $f(x)=100^{x}$ , $f(x)=2(25)^{x}$ , or $f(x)=4(25)^{x}$ ?

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Problem 2098

Find the equation that gives the number of bricks remaining in a pile of 40 bricks after removing 3 per week for 5 weeks. Equations: $b=40-9$ , $b=40-3(5)$ , $b=40+3(5)$

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Problem 2099

Find the value of $w$ when $m=7$ using the equation $w=m+4$ .

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Problem 2100

Solve the quadratic equation $(k+1) x^{2}+(4 k+1) x+(k-5)=0$ with two equal roots. Prove that $4 k^{2}+8 k+7=0$ has no real solutions. Find the range of $x$ satisfying $4 x^{2}-9 x-9 \geqslant 0$ .

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Math

Problem 2001

Find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) and (f⋅g)(1)(f \cdot g)(1)(f⋅g)(1) for f(x)=−7x+3f(x)=-7x+3f(x)=−7x+3 and g(x)=3x2−4x−1g(x)=3x^2-4x-1g(x)=3x2−4x−1.

Problem 2002

Determine the function describing a toy rocket's height, its maximum height and time, the time interval it's above 268 feet, and when it hits the ground, given an initial velocity of 180180180 feet/second from a 145145145-foot building.

Problem 2003

Solve the system of linear and quadratic equations x−6y=10,3y2=4x+1x-6y=10, 3y^2=4x+1x−6y=10,3y2=4x+1. Show that 3y2−24y−41=03y^2-24y-41=03y2−24y−41=0.

Problem 2004

Find equations of horizontal and vertical lines through point (−2,−8)(-2,-8)(−2,−8).

Problem 2005

Solve the linear equation 2(x+1)=102(x+1)=102(x+1)=10 for the variable xxx.

Problem 2006

Evaluate the expression 8−28^{-2}8−2 and write the answer as a fraction or whole number without exponents.

Problem 2007

Problem 2008

Find the time ttt when the velocity v(t)v(t)v(t) is equal to 3, given the velocity function v(t)=−10t+11v(t)=-10t+11v(t)=−10t+11.

Problem 2009

Find the result of adding 13.213.213.2 and 0.90.90.9, then dividing the sum by 0.60.60.6.

Problem 2010

Find the value of ppp that satisfies the inequality −31p+79>−59p+81-31p + 79 > -59p + 81−31p+79>−59p+81. Express the solution in simplest form.

Problem 2011

Find the degree and leading coefficient of f(x)=5x−4f(x)=5x-4f(x)=5x−4, and state the end behavior of its graph.

Problem 2012

Solve the linear equation g3−2=1\frac{g}{3} - 2 = 13g​−2=1 for the variable ggg.

Problem 2013

Find the solution set for the absolute value inequality ∣5x−6∣<12|5x - 6| < 12∣5x−6∣<12.

Problem 2014

Simplify 2730\frac{27}{30}3027​ to its simplest form using the Greatest Common Factor (GCF).

Problem 2015

Expand the equation f(x)=(3x+2)3(x+1)f(x)=(3x+2)^3(x+1)f(x)=(3x+2)3(x+1). What is the first term and the constant term?

Problem 2016

Determine which statements are true: 4\sqrt{4}4​ is rational and integer, 3\sqrt{3}3​ is rational, 0 is neither rational nor irrational, −6.133‾-6.1\overline{33}−6.133 is irrational.

Problem 2017

Use the distributive property to solve 5x3−x=x15−65\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}35x​−x=15x​−56​.

Problem 2018

Solve the equation −3(x+4)=2x+8-3(x+4)=2x+8−3(x+4)=2x+8 to find the value of xxx.

