Browse Algebra problems in the Studdy Learning Bank!

Problem 801

Rewrite $y=\frac{1}{4}x+3$ to solve for $x$ . What feature of the line can be found using the rearranged equation $x=\frac{4y-12}{1}$ ?

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Problem 802

Find the property that applies to the equation $7(6x) = 42x$ .

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Problem 803

Solve for $x$ in the linear equation $5 x + 10 = 10 + 5 x$ and determine the type of solution.

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Problem 804

Solve the polynomial equation $9y^3 - 16y = 0$ by grouping and factoring. Enter the exact solutions.

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Problem 805

Find the equation that represents "The sum of $-4 x$ and 2 is 9".

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Problem 806

Find the value of $\frac{x-5}{8x+2}$ when $x=2$ , and simplify the result.

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Problem 807

Find the rule for the pattern: 2, 10, 8, 16, 14. Options: A. $+8, \times 2$ , B. $+8,-2$ , C. $x 5,-2$ , D. $x 8,-4$ .

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Problem 808

Find the value of $x$ to the nearest ten-thousandth that satisfies the equation $9^{-3 x+2}=48$ .

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Problem 809

Determine if $t(x)$ is a linear function given the values in the table: $x = \{0, 1, 2, 3\}$ , $f(x) = \{-8, -4, 0, 4\}$ . Select: A. $f(x) =$ __ or B. The function is not linear.

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Problem 810

Determine if the relationship $y=5x(x+3)$ is linear. Explain your reasoning.

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Problem 811

Evaluate the expression: $2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc$ where $a=2, b=5, c=3$ .

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Problem 812

Write the expression using radical notation and simplify if possible, assuming all variables represent nonnegative quantities. $\sqrt{64 x^{4}}$

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Problem 813

Solve the quadratic equation $6n^2 + 42n - 48 = 6$ for the value of $n$ .

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Problem 814

Graph the complex number $-3+i$ .

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Problem 815

Multiply the expression $(x+5)(x-7)$ and simplify.

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Problem 816

Solve the quadratic equation $4x^2 - 27 = 1756$ using the square root property. Provide the exact and approximate answers.
Exact answers: $x = \frac{\sqrt{1783}}{2}, -\frac{\sqrt{1783}}{2}$ Approximate answers: $x \approx 23.83, -23.83$

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Problem 817

Find the value of $x$ that satisfies the equation $-2 x^{2} - 8 x = -64$ when the current time is 291.4.

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Problem 818

Find the equations equivalent to $n-11=8$ using properties of equality.

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Problem 819

Find the value of $x$ that satisfies the quadratic equation $3 x^{2} + 6 x = -3$ .

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Problem 820

Rahkim solved the equation $x-6=30$ , but his reasoning had a flaw. The best statement to describe the flaw is: B. Rahkim is confused about which number the 6 is being subtracted from.

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Problem 821

Write a degree 2 trinomial with leading coef 8 and constant -5. Write two degree 1 binomials, then multiply and simplify.
$8 x^{2} - 5$

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Problem 822

Maximize $9t + 8.50v$ under constraints $9t + 8.50v \leq 150$ and $v \geq 5$ .

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Problem 823

Multiply and simplify $(4x+2)(4x+5)$

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Problem 824

Find the composite function of two given linear functions. Given $f(x) = 4x + 14$ and $g(x) = 2x - 1$ , find $(f \circ g)(x)$ .

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Problem 825

Solve the equation: $\left(\frac{1}{16}\right)^{-x}=\left(\frac{1}{32}\right)^{-x-1}$

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Problem 826

Complete the table for $f(j) = j^2 + j$ given values of $j$ .

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Problem 827

Add or subtract complex numbers. Find the result in standard form. $-7-(4-5i)-(2-4i)$

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Problem 828

Rewrite the polynomial $-8m+7$ in factored form with a positive leading coefficient.

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Problem 829

Solve for the value of $k$ in the equation $2+\frac{k}{3}=5$ .

