Browse Math problems in the Studdy Learning Bank!

Problem 7101

Find the marginal revenue function. $R(x)=8x-0.07x^2$ , then $R'(x)=$

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Problem 7102

Solve for $\mathrm{f}$ in $3(9+3 f)-74=27 f+42-2(32-4 f)$ . Verify the solution by checking the equation.

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Problem 7103

Write an equation for the relationship between $x$ and $y$ where $y = 6 - x^2$ , then graph the equation.

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Problem 7104

Solve the equation $2x + 4 = 10$ and find the correct solution, given Oliver's incorrect solution of $x = 7$ .

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Problem 7105

Evaluar la expresión $-6a + c$ cuando $a=5$ y $c=-6$ .

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Problem 7106

Find the value of $g(30)$ for the linear function $g(x) = 19.60 + 1.74x$ .

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Problem 7107

Find the value of $x$ if the ratio $(x+6):5$ is equivalent to the ratio $7x:20$ . Give the answer as an integer or simplified fraction.

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Problem 7108

Find the total copies sold to date given that the first month's sales of 33,600 copies represent $6.8\%$ of the total.

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Problem 7109

Resolver $w^{3}=1000$ , donde $w$ es un número real. Simplificar solución. Si más de una, separarlas con comas. Si no tiene solución, indicar "No tiene solución".

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Problem 7110

Find the value of $2,158 \div 26$ .

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Problem 7111

Find the value of $128^{\frac{1}{7}}$ .

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Problem 7112

Find the value of the constant $A$ that makes the rational expression $\frac{8 x}{2 x+5}$ equivalent to $4+\frac{A}{2 x+5}$ .

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Problem 7113

Solve for the value of $v$ in the equation $14+12v = -16+9v$ . Simplify the solution for $v$ .

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Problem 7114

Solve for $x$ in $125^{3x+2} = \frac{1}{25}$ . The value of $A$ in the solution $-\frac{A}{B}$ is \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

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Problem 7115

Solve the quadratic equation $4x(x-2) = 6-3x$ by completing the square and simplifying the solution set.

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Problem 7116

Find the value of $y$ that solves the equation $-20=2(11+y)+5y$ , where $y=-7$ or $y=-6$ .

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Problem 7117

Determine the range of a polynomial function with the highest exponent being $\square$ . Options: all real numbers, even, odd, positive, negative.

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Problem 7118

Divide the expression $\frac{x^{2}+7 x+10}{4}$ by $\frac{3 x+6}{2 x+10}$ and write the quotient in simplest form.

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Problem 7119

Find the domain of the rational expression $\frac{x-5}{3x-6}$ .

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Problem 7120

Find the $y$ -value for the point $(0, ?)$ on the line $y = -8x + 5$ .

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Problem 7121

Simplify the fraction $\frac{24}{80}$ and express the result as a percentage.

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Problem 7122

Find the value of $w$ when $t=9$ using the function $w=3t$ .

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Problem 7123

Given point $P(2|3|4)$ . a) Project $P$ parallel to $x_2$ -axis onto $x_1 x_3$ plane, obtain $P'$ coordinates. b) Project $P$ onto $x_1 x_2$ and $x_2 x_3$ planes, obtain $P''$ and $P'''$ coordinates. c) Reflect $P$ across $x_1 x_3$ plane, give coordinates of reflected point.

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Problem 7124

Find the value of $p$ when $h=9$ using the function $p=5h$ .

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Problem 7125

Solve the system of linear equations $y = 2x + 6$ and $y = \frac{-1}{2}x + 1$ to find the point of intersection.

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Problem 7126

Solve the initial tableau of a linear programming problem using the simplex method. The maximum is $-3$ when $x_1=\frac{11}{5}$ , $x_2=0$ , $x_3=\frac{11}{4}$ , $s_1=\frac{11}{2}$ , and $s_2=0$ .

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Problem 7127

Find the values of integers $c$ and $d$ that satisfy the equation $4cx - 5c = -12x + d$ .

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Problem 7128

Perform arithmetic operations: a. $2 \frac{4}{12} \div 4 \frac{1}{6} \times \frac{2}{9}$ b. $\frac{9}{6} \times 5 \frac{2}{5} \div 3 \frac{1}{5}$

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Problem 7129

Solve the linear equation $11x + 9 - 9x = 0$ for $x$ .