Problem 2019

Probability that a randomly selected teacher in Connecticut makes less than 54,500peryear.54,500 per year. 54,500peryear.P(X<54,500)=Φ(54,500−57,3377,500)≈□ P(X < 54,500) = \Phi \left( \frac{54,500 - 57,337}{7,500} \right) \approx \square P(X<54,500)=Φ(7,50054,500−57,337​)≈□$

Problem 2020

Deshaun estimates 7×747 \times 747×74 by computing 7×707 \times 707×70. What is his estimate?

Problem 2021

Solve the equation 9v−1(2u+4)=09v - 1(2u + 4) = 09v−1(2u+4)=0 for variable vvv.

Problem 2022

Evaluate g(2)g(2)g(2) for the function g(x)=9x2+4x−21g(x) = 9x^2 + 4x - 21g(x)=9x2+4x−21.

Problem 2023

Solve for xxx if 4(2x+3x)=304(2x + 3x) = 304(2x+3x)=30. Options: A) 1.50, B) 1.75, C) 2.00, D) 2.50.

Problem 2024

Rewrite cosh⁡6x−sinh⁡6x\cosh 6x - \sinh 6xcosh6x−sinh6x in terms of exponentials and simplify.

Problem 2025

Find the value of qqq given the equation k=4pq2k=4pq^2k=4pq2.

Problem 2026

Which expression equals -4? A) −8÷−2-8 \div-2−8÷−2 B) −2×−2-2 \times-2−2×−2 C) −7−11-7-11−7−11 D) 7+−117+-117+−11

Problem 2027

Find the solution to the inequality 3x<3x+53x < 3x + 53x<3x+5.

Problem 2028

Find the exact value of yyy where y=arcsin⁡(1/2)y = \arcsin(1/2)y=arcsin(1/2) without using a calculator.

Problem 2029

Solve the linear equation u−3=2u - 3 = 2u−3=2 for the unknown variable uuu.

Problem 2030

Solve the linear equation −x+7=−6-x+7=-6−x+7=−6 for the unknown variable xxx.

Problem 2031

Solve the equation −5+B=h-5+B=h−5+B=h for the variable BBB, accounting for capitalization.

Problem 2032

Which statement best describes f(6)=12f(6)=12f(6)=12? The input is 6 and the output is 12.

Problem 2033

Find a positive or negative integer representing the altitude (in feet) of a commercial airplane climbing to 37,500 feet.

Problem 2034

Determine if the statement −33=27-3^{3}=27−33=27 is true or false. If false, provide the correct statement.

Problem 2035

Find the inverse function h−1(x)h^{-1}(x)h−1(x) of h(x)=7xx−4h(x)=\frac{7x}{x-4}h(x)=x−47x​ and its domain and range in interval notation.

Problem 2036

Find the distance between the points L=(1,0)L=(1,0)L=(1,0) and N=(−5,3)N=(-5,3)N=(−5,3) in the coordinate plane, giving the exact answer.

Problem 2037

Find an integer that has remainders of 2, 2, and 3 when divided by 3, 7, and 5 respectively, as described by Sun Zi's Chinese Remainder Theorem.

Problem 2038

Solve the system of linear equations y=−2.89x+7.07,y=1.56x−7.26y=-2.89x+7.07, y=1.56x-7.26y=−2.89x+7.07,y=1.56x−7.26 and select the correct solution.

Problem 2039

Find the complement of ∠A\angle A∠A given that BBB is the midpoint of ACACAC and AB=BC=6x−3=4x+9AB = BC = 6x - 3 = 4x + 9AB=BC=6x−3=4x+9.

Problem 2040

Écrivez une fonction polynomiale satisfaisant les conditions: a) xxx dans les quadrants III-IV, 1 point d'inflexion, yyy-int: 2. b) xxx dans les quadrants III-I, 3 abscisses à l'origine. c) croissante, degré 1, yyy-int: -3. d) 2 points d'inflexion, yyy-int: 5. e) y≤2y \leq 2y≤2, yyy-int: 2.

Find $(f \cdot g)(x)$ and $(f \cdot g)(1)$ for $f(x)=-7x+3$ and $g(x)=3x^2-4x-1$ .

