Browse Algebra problems in the Studdy Learning Bank!

Problem 1601

Solve the equation $x+1=11$ and find all real solutions.

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Problem 1602

Divide the polynomial $\left(x^{2}-4\right)$ by $(x-2)$ using factoring.

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Problem 1603

Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

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Problem 1604

Find $a$ and $b$ such that $P(x) = (2a - b)x^2 + (b - 6)x + a - 3$ is the zero polynomial.

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Problem 1605

Determine if the equation $y^{2}=3x-2$ represents a function.

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Problem 1606

Find the value of the expression $\frac{6^{\frac{5}{2}}}{6}$ .

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Problem 1607

Solve for $w$ in the quadratic equation $4 w^{2} = -11 w - 6$ . If there are multiple solutions, list them separately.

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Problem 1608

Find the expression equivalent to $5.8 \div 1.15$ .

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Problem 1609

Find the value of $c$ given the equation $-0.1 = -10c$ .

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Problem 1610

Graph the linear function $y = -2x$ .

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Problem 1611

Describe the linear relationship between $x$ and $y$ . Write the equation $x + 12 = y$ . Find the flower's height after 9 days.

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Problem 1612

Expand the expression $(2x+6)(2x+5)$ and express the result as a trinomial.

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Problem 1613

Solve the quadratic equation $b(b-1) = 2 + b^{2}$ for $b$ .

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Problem 1614

Find the possible values of $x$ and $y$ for two distinct points, $(5, -2)$ and $(x, y)$ , to represent a function.

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Problem 1615

Redefine the problem: Skateboard shop gets 92 wheels, puts 4 per board. Write a function $g(x)$ to describe the number of wheels left after assembling $x$ boards.

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Problem 1616

Solve the equation $8|\ln x|-16=0$ . The solution set is $\{e^{2}, e^{-2}\}$ .

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Problem 1617

Find the value of $x$ in the equation $y^{12} = y^{2x}$ .

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Problem 1618

Rewrite the equation $y = \frac{9}{4x^5}$ to not be a fraction.

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Problem 1619

Trouver l'ordonnée à l'origine de la fonction $y=5^{x}$ .

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Problem 1620

Solve the equation $32-32x = (6x+4)(x-1)$ by factoring. The solution set is $\{-4, 1\}$ .

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Problem 1621

Solve for $u$ in the equation $9=u-8$ .

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Problem 1622

Identify the independent and dependent variables in the relationship between paycheck and work hours for an hourly wage job. $Paycheck$ is the $dependent$ variable and $number\ of\ hours\ of\ work$ is the $independent$ variable.

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Problem 1623

Find the equation equivalent to $2x + 180 = 2x^2$ . Options: $2x^2 + 2x + 180 = 0$ , $2x^2 - 2x + 180 = 0$ , $2x^2 + 2x - 180 = 0$ , $2x^2 - 2x - 180 = 0$ .

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Problem 1624

Find the other factor in the denominator when $x = -3$ is a restricted value for $f(x) = \frac{\text{anything}}{\text{not zero}}$ .

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Problem 1625

Hani maximizes utility with goods $X$ and $Y$ given prices $\$ 5$ and $\$ 8$ and income $\$ 120$ . What are the optimal units of $X$ and $Y$ ?

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Problem 1626

Solve for $w$ where $\frac{3}{9}=\frac{w}{12}$ . Simplify the solution $w$ as much as possible.

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Problem 1627

Determine why the equation $y=-x^{2}+1$ does not represent a line.

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Problem 1628

Solve the system of linear equations $y=5$ and $-3x+4y=8$ .

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Problem 1629

Solve the equation $\frac{1}{4}t-6=-4$ for $t$ .

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Problem 1630

Solve for $m$ in the equation $2(-3 m-9)=54$ .

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Problem 1631

Solve the system by graphing: $x-y=5$ and $y=-2$ .

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Problem 1632

Solve the linear equation $7 = -10s - 3$ for the unknown variable $s$ .

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Problem 1633

Find the missing value in the solution to the linear equation $4x + y = 10$ , given the point $(\quad, -6)$ .

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Problem 1634

Solve $2(g-h)=b+4$ for $g$ . Options: (A) $g=b+h+4$ (B) $g=b+2h+4$ (C) $g=b+h+2$ $g=\frac{b}{2}+h+2$

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Problem 1635

Scientists study distant planet's temperature $y$ (°C) and height $x$ (km). The equation is $-7x + 38 = y$ . What is the temperature change per kilometer?