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Problem 7130

Determine the product of $8.9 \times 10^{19}$ and $1.2 \times 10^{2}$ using a calculator.

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Problem 7131

Find the exact value of $\sec A$ given $\sin A = \frac{4}{\sqrt{97}}$ and $A$ is in Quadrant I, in simplest radical form with a rational denominator.

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Problem 7132

Solve the linear equation $5c - 15 = 2c + 6$ for the variable $c$ .

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Problem 7133

Solve for the variable $v$ in the equation $-7v = 8 - 8v$ .

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Problem 7134

Find the product of two fractions: $-\frac{4}{9}$ and $-\frac{3}{8}$ .

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Problem 7135

Solve for the value of $w$ in the linear equation $-20 = 10w$ .

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Problem 7136

Solve the equation $15x + 4 = 7x + 52$ and write the answer in the box.

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Problem 7137

Find the break-even point when $C=25x+4,825$ and $R=165x$ , where $x$ is the number of units produced. (Round to nearest whole digit)

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Problem 7138

Find the derivative of $y=e^{\cosh (2 x)}$ .

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Problem 7139

Gravel is dumped at $30 \mathrm{ft}^{3} / \mathrm{min}$ onto a conical pile with equal base diameter and height. Find the rate of height increase when the pile is $10 \mathrm{ft}$ high.

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Problem 7140

Solve the linear equation $5k - 10 = -10$ for the variable $k$ .

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Problem 7141

Solve the two-step equation $-4x - 8 = 16$ and write the answer.

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Problem 7142

Which equation represents the graph of $y=7|x-6|$ reflected across the y-axis? $y=7|-x+6|$ $y=-7|x-6|$

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Problem 7143

Evaluate $w^{2}-8$ when $w=7$ .

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Problem 7144

Shift $f(x)=6^{x}$ to get $g(x)=6^{x-5}-7$ . Which steps work?

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Problem 7145

Find the upper bound of the inequality $y \leq x^2 + 6x + 4$ .

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Problem 7146

Determine the points in the interval $[0 ; 4 \pi]$ where the sine function takes the value $-0.7$ using the graph.

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Problem 7147

Find the percentage value of the fraction $\frac{4}{8}$ .

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Problem 7148

Find the equation of a line with y-intercept $9$ and x-intercept $-4$ .

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Problem 7149

Prove the identity $\cosh(-x) = \cosh(x)$ , showing that cosh is an even function.

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Problem 7150

Solve $-2^{x}=0.5 x$ by finding the values of $x$ where the functions $f(x)=-2^{x}$ and $g(x)=0.5 x$ intersect.

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Problem 7151

Solve the absolute value equations: $|v-1|=7$ , $\left|\frac{y}{4}\right|=2$ , $|-10 k|=30$ , $|n+8|=1$ .

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Problem 7152

Find the value of $a$ in the equation $g(x)=a \sqrt{a(1-x)}$ if $g(-8)=375$ .

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Problem 7153

Solve the quadratic equation $2n^2 = 27 - 15n$ for the value of $n$ .

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Problem 7154

Find the value of the derivative $f_{x}$ given the expression $f_{x}=7+2 \cdot 3$ .

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Problem 7155

Convert 169 mg to g. Evaluate 9.

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Problem 7156

Solve the quadratic equation $3x^2 + 5x = 12$ for real values of x.

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Problem 7157

Helena earns $\$ 4$ per kid for babysitting. She needs to make at least $\$ 69$ . Write the inequality $4x + 53 \geq 69$ to find the minimum number of kids she needs to babysit, where $x$ is the number of kids.

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Problem 7158

Solve the exponential equation $y=9^{x}$ for $x$ in terms of $y$ .

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Problem 7159

Solve the linear equation $-8y - 8 = 6y + 6$ for the unknown variable $y$ .

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Problem 7160

Find the value of $n$ in the equation $4n-3=5$ by drawing a flowchart and using backtracking. (4 marks)

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Problem 7161

Solve for $x$ in the equation $\frac{x+y}{3} = 5$ .

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Problem 7162

Find the five-number summary and interquartile range for the distances (in miles) to the nearest airport for 11 families: $8, 13, 19, 19, 21, 23, 28, 28, 31, 37, 42$ .