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Problem 830

Find the value of $y$ that satisfies the equation $|y-6|+8=12$ .

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Problem 831

Solve the linear equation $3x + 5 = 17$ for the value of $x$ .

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Problem 832

Solve for $x$ in the equation $w + x = 17$ .

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Problem 833

Write inequalities to represent the distance to the nearest exit door and the weight of the cargo. The distance must be less than 150 feet ( $d < 150$ ) and the cargo weight must be no more than 2,400 pounds ( $w \le 2,400$ ).

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Problem 834

Find $x$ and $y$ given $xy=144$ , $x+y=30$ , and $x \geq y$ . What is the value of $x-y$ ?

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Problem 835

Solve the equation $x=-2-5x$ for $x$ .

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Problem 836

Describe the transformations for the quadratic $f(x) = (x-3)^2 + 2$ . Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

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Problem 837

Solve for $y$ where $|7y| = 14$ . Write the solution as an integer or simplified fraction.

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Problem 838

Solve the equation $(3x+8)(x+2)=0$ and write the answer in reduced fraction form.

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Problem 839

Find the equation of a line passing through $(-2,2)$ and perpendicular to $y=\frac{1}{2} x-3$ . A. $y=-2 x+2$ B. $y=-2 x-2$ C. $y=\frac{1}{2} x-2$ D. $y=\frac{1}{2} x+2$

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Problem 840

Solve the absolute value equation $|x| = 13$ .

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Problem 841

Simplify the expression $\frac{11(x-3) \cdot 7 \cdot 7}{5 \cdot 7 \cdot 5 \cdot 11(x-3)}$ by dividing out common factors.

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Problem 842

Solve for the value of $m$ in the equation $9m + 7 = 8m$ .

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Problem 843

Find the temperature range that Andrew considers comfortable. Write an absolute value equation to represent the situation, then solve for the minimum and maximum temperatures.
Part A: $|T - 70^{\circ} \mathrm{F}| \leq 5^{\circ} \mathrm{F}$ Part B: Minimum: $65^{\circ} \mathrm{F}$ , Maximum: $75^{\circ} \mathrm{F}$

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Problem 844

Find the equation of the line passing through the points (1,6) and (2,7).

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Problem 845

Solve the absolute value equation $|2x-1| = 9$ or indicate if it has no solution.

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Problem 846

Find the equation equivalent to $0=-3 x^{2}+27 x+30$ .

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Problem 847

Simplify the complex fraction $\frac{\frac{2}{5 t}-\frac{3}{3 t}}{\frac{1}{2 t}+\frac{1}{2 t}}$ . (1 point) $-\frac{3}{5}$ , $-4$ , $-\frac{5}{3}$ , $-\frac{1}{4}$

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Problem 848

Find the value of $d$ where $d$ increased by 4 is -1.

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Problem 849

Evaluate the expression $2 \cdot(-1 \div 6)^{4}$ to find the equivalent value.

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Problem 850

Find the value of $q$ in the equation $-4 q - 3 = 1$ . The correct answer is B) $-15$ .

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Problem 851

Identify the property illustrated by the equation $x y = y x$ .

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Problem 852

Solve for $u$ in the equation $45=3+2(3+4u)$ .

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Problem 853

Solve for $x$ in $9.8(x-2.14)=53.9$ by dividing the left side by 9.8 and adding 2.14 to both sides.

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Problem 854

Find the total number of questions on a math exam if a student answered 21 problems correctly, which is $70\%$ of the total.

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Problem 855

Solve the absolute value equation $|5c-18|=30$ for the value of $c$ .

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Problem 856

Solve the quadratic equation $2x^2 - 14x = -20$ by graphing the corresponding function.

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Problem 857

Solve the quadratic equation $9x^2 + 12x = -6$ for the value of $x$ .