Determine the function describing a toy rocket's height, its maximum height and time, the time interval it's above 268 feet, and when it hits the ground, given an initial velocity of $180$ feet/second from a $145$ -foot building.

Solve the system of linear and quadratic equations $x-6y=10, 3y^2=4x+1$ . Show that $3y^2-24y-41=0$ .

Find equations of horizontal and vertical lines through point $(-2,-8)$ .

Solve the linear equation $2(x+1)=10$ for the variable $x$ .

Evaluate the expression $8^{-2}$ and write the answer as a fraction or whole number without exponents.

Find the time $t$ when the velocity $v(t)$ is equal to 3, given the velocity function $v(t)=-10t+11$ .

Find the result of adding $13.2$ and $0.9$ , then dividing the sum by $0.6$ .

Find the value of $p$ that satisfies the inequality $-31p + 79 > -59p + 81$ . Express the solution in simplest form.

Find the degree and leading coefficient of $f(x)=5x-4$ , and state the end behavior of its graph.

Solve the linear equation $\frac{g}{3} - 2 = 1$ for the variable $g$ .

Find the solution set for the absolute value inequality $|5x - 6| < 12$ .

Simplify $\frac{27}{30}$ to its simplest form using the Greatest Common Factor (GCF).

Expand the equation $f(x)=(3x+2)^3(x+1)$ . What is the first term and the constant term?

Determine which statements are true: $\sqrt{4}$ is rational and integer, $\sqrt{3}$ is rational, 0 is neither rational nor irrational, $-6.1\overline{33}$ is irrational.

Use the distributive property to solve $\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}$ .

Solve the equation $-3(x+4)=2x+8$ to find the value of $x$ .

Probability that a randomly selected teacher in Connecticut makes less than $54,500 per year.$ $P(X < 54,500) = \Phi \left( \frac{54,500 - 57,337}{7,500} \right) \approx \square$ $

Deshaun estimates $7 \times 74$ by computing $7 \times 70$ . What is his estimate?

Solve the equation $9v - 1(2u + 4) = 0$ for variable $v$ .

Evaluate $g(2)$ for the function $g(x) = 9x^2 + 4x - 21$ .

Solve for $x$ if $4(2x + 3x) = 30$ . Options: A) 1.50, B) 1.75, C) 2.00, D) 2.50.

Rewrite $\cosh 6x - \sinh 6x$ in terms of exponentials and simplify.

Find the value of $q$ given the equation $k=4pq^2$ .

Which expression equals -4? A) $-8 \div-2$ B) $-2 \times-2$ C) $-7-11$ D) $7+-11$

Find the solution to the inequality $3x < 3x + 5$ .

Find the exact value of $y$ where $y = \arcsin(1/2)$ without using a calculator.

Solve the linear equation $u - 3 = 2$ for the unknown variable $u$ .

Solve the linear equation $-x+7=-6$ for the unknown variable $x$ .

Solve the equation $-5+B=h$ for the variable $B$ , accounting for capitalization.

Which statement best describes $f(6)=12$ ? The input is 6 and the output is 12.

Determine if the statement $-3^{3}=27$ is true or false. If false, provide the correct statement.

Find the inverse function $h^{-1}(x)$ of $h(x)=\frac{7x}{x-4}$ and its domain and range in interval notation.

Find the distance between the points $L=(1,0)$ and $N=(-5,3)$ in the coordinate plane, giving the exact answer.

Solve the system of linear equations $y=-2.89x+7.07, y=1.56x-7.26$ and select the correct solution.

Find the complement of $\angle A$ given that $B$ is the midpoint of $AC$ and $AB = BC = 6x - 3 = 4x + 9$ .