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Problem 7163

Find the slope of the line with the given $(x, y)$ values, then write the equation in point-slope form.
Slope $= \frac{-34 - (-19)}{4 - 1} = -5$ Equation in point-slope form: $y - (-19) = -5(x - 1)$

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Problem 7164

Find the statement that represents the equation $3 \times 9 = 27$ .

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Problem 7165

Find the first term $u_1$ and the common difference $d$ given $u_7=11$ and $u_{12}=56$ in an arithmetic sequence.

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Problem 7166

Solve for $x$ in the equation $7=\frac{x}{3}$ .

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Problem 7167

Find the value of $\frac{a+2bc}{3a}$ when $a=4, b=-5, c=-7$ .

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Problem 7168

Is the point ( $7, 10$ ) a solution to the equation $y = 8x - 7$ ?

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Problem 7169

Find the zero of $9x + 2y = 18$ by setting $9x + 2y = 0$ and solving for $x$ .

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Problem 7170

Solve the linear equation $4x - 5 = -x$ for the unknown variable $x$ .

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Problem 7171

Find the value of $y$ when $x$ is -9, given the equation $y=|x|+12$ .

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Problem 7172

Solve the equation $\frac{4}{x+7}=2$ and select the correct solution from the options provided.

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Problem 7173

Solve the linear equation $-2 = -8 + w$ and plot the solution on the number line.

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Problem 7174

Solve the quadratic equation $2 \tan^2 x - 5 \tan x - 3 = 0$ for $0 \leq x \leq 2 \pi$ .

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Problem 7175

Find the number of unique passwords with 2 digits, where each digit can be a number or a letter.
Solution: There are 10 digits (0-9) and 26 letters (A-Z), so each digit can be chosen from 36 possibilities. Therefore, the total number of possible passwords is $36 \times 36 = 1,296$ .

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Problem 7176

Solve the cubic equation $\sqrt[3]{5x-3}-2=0$ for $x$ .

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Problem 7177

What is the unemployment rate if the job separation rate is $0.05$ and the job finding rate is $0.35$ ?

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Problem 7178

Which of the following statements about quadratic number patterns is correct? $A. \text{The first difference is constant.}$ $B. \text{The third difference is greater than zero.}$

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Problem 7179

Find the equilibrium output given $Z = C + I + G$ , $C = 500 + 0.5Y$ , and $Y = Z$ with $I = 200$ and $G = 300$ .

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Problem 7180

Determine the inflation rate in an economy with 3% real GDP growth and 4% money growth.
$\pi = \mu - g$ , where $\pi$ is the inflation rate, $\mu$ is the money growth rate, and $g$ is the real GDP growth rate.

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Problem 7181

Calculate the sample standard deviation of ages in a dataset of 23, 62, 22, 67. The closest approximation is $2 \sqrt{10}$ .

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Problem 7182

Rewrite the expression $x^{\frac{9}{7}}$ . Select the correct answer: A. $\left(\frac{1}{\sqrt{x}}\right)^{9}$ , B. $x \sqrt[7]{x^{2}}$ , C. $\sqrt[9]{x^{7}}$ , D. $x \sqrt[7]{x}$ .

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Problem 7183

Evaluate time series model for quarterly raincoat sales data (2010-2015) in London. Determine if statements about $Y = T + S + E$ model are true or false.

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Problem 7184

Hangi seçenek $f(x) = \frac{|x|}{x}$ için doğrudur? A) $x=1$ noktasında kaldırılabilir süreksizliği vardır B) $x=1$ noktasında sıçrama süreksizliği vardır C) $x=0$ noktasında silinmez süreksizliği vardır D) $x=0$ noktasında kaldırılabilir süreksizliği vardır E) $x=0$ noktasında sıçrama süreksizliği vardır

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Problem 7185

Find the value of $125 z^{3} y^{12}$ .

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Problem 7186

Find the value of $x$ in the equation $x=\sqrt[3]{(-245)^{-\frac{1}{5}}}$ rounded to the nearest hundredth.

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Problem 7187

Rewrite the equation $y=2x^2+8x+9$ in vertex form by completing the square, then graph the resulting function.

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Problem 7188

Find the range of the function $h(x) = 5 + \log_5 x$ . Simplify your answer in interval notation.

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Problem 7189

Examine the given price and quantity data for TVs and milk in 2015 and 2019. Calculate the nominal and real GDP in 2015 and 2019 using $£ 31,000$ , $£ 38,125$ , $£ 32,600$ .