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Problem 858

Find an equation with solution $n=5$ using multiplication. Select all correct answers.
$4=\frac{20}{n}$ $2(n+1)=10$ $36=8 n$ $7 n=28$ $4=4 n$ $36=9 n$

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Problem 859

Complete the table by finding the logarithmic or exponential forms of $\log_8(8)=1$ , $\log_8(64)=2$ , $8^3=512$ , and $\log_8(1/8)=-1$ .

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Problem 860

Match equations with corresponding slopes: $x=4$ , $y=-2$ , $y=x$

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Problem 861

Solve the equation $z - 9 = 26$ to find the value of $z$ .

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Problem 862

Solve the equation $3 x(x+5)=-8$ and select the correct solution set from the provided options.

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Problem 863

Find the value of $2^{4}$ , the base and exponent of a power expression.

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Problem 864

Allison's lawn had 20 inches of snow that melted at 1.25 inches/hour. Write an equation for $S$ , the snow depth in inches, in terms of $t$ hours after the storm.

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Problem 865

Solve the system of linear equations $5x - y = 5$ and $5x + y = 5$ .

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Problem 866

Simplify the given expressions involving square roots and exponents: $\frac{\sqrt{3 x^{3}}}{\sqrt{5 x}} \cdot \sqrt{15 x^{4}}$ , $9 x^{6}$ , $3 x^{3}$ , $\sqrt{9 x^{6}}$ , $3 x^{2} \sqrt{x^{3}}$ .

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Problem 867

Solve for the variable $e$ in the equation $e + 1.2 = 2$ .

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Problem 868

Solve the equation $|x-2| = 6x + 13$ , checking for extraneous solutions. $x = 0$

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Problem 869

Find the value of $c$ in the equation $c-4=12$ .

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Problem 870

Solve for the value of $z$ in the equation $z-85=-49$ .

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Problem 871

Find the value of $y$ in the equation $y = 2x^2 + 12x + 5$ by completing the square and solving for $y$ .

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Problem 872

Find the two integers between which a certain number lies, given that its perfect square is approximately $11.1147$ .

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Problem 873

Find the number $x$ where subtracting 16 from $x$ results in -3.

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Problem 874

Solve the linear equation $9x - 10 = 7t + 2t$ for $x$ and $t$ .

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Problem 875

Find 5 times the sum of 6 and a number $x$ .

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Problem 876

Solve for $m$ in the equation $42 = 6m$ .

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Problem 877

Write 3 equations with different relationships to $y=-\frac{1}{2}x-7$ : (a) 1 common solution, (b) no common solutions, (c) infinitely many common solutions.

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Problem 878

Simplify $6 \times\left(2^{3}+7\right)$ using order of operations.

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Problem 879

Solve for the value of $d$ given the inequality $-4 > -2d$ .

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Problem 880

Find the values of $b$ that satisfy the equation $-8=\frac{b}{2}-11$ . The solution is $b=-4$ or $b=6$ .

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Problem 881

Solve the equation: $\{6\}$ , $\{-9,2\}$ , $\{-6,3\}$ , $\{-3,6\}$ . Also, solve the equation $x^{2}-3 x=18$ .

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Problem 882

Identify expressions that represent a 5% increase on a value. Options include $1.5x$ , $x(1+0.5)$ , $x(1+0.05)$ , $0.95x$ , $x+0.05x$ , and $1.05x$ .

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Problem 883

Solve the inequality $x-\frac{1}{3} \leq \frac{1}{2}$ and find the solution set.

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Problem 884

Determine the expression for multiplying 7 by the variable $q$ .

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Problem 885

Find the value of the expression $4 g + 6 g - 3 g$ .

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Problem 886

Find the value of $g$ that satisfies the equation $g^2 = 4$ . Express the solution as an integer or simplified fraction.

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Problem 887

Rewrite the rational equation $\frac{5}{x-1}+\frac{3}{4}=\frac{1}{x}$ using the least common denominator.

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Problem 888

Solve the quadratic equation $144=-4(t-3.5)^{2}+169$ for the variable $t$ .