Écrivez une fonction polynomiale satisfaisant les conditions: a) $x$ dans les quadrants III-IV, 1 point d'inflexion, $y$ -int: 2. b) $x$ dans les quadrants III-I, 3 abscisses à l'origine. c) croissante, degré 1, $y$ -int: -3. d) 2 points d'inflexion, $y$ -int: 5. e) $y \leq 2$ , $y$ -int: 2.

Simplify the fraction $\frac{2 q^{8} r}{6 q^{4}}$ .

Write a system of equations to find the cost of pens and pencils, where $x$ is the number of pens and $y$ is the number of pencils. Gabby bought $4$ pens and $5$ pencils for $\$ 6.71$ , and Sydney bought $5$ pens and $3$ pencils for $\$ 7.12$ .

Find the number of students who chose Drama, Other, or Historical genres from a college with 15,000 students, given the percentages: $27\%$ Drama, $23\%$ Other, and $20\%$ Historical.

Multiply $6 \times \frac{5}{9}$ and write the answer as a simplified fraction.

Find the critical value(s) for the left-tailed $t$ -test with $\alpha=0.025$ and $n=27$ . The critical value(s) is/are $t_{\alpha, n-1}$ .

Explain: Think of an even number. Multiply it by $5$ . What is the last digit of the $5x$ product? Explain why the last digit is always $0$ or $5$ .

Find the expression that represents $-30+9k$ as a product with -3 as one of the factors.

Solve the linear equation $4x + 6 = 17$ for the value of $x$ .

Solve for $x$ in the equation $\sqrt{x-8}+2=7$ . The solutions are $x=1, 13, 17, 33$ .

Solve the linear equation $21+2f=9f$ for the unknown variable $f$ .

Solve the equation $10b = 50$ for $b$ .

Find the number of jumpers in Jacob's wardrobe given the ratio of T-shirts to jumpers is $8: 7$ and there are 24 T-shirts.

Solve for $h$ in the equation $2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h$ .

Solve the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ to find the possible values of $m$ .

Solve the equation $2(x+1)=12$ for $x$ .

Find the true statement about the opposite and absolute value of 45 and -45.
The opposite of -45 is equal to the absolute value of -45.

Find the number of elements in the set $A = \{1, 3, 5, \ldots, 31\}$ .

Find the value of $\frac{2}{8}$ .

Find the values of the constant $c$ and the $y$ -intercept in the linear equation $y=\frac{1}{\sqrt{1}}x+0$ .

Elijah's town voted on a new speed limit. $\frac{36}{60}$ of the votes were in favor. What is the percentage of votes in favor?

Find the proportion of steel rods with length less than $24.9 \mathrm{cm}$ , given the rods have a mean length of $25 \mathrm{cm}$ and standard deviation of $0.07 \mathrm{cm}$ .

Solve the linear equation $10x + 8(10x - 6) = 0$ for $x$ .

Find the solutions to the equation $\sqrt{2x-1}-2=0$ .

Find the equation of a line given the slope $m=-4$ and a point $(1,8)$ on the line.

Simplify the expression $\left(16 b^{\frac{1}{3}}\right)^{\frac{3}{2}}$ as a power of $b$ .

Convert $135^{\circ}$ to radian measure.

Determine the possible number of positive and negative real zeros for $f(x) = -4x^4 + 3x^3 - 9x^2 + 6x - 9$ using Descartes' Rule of Signs.

Determine how the graph of $y=-\frac{1}{3}x+3$ changes when it is modified to $y=-\frac{1}{3}x-1$ .

Solve the equation $\frac{1}{2}(x-9)+\frac{1}{3}(x+5)=-2$ for $x$ .

Find the value of $3 \sqrt[3]{x+y}-\sqrt{x}$ when $x=4$ and $y=-12$ .

Find the number of adult tickets sold for a school play where 752 total tickets were sold, with 52 more student tickets than adult tickets.
Let $x$ be the number of adult tickets and $y$ be the number of student tickets. Then, $x + y = 752$ and $y = x + 52$ .