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Problem 7190

Classify equations as Linear, Exponential, or Neither: $y=-5x-2$ (Linear), $y=4x^2+5$ (Quadratic), $y=-2+3/4x$ (Rational), $y=(1.5)^x$ (Exponential), $g\approx2(5)^2$ (Exponential), $y=5(x-4)^2$ (Quadratic), $y=2-5(0.6)^x$ (Exponential), $y=\sqrt{4x+3}$ (Square Root), $y=17-5x$ (Linear), $y=7x+18x^3$ (Polynomial), $y=(1.23)^x$ (Exponential), $y=(x+4)^2+3$ (Quadratic), $y=7-5x$ (Linear), $y=4x+5x^2$ (Polynomial), $y=5(2.4)^x$ (Exponential), $y=2x-4^x$ (Exponential).

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Problem 7191

Find the value of $a$ that satisfies the equation $3(a+1.5)=-1.5$ .

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Problem 7192

Evaluate the sum of $f(-3)$ and $f(-2)$ for the piecewise function $f(x) = \begin{cases} -3-2x, & x \geq -3 \\ -x^2+7, & x < -3 \end{cases}$ .

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Problem 7193

Determine if each equation is Linear, Exponential, or Neither: A) $y=-5x-2$ (Linear), B) $y=4x^2+5$ (Neither), C) $y=-2+3/4x$ (Neither), D) $y=(1.5)^x$ (Exponential), E) $y=2(5)^2$ (Exponential), F) $y=5(x-4)^2$ (Neither), G) $y=2-5(0.6)^x$ (Exponential), H) $y=\sqrt{4x+3}$ (Neither), M) $4=7-5x$ (Linear), N) $y=4x+5x^2$ (Neither), O) $y=5(2.4)^x$ (Exponential), P) $y=2x-4^x$ (Neither).

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Problem 7194

Solve for $g$ given the equation $f=\frac{1}{7}(g+h-k)$ .

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Problem 7195

Find equivalent linear equations given $14x + 7y = 21$ . Options: $y = 2x + 3$ , $y + 1 = -2(x - 2)$ , $y = -2x + 3$ , $y - 1 = 2(x + 2)$ , $y - 3 = -2x$ .

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Problem 7196

Find $f(-3)$ for the piecewise function $f(x) = \begin{cases} 9x+4 & \text{if } x \leq -5 \\ -\frac{1}{2}x+2 & \text{if } x > -5 \end{cases}$ .

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Problem 7197

Find the value of $t$ when $6e^{9t} = 96$ .

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Problem 7198

Find the composite function $(r \circ s)(x)$ where $r(x) = x + 1$ and $s(x) = 2x$ . Write the answer as a simplified polynomial.

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Problem 7199

Find the value of $a$ when $f(x)=2x^3-9x^2+7x+a=0$ with $x=2$ .

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Problem 7200

Solve the linear equation $\frac{x+10}{x}=9$ for $x$ , where $x \neq 0$ .

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Math

Problem 7101

Find the marginal revenue function. R(x)=8x−0.07x2R(x)=8x-0.07x^2R(x)=8x−0.07x2, then R′(x)=R'(x)=R′(x)=

Problem 7102

Solve for f\mathrm{f}f in 3(9+3f)−74=27f+42−2(32−4f)3(9+3 f)-74=27 f+42-2(32-4 f)3(9+3f)−74=27f+42−2(32−4f). Verify the solution by checking the equation.

Problem 7103

Write an equation for the relationship between xxx and yyy where y=6−x2y = 6 - x^2y=6−x2, then graph the equation.

Problem 7104

Solve the equation 2x+4=102x + 4 = 102x+4=10 and find the correct solution, given Oliver's incorrect solution of x=7x = 7x=7.

Problem 7105

Evaluar la expresión −6a+c-6a + c−6a+c cuando a=5a=5a=5 y c=−6c=-6c=−6.

Problem 7106

Find the value of g(30)g(30)g(30) for the linear function g(x)=19.60+1.74xg(x) = 19.60 + 1.74xg(x)=19.60+1.74x.

Problem 7107

Find the value of xxx if the ratio (x+6):5(x+6):5(x+6):5 is equivalent to the ratio 7x:207x:207x:20. Give the answer as an integer or simplified fraction.