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Problem 889

Solve for $x$ in simplest form: $11 = \frac{1}{3}(10x + 15)$

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Problem 890

Solve for $y$ in terms of $x$ given the equation $2x + 3y^3 = 2$ .

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Problem 891

Find the value of $x$ from $\{10.5,15.5,18.5\}$ that satisfies $x+1.4=19.9$ .

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Problem 892

Solve for the value of $x$ that satisfies the equation $-5+\log_{2}(x+8)=-1$ .

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Problem 893

Vanessa's height ( $v$ ) plus 22 equals 65.

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Problem 894

Solve the equation $35-3y=45$ and check the solution.

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Problem 895

Find the values of $h$ and $m$ that satisfy the equations $-2h-5m=7$ and $-h-5m=1$ .

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Problem 896

Find the expression equivalent to $(x^2 - 4x - 10) \div (x^2 - 6x - 41)$ .

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Problem 897

Find the value of $m$ given the equation $n=5+m$ .

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Problem 898

Solve the equation $6x + 1.6 = 58$ by applying the Subtraction and Division Properties of Equality.

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Problem 899

Solve the linear equation $\frac{3}{x}-8=-7$ for $x$ .

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Problem 900

Find the values of $x$ where $x+2 > 5-x$ .

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Algebra

Problem 801

Rewrite y=14x+3y=\frac{1}{4}x+3y=41​x+3 to solve for xxx. What feature of the line can be found using the rearranged equation x=4y−121x=\frac{4y-12}{1}x=14y−12​?

Problem 802

Find the property that applies to the equation 7(6x)=42x7(6x) = 42x7(6x)=42x.

Problem 803

Solve for xxx in the linear equation 5x+10=10+5x5 x + 10 = 10 + 5 x5x+10=10+5x and determine the type of solution.

Problem 804

Solve the polynomial equation 9y3−16y=09y^3 - 16y = 09y3−16y=0 by grouping and factoring. Enter the exact solutions.

Problem 805

Find the equation that represents "The sum of −4x-4 x−4x and 2 is 9".

Problem 806

Find the value of x−58x+2\frac{x-5}{8x+2}8x+2x−5​ when x=2x=2x=2, and simplify the result.

Problem 807

Find the rule for the pattern: 2, 10, 8, 16, 14. Options: A. +8,×2+8, \times 2+8,×2, B. +8,−2+8,-2+8,−2, C. x5,−2x 5,-2x5,−2, D. x8,−4x 8,-4x8,−4.

Problem 808

Find the value of xxx to the nearest ten-thousandth that satisfies the equation 9−3x+2=489^{-3 x+2}=489−3x+2=48.

Problem 809

Determine if t(x)t(x)t(x) is a linear function given the values in the table: x={0,1,2,3}x = \{0, 1, 2, 3\}x={0,1,2,3}, f(x)={−8,−4,0,4}f(x) = \{-8, -4, 0, 4\}f(x)={−8,−4,0,4}. Select: A. f(x)=f(x) = f(x)=__ or B. The function is not linear.

Problem 810

Determine if the relationship y=5x(x+3)y=5x(x+3)y=5x(x+3) is linear. Explain your reasoning.

Problem 811

Evaluate the expression: 2ab2c−3(9+b)÷14a2c3−abc2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc2ab2c−3(9+b)÷41​a2c3−abc where a=2,b=5,c=3a=2, b=5, c=3a=2,b=5,c=3.

Problem 812

Write the expression using radical notation and simplify if possible, assuming all variables represent nonnegative quantities. 64x4\sqrt{64 x^{4}}64x4​

Problem 813

Solve the quadratic equation 6n2+42n−48=66n^2 + 42n - 48 = 66n2+42n−48=6 for the value of nnn.

Problem 814

Graph the complex number −3+i-3+i−3+i.

Problem 815

Multiply the expression (x+5)(x−7)(x+5)(x-7)(x+5)(x−7) and simplify.

Problem 816

Problem 817

Find the value of xxx that satisfies the equation −2x2−8x=−64-2 x^{2} - 8 x = -64−2x2−8x=−64 when the current time is 291.4.