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Problem 1636

Find the solution set for the inequality $\frac{-6 t}{7} \leq 72$ . Options: a) $t \leq-62$ , b) $t \geq-62$ , c) $t \leq-84$ , d) $t \geq-84$ .

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Problem 1637

Solve for the value of $d$ that satisfies the equation $(d-7)(5d-2)=0$ .

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Problem 1638

Simplify the expression $-4(3+9)$ and select the correct answer.

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Problem 1639

Write inequality $10x + 10y < -10$ in slope-intercept form.

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Problem 1640

Rewrite the product $(x+3)(x-3)$ as a difference of two squares.

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Problem 1641

Find the equation that correctly expresses $r$ as the subject of $S=800(1-r)$ .
A. $r=\frac{800-S}{800}$ B. $r=\frac{S-800}{800}$ C. $r=800-S$ D. $r=S-800$

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Problem 1642

The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation $3x + 4y = 240$ represents this relationship. The graph of this equation is a line through the points $(60,0)$ and $(0,80)$ .

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Problem 1643

Solve the inequality $2(3x-1)<2$ for real values of $x$ .

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Problem 1644

Solve the system of linear equations with constants $b$ and $c$ . If $b = c - \frac{1}{2}$ , determine which statement about $x$ and $y$ is true.

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Problem 1645

Find the equation with solution $x=5$ . Possible equations: $8x+1=41$ $5x+7=35$ $9x-4=-41$ $4x+1=61$

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Problem 1646

Find the sum of the expressions $7x + 7$ and $3 - 3x$ .

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Problem 1647

Solve for $w$ where $w + 12 \geq 16$ .

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Problem 1648

Find equivalent rational expression with denominator $a^2 b^2 c^2$ for $\frac{8 + 7c}{a^2 b^2 c}$ .

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Problem 1649

Use the product rule to simplify and find the values of $4^{5} \times 4^{2}$ , $(-2)^{2} \times(-2)^{4} \times(-2)$ , $2^{3} \times 2^{2} \times 2^{2}$ , and $\left(\frac{3}{4}\right)^{3} \times\left(\frac{3}{4}\right)^{3}$ .

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Problem 1650

Assemble $x$ chain saws and $y$ wood chippers to maximize profit, given 7 hours for chain saw and 2 hours for chipper, with 42 hours total.

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Problem 1651

Graph the absolute value function $y = -5|x|$ . Click to plot the vertex.

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Problem 1652

Simplify the quotient $\sqrt{16 x^{3}} \div \sqrt{8 x}$ when $x>0$ .

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Problem 1653

Construct a function that expresses the relationship between your test grade $P$ and study hours $s$ , where $P = k \cdot s$ .

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Problem 1654

Identify the ordered pair that does not solve the linear equation $5x + y = 10$ .

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Problem 1655

Find the value of $y$ when $x = -4$ , where $y = (x - 2)^2$ .

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Problem 1656

Kira made 6 hats, 3 times as many as Henry. Find the number of hats Henry made, $n$ , using the equation $6 = 3n$ .

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Problem 1657

Solve the equation $\sqrt{x^{3}-2}=5$ exactly, using an inverse function when appropriate.

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Problem 1658

Solve for variable $x$ in the equation $8x = -16$ . Express the solution in fraction form if applicable.

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Problem 1659

Solve the quadratic equation $x^{2} + x - 61 = -5$ for the real-valued solutions.

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Problem 1660

Determine if $f(x) = x^3 + 5x^2 - 8x - 16$ has a real zero between $a = -7$ and $b = -3$ using the intermediate value theorem. A. $f(a) = \square$ and $f(b) = \square$ show the function has at least one real zero. B. $f(a) = \square$ and $f(b) = \square$ show the function does not have a real zero. C. It is impossible to use the intermediate value theorem in this case.

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Problem 1661

Distribute $3 x(x-7)$ and select the simplified answer.

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Problem 1662

Solve the linear equation $6b = -42$ for the variable $b$ .

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Problem 1663

29. Mikaela's scores were $89, 90, 92$ . What should her last score be to get an average of at least $91$ ? a. $93$ and above b. $92$ and above c. $92$ and below d. $93$ and below
30. To solve $-5x > 15$ , which property of inequality should be used? a. addition property b. multiplication property c. transitive property d. reflexive property

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Problem 1664

Find the proportional coefficient for $2Y + 4X = 0$ .

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Problem 1665

Solve for a variable by rewriting the formula to $\text{isolate the variable on one side}$ .

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Problem 1666

Find the value of $w$ that satisfies the equation $-9=-8w+7$ . Express the solution as an integer, simplified fraction, or decimal rounded to two decimal places.

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Problem 1667

Identify the odd functions