Problem 7108

Find the total copies sold to date given that the first month's sales of 33,600 copies represent 6.8%6.8\%6.8% of the total.

Problem 7109

Resolver w3=1000w^{3}=1000w3=1000, donde www es un número real. Simplificar solución. Si más de una, separarlas con comas. Si no tiene solución, indicar "No tiene solución".

Problem 7110

Find the value of 2,158÷262,158 \div 262,158÷26.

Problem 7111

Find the value of 12817128^{\frac{1}{7}}12871​.

Problem 7112

Find the value of the constant AAA that makes the rational expression 8x2x+5\frac{8 x}{2 x+5}2x+58x​ equivalent to 4+A2x+54+\frac{A}{2 x+5}4+2x+5A​.

Problem 7113

Solve for the value of vvv in the equation 14+12v=−16+9v14+12v = -16+9v14+12v=−16+9v. Simplify the solution for vvv.

Problem 7114

Problem 7115

Solve the quadratic equation 4x(x−2)=6−3x4x(x-2) = 6-3x4x(x−2)=6−3x by completing the square and simplifying the solution set.

Problem 7116

Find the value of yyy that solves the equation −20=2(11+y)+5y-20=2(11+y)+5y−20=2(11+y)+5y, where y=−7y=-7y=−7 or y=−6y=-6y=−6.

Problem 7117

Determine the range of a polynomial function with the highest exponent being □\square□. Options: all real numbers, even, odd, positive, negative.

Problem 7118

Divide the expression x2+7x+104\frac{x^{2}+7 x+10}{4}4x2+7x+10​ by 3x+62x+10\frac{3 x+6}{2 x+10}2x+103x+6​ and write the quotient in simplest form.

Problem 7119

Find the domain of the rational expression x−53x−6\frac{x-5}{3x-6}3x−6x−5​.

Problem 7120

Find the yyy-value for the point (0,?)(0, ?)(0,?) on the line y=−8x+5y = -8x + 5y=−8x+5.

Problem 7121

Simplify the fraction 2480\frac{24}{80}8024​ and express the result as a percentage.

Problem 7122

Find the value of www when t=9t=9t=9 using the function w=3tw=3tw=3t.

Problem 7123

Problem 7124

Find the value of ppp when h=9h=9h=9 using the function p=5hp=5hp=5h.

Problem 7125

Solve the system of linear equations y=2x+6y = 2x + 6y=2x+6 and y=−12x+1y = \frac{-1}{2}x + 1y=2−1​x+1 to find the point of intersection.

Problem 7126

Solve the initial tableau of a linear programming problem using the simplex method. The maximum is −3-3−3 when x1=115x_1=\frac{11}{5}x1​=511​, x2=0x_2=0x2​=0, x3=114x_3=\frac{11}{4}x3​=411​, s1=112s_1=\frac{11}{2}s1​=211​, and s2=0s_2=0s2​=0.

Problem 7127

Find the values of integers ccc and ddd that satisfy the equation 4cx−5c=−12x+d4cx - 5c = -12x + d4cx−5c=−12x+d.

Problem 7128

Perform arithmetic operations: a. 2412÷416×292 \frac{4}{12} \div 4 \frac{1}{6} \times \frac{2}{9}2124​÷461​×92​ b. 96×525÷315\frac{9}{6} \times 5 \frac{2}{5} \div 3 \frac{1}{5}69​×552​÷351​

Problem 7129

Solve the linear equation 11x+9−9x=011x + 9 - 9x = 011x+9−9x=0 for xxx.

Problem 7130

Determine the product of 8.9×10198.9 \times 10^{19}8.9×1019 and 1.2×1021.2 \times 10^{2}1.2×102 using a calculator.

Problem 7131

Find the exact value of sec⁡A\sec AsecA given sin⁡A=497\sin A = \frac{4}{\sqrt{97}}sinA=97​4​ and AAA is in Quadrant I, in simplest radical form with a rational denominator.

Problem 7132

Solve the linear equation 5c−15=2c+65c - 15 = 2c + 65c−15=2c+6 for the variable ccc.

Problem 7133

Solve for the variable vvv in the equation −7v=8−8v-7v = 8 - 8v−7v=8−8v.

Problem 7134

Find the product of two fractions: −49-\frac{4}{9}−94​ and −38-\frac{3}{8}−83​.