Problem 818

Find the equations equivalent to n−11=8n-11=8n−11=8 using properties of equality.

Problem 819

Find the value of xxx that satisfies the quadratic equation 3x2+6x=−33 x^{2} + 6 x = -33x2+6x=−3.

Problem 820

Rahkim solved the equation x−6=30x-6=30x−6=30, but his reasoning had a flaw. The best statement to describe the flaw is: B. Rahkim is confused about which number the 6 is being subtracted from.

Problem 821

Write a degree 2 trinomial with leading coef 8 and constant -5. Write two degree 1 binomials, then multiply and simplify.8x2−58 x^{2} - 58x2−5

Problem 822

Maximize 9t+8.50v9t + 8.50v9t+8.50v under constraints 9t+8.50v≤1509t + 8.50v \leq 1509t+8.50v≤150 and v≥5v \geq 5v≥5.

Problem 823

Multiply and simplify (4x+2)(4x+5)(4x+2)(4x+5)(4x+2)(4x+5)

Problem 824

Find the composite function of two given linear functions. Given f(x)=4x+14f(x) = 4x + 14f(x)=4x+14 and g(x)=2x−1g(x) = 2x - 1g(x)=2x−1, find (f∘g)(x)(f \circ g)(x)(f∘g)(x).

Problem 825

Solve the equation: (116)−x=(132)−x−1\left(\frac{1}{16}\right)^{-x}=\left(\frac{1}{32}\right)^{-x-1}(161​)−x=(321​)−x−1

Problem 826

Complete the table for f(j)=j2+jf(j) = j^2 + jf(j)=j2+j given values of jjj.

Problem 827

Add or subtract complex numbers. Find the result in standard form. −7−(4−5i)−(2−4i)-7-(4-5i)-(2-4i)−7−(4−5i)−(2−4i)

Problem 828

Rewrite the polynomial −8m+7-8m+7−8m+7 in factored form with a positive leading coefficient.

Problem 829

Solve for the value of kkk in the equation 2+k3=52+\frac{k}{3}=52+3k​=5.

Problem 830

Find the value of yyy that satisfies the equation ∣y−6∣+8=12|y-6|+8=12∣y−6∣+8=12.

Problem 831

Solve the linear equation 3x+5=173x + 5 = 173x+5=17 for the value of xxx.

Problem 832

Solve for xxx in the equation w+x=17w + x = 17w+x=17.

Problem 833

Write inequalities to represent the distance to the nearest exit door and the weight of the cargo. The distance must be less than 150 feet (d<150d < 150d<150) and the cargo weight must be no more than 2,400 pounds (w≤2,400w \le 2,400w≤2,400).

Problem 834

Find xxx and yyy given xy=144xy=144xy=144, x+y=30x+y=30x+y=30, and x≥yx \geq yx≥y. What is the value of x−yx-yx−y?

Problem 835

Solve the equation x=−2−5xx=-2-5xx=−2−5x for xxx.

Problem 836

Describe the transformations for the quadratic f(x)=(x−3)2+2f(x) = (x-3)^2 + 2f(x)=(x−3)2+2. Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

Problem 837

Solve for yyy where ∣7y∣=14|7y| = 14∣7y∣=14. Write the solution as an integer or simplified fraction.

Problem 838

Solve the equation (3x+8)(x+2)=0(3x+8)(x+2)=0(3x+8)(x+2)=0 and write the answer in reduced fraction form.

Problem 839

Find the equation of a line passing through (−2,2)(-2,2)(−2,2) and perpendicular to y=12x−3y=\frac{1}{2} x-3y=21​x−3. A. y=−2x+2y=-2 x+2y=−2x+2 B. y=−2x−2y=-2 x-2y=−2x−2 C. y=12x−2y=\frac{1}{2} x-2y=21​x−2 D. y=12x+2y=\frac{1}{2} x+2y=21​x+2

Problem 840

Solve the absolute value equation ∣x∣=13|x| = 13∣x∣=13.