Problem 7135

Solve for the value of www in the linear equation −20=10w-20 = 10w−20=10w.

Problem 7136

Solve the equation 15x+4=7x+5215x + 4 = 7x + 5215x+4=7x+52 and write the answer in the box.

Problem 7137

Find the break-even point when C=25x+4,825C=25x+4,825C=25x+4,825 and R=165xR=165xR=165x, where xxx is the number of units produced. (Round to nearest whole digit)

Problem 7138

Find the derivative of y=ecosh⁡(2x)y=e^{\cosh (2 x)}y=ecosh(2x).

Problem 7139

Gravel is dumped at 30ft3/min30 \mathrm{ft}^{3} / \mathrm{min}30ft3/min onto a conical pile with equal base diameter and height. Find the rate of height increase when the pile is 10ft10 \mathrm{ft}10ft high.

Problem 7140

Solve the linear equation 5k−10=−105k - 10 = -105k−10=−10 for the variable kkk.

Problem 7141

Find the marginal revenue function. $R(x)=8x-0.07x^2$ , then $R'(x)=$

Solve for $\mathrm{f}$ in $3(9+3 f)-74=27 f+42-2(32-4 f)$ . Verify the solution by checking the equation.

Write an equation for the relationship between $x$ and $y$ where $y = 6 - x^2$ , then graph the equation.

Solve the equation $2x + 4 = 10$ and find the correct solution, given Oliver's incorrect solution of $x = 7$ .

Evaluar la expresión $-6a + c$ cuando $a=5$ y $c=-6$ .

Find the value of $g(30)$ for the linear function $g(x) = 19.60 + 1.74x$ .

Find the value of $x$ if the ratio $(x+6):5$ is equivalent to the ratio $7x:20$ . Give the answer as an integer or simplified fraction.

Find the total copies sold to date given that the first month's sales of 33,600 copies represent $6.8\%$ of the total.

Resolver $w^{3}=1000$ , donde $w$ es un número real. Simplificar solución. Si más de una, separarlas con comas. Si no tiene solución, indicar "No tiene solución".

Find the value of $2,158 \div 26$ .

Find the value of $128^{\frac{1}{7}}$ .

Find the value of the constant $A$ that makes the rational expression $\frac{8 x}{2 x+5}$ equivalent to $4+\frac{A}{2 x+5}$ .

Solve for the value of $v$ in the equation $14+12v = -16+9v$ . Simplify the solution for $v$ .

Solve the quadratic equation $4x(x-2) = 6-3x$ by completing the square and simplifying the solution set.

Find the value of $y$ that solves the equation $-20=2(11+y)+5y$ , where $y=-7$ or $y=-6$ .

Determine the range of a polynomial function with the highest exponent being $\square$ . Options: all real numbers, even, odd, positive, negative.

Divide the expression $\frac{x^{2}+7 x+10}{4}$ by $\frac{3 x+6}{2 x+10}$ and write the quotient in simplest form.

Find the domain of the rational expression $\frac{x-5}{3x-6}$ .

Find the $y$ -value for the point $(0, ?)$ on the line $y = -8x + 5$ .

Simplify the fraction $\frac{24}{80}$ and express the result as a percentage.

Find the value of $w$ when $t=9$ using the function $w=3t$ .

Find the value of $p$ when $h=9$ using the function $p=5h$ .

Solve the system of linear equations $y = 2x + 6$ and $y = \frac{-1}{2}x + 1$ to find the point of intersection.

Solve the initial tableau of a linear programming problem using the simplex method. The maximum is $-3$ when $x_1=\frac{11}{5}$ , $x_2=0$ , $x_3=\frac{11}{4}$ , $s_1=\frac{11}{2}$ , and $s_2=0$ .

Find the values of integers $c$ and $d$ that satisfy the equation $4cx - 5c = -12x + d$ .

Perform arithmetic operations: a. $2 \frac{4}{12} \div 4 \frac{1}{6} \times \frac{2}{9}$ b. $\frac{9}{6} \times 5 \frac{2}{5} \div 3 \frac{1}{5}$

Solve the linear equation $11x + 9 - 9x = 0$ for $x$ .

Determine the product of $8.9 \times 10^{19}$ and $1.2 \times 10^{2}$ using a calculator.

Find the exact value of $\sec A$ given $\sin A = \frac{4}{\sqrt{97}}$ and $A$ is in Quadrant I, in simplest radical form with a rational denominator.

Solve the linear equation $5c - 15 = 2c + 6$ for the variable $c$ .

Solve for the variable $v$ in the equation $-7v = 8 - 8v$ .

Find the product of two fractions: $-\frac{4}{9}$ and $-\frac{3}{8}$ .

Solve for the value of $w$ in the linear equation $-20 = 10w$ .

Solve the equation $15x + 4 = 7x + 52$ and write the answer in the box.

Find the break-even point when $C=25x+4,825$ and $R=165x$ , where $x$ is the number of units produced. (Round to nearest whole digit)

Find the derivative of $y=e^{\cosh (2 x)}$ .

Gravel is dumped at $30 \mathrm{ft}^{3} / \mathrm{min}$ onto a conical pile with equal base diameter and height. Find the rate of height increase when the pile is $10 \mathrm{ft}$ high.

Solve the linear equation $5k - 10 = -10$ for the variable $k$ .

Solve the two-step equation $-4x - 8 = 16$ and write the answer.

Which equation represents the graph of $y=7|x-6|$ reflected across the y-axis? $y=7|-x+6|$ $y=-7|x-6|$

Evaluate $w^{2}-8$ when $w=7$ .

Shift $f(x)=6^{x}$ to get $g(x)=6^{x-5}-7$ . Which steps work?

Find the upper bound of the inequality $y \leq x^2 + 6x + 4$ .

Determine the points in the interval $[0 ; 4 \pi]$ where the sine function takes the value $-0.7$ using the graph.

Find the percentage value of the fraction $\frac{4}{8}$ .

Find the equation of a line with y-intercept $9$ and x-intercept $-4$ .

Prove the identity $\cosh(-x) = \cosh(x)$ , showing that cosh is an even function.

Solve $-2^{x}=0.5 x$ by finding the values of $x$ where the functions $f(x)=-2^{x}$ and $g(x)=0.5 x$ intersect.

Solve the absolute value equations: $|v-1|=7$ , $\left|\frac{y}{4}\right|=2$ , $|-10 k|=30$ , $|n+8|=1$ .

Find the value of $a$ in the equation $g(x)=a \sqrt{a(1-x)}$ if $g(-8)=375$ .

Solve the quadratic equation $2n^2 = 27 - 15n$ for the value of $n$ .

Find the value of the derivative $f_{x}$ given the expression $f_{x}=7+2 \cdot 3$ .

Solve the quadratic equation $3x^2 + 5x = 12$ for real values of x.

Helena earns $\$ 4$ per kid for babysitting. She needs to make at least $\$ 69$ . Write the inequality $4x + 53 \geq 69$ to find the minimum number of kids she needs to babysit, where $x$ is the number of kids.

Solve the exponential equation $y=9^{x}$ for $x$ in terms of $y$ .

Solve the linear equation $-8y - 8 = 6y + 6$ for the unknown variable $y$ .

Find the value of $n$ in the equation $4n-3=5$ by drawing a flowchart and using backtracking. (4 marks)

Solve for $x$ in the equation $\frac{x+y}{3} = 5$ .

Find the five-number summary and interquartile range for the distances (in miles) to the nearest airport for 11 families: $8, 13, 19, 19, 21, 23, 28, 28, 31, 37, 42$ .

Find the statement that represents the equation $3 \times 9 = 27$ .

Find the first term $u_1$ and the common difference $d$ given $u_7=11$ and $u_{12}=56$ in an arithmetic sequence.

Solve for $x$ in the equation $7=\frac{x}{3}$ .

Find the value of $\frac{a+2bc}{3a}$ when $a=4, b=-5, c=-7$ .

Is the point ( $7, 10$ ) a solution to the equation $y = 8x - 7$ ?

Find the zero of $9x + 2y = 18$ by setting $9x + 2y = 0$ and solving for $x$ .

Solve the linear equation $4x - 5 = -x$ for the unknown variable $x$ .

Find the value of $y$ when $x$ is -9, given the equation $y=|x|+12$ .

Solve the equation $\frac{4}{x+7}=2$ and select the correct solution from the options provided.

Solve the linear equation $-2 = -8 + w$ and plot the solution on the number line.

Solve the quadratic equation $2 \tan^2 x - 5 \tan x - 3 = 0$ for $0 \leq x \leq 2 \pi$ .