Rewrite $y=\frac{1}{4}x+3$ to solve for $x$ . What feature of the line can be found using the rearranged equation $x=\frac{4y-12}{1}$ ?

Find the property that applies to the equation $7(6x) = 42x$ .

Solve for $x$ in the linear equation $5 x + 10 = 10 + 5 x$ and determine the type of solution.

Solve the polynomial equation $9y^3 - 16y = 0$ by grouping and factoring. Enter the exact solutions.

Find the equation that represents "The sum of $-4 x$ and 2 is 9".

Find the value of $\frac{x-5}{8x+2}$ when $x=2$ , and simplify the result.

Find the rule for the pattern: 2, 10, 8, 16, 14. Options: A. $+8, \times 2$ , B. $+8,-2$ , C. $x 5,-2$ , D. $x 8,-4$ .

Find the value of $x$ to the nearest ten-thousandth that satisfies the equation $9^{-3 x+2}=48$ .

Determine if $t(x)$ is a linear function given the values in the table: $x = \{0, 1, 2, 3\}$ , $f(x) = \{-8, -4, 0, 4\}$ . Select: A. $f(x) =$ __ or B. The function is not linear.

Determine if the relationship $y=5x(x+3)$ is linear. Explain your reasoning.

Evaluate the expression: $2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc$ where $a=2, b=5, c=3$ .

Write the expression using radical notation and simplify if possible, assuming all variables represent nonnegative quantities. $\sqrt{64 x^{4}}$

Solve the quadratic equation $6n^2 + 42n - 48 = 6$ for the value of $n$ .

Graph the complex number $-3+i$ .

Multiply the expression $(x+5)(x-7)$ and simplify.

Find the value of $x$ that satisfies the equation $-2 x^{2} - 8 x = -64$ when the current time is 291.4.

Find the equations equivalent to $n-11=8$ using properties of equality.

Find the value of $x$ that satisfies the quadratic equation $3 x^{2} + 6 x = -3$ .

Rahkim solved the equation $x-6=30$ , but his reasoning had a flaw. The best statement to describe the flaw is: B. Rahkim is confused about which number the 6 is being subtracted from.

Write a degree 2 trinomial with leading coef 8 and constant -5. Write two degree 1 binomials, then multiply and simplify.
$8 x^{2} - 5$

Maximize $9t + 8.50v$ under constraints $9t + 8.50v \leq 150$ and $v \geq 5$ .

Multiply and simplify $(4x+2)(4x+5)$

Find the composite function of two given linear functions. Given $f(x) = 4x + 14$ and $g(x) = 2x - 1$ , find $(f \circ g)(x)$ .

Solve the equation: $\left(\frac{1}{16}\right)^{-x}=\left(\frac{1}{32}\right)^{-x-1}$

Complete the table for $f(j) = j^2 + j$ given values of $j$ .

Add or subtract complex numbers. Find the result in standard form. $-7-(4-5i)-(2-4i)$

Rewrite the polynomial $-8m+7$ in factored form with a positive leading coefficient.

Solve for the value of $k$ in the equation $2+\frac{k}{3}=5$ .

Find the value of $y$ that satisfies the equation $|y-6|+8=12$ .

Solve the linear equation $3x + 5 = 17$ for the value of $x$ .

Solve for $x$ in the equation $w + x = 17$ .

Write inequalities to represent the distance to the nearest exit door and the weight of the cargo. The distance must be less than 150 feet ( $d < 150$ ) and the cargo weight must be no more than 2,400 pounds ( $w \le 2,400$ ).

Find $x$ and $y$ given $xy=144$ , $x+y=30$ , and $x \geq y$ . What is the value of $x-y$ ?

Solve the equation $x=-2-5x$ for $x$ .

Describe the transformations for the quadratic $f(x) = (x-3)^2 + 2$ . Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

Solve for $y$ where $|7y| = 14$ . Write the solution as an integer or simplified fraction.

Solve the equation $(3x+8)(x+2)=0$ and write the answer in reduced fraction form.

Find the equation of a line passing through $(-2,2)$ and perpendicular to $y=\frac{1}{2} x-3$ . A. $y=-2 x+2$ B. $y=-2 x-2$ C. $y=\frac{1}{2} x-2$ D. $y=\frac{1}{2} x+2$

Solve the absolute value equation $|x| = 13$ .

Simplify the expression $\frac{11(x-3) \cdot 7 \cdot 7}{5 \cdot 7 \cdot 5 \cdot 11(x-3)}$ by dividing out common factors.

Solve for the value of $m$ in the equation $9m + 7 = 8m$ .

Solve the absolute value equation $|2x-1| = 9$ or indicate if it has no solution.

Find the equation equivalent to $0=-3 x^{2}+27 x+30$ .

Simplify the complex fraction $\frac{\frac{2}{5 t}-\frac{3}{3 t}}{\frac{1}{2 t}+\frac{1}{2 t}}$ . (1 point) $-\frac{3}{5}$ , $-4$ , $-\frac{5}{3}$ , $-\frac{1}{4}$

Find the value of $d$ where $d$ increased by 4 is -1.

Evaluate the expression $2 \cdot(-1 \div 6)^{4}$ to find the equivalent value.

Find the value of $q$ in the equation $-4 q - 3 = 1$ . The correct answer is B) $-15$ .

Identify the property illustrated by the equation $x y = y x$ .

Solve for $u$ in the equation $45=3+2(3+4u)$ .

Solve for $x$ in $9.8(x-2.14)=53.9$ by dividing the left side by 9.8 and adding 2.14 to both sides.

Find the total number of questions on a math exam if a student answered 21 problems correctly, which is $70\%$ of the total.

Solve the absolute value equation $|5c-18|=30$ for the value of $c$ .

Solve the quadratic equation $2x^2 - 14x = -20$ by graphing the corresponding function.

Solve the quadratic equation $9x^2 + 12x = -6$ for the value of $x$ .

Find an equation with solution $n=5$ using multiplication. Select all correct answers.
$4=\frac{20}{n}$ $2(n+1)=10$ $36=8 n$ $7 n=28$ $4=4 n$ $36=9 n$

Complete the table by finding the logarithmic or exponential forms of $\log_8(8)=1$ , $\log_8(64)=2$ , $8^3=512$ , and $\log_8(1/8)=-1$ .

Match equations with corresponding slopes: $x=4$ , $y=-2$ , $y=x$

Solve the equation $z - 9 = 26$ to find the value of $z$ .

Solve the equation $3 x(x+5)=-8$ and select the correct solution set from the provided options.

Find the value of $2^{4}$ , the base and exponent of a power expression.

Allison's lawn had 20 inches of snow that melted at 1.25 inches/hour. Write an equation for $S$ , the snow depth in inches, in terms of $t$ hours after the storm.

Solve the system of linear equations $5x - y = 5$ and $5x + y = 5$ .

Simplify the given expressions involving square roots and exponents: $\frac{\sqrt{3 x^{3}}}{\sqrt{5 x}} \cdot \sqrt{15 x^{4}}$ , $9 x^{6}$ , $3 x^{3}$ , $\sqrt{9 x^{6}}$ , $3 x^{2} \sqrt{x^{3}}$ .

Solve for the variable $e$ in the equation $e + 1.2 = 2$ .

Solve the equation $|x-2| = 6x + 13$ , checking for extraneous solutions. $x = 0$

Find the value of $c$ in the equation $c-4=12$ .

Solve for the value of $z$ in the equation $z-85=-49$ .

Find the value of $y$ in the equation $y = 2x^2 + 12x + 5$ by completing the square and solving for $y$ .

Find the two integers between which a certain number lies, given that its perfect square is approximately $11.1147$ .

Find the number $x$ where subtracting 16 from $x$ results in -3.

Solve the linear equation $9x - 10 = 7t + 2t$ for $x$ and $t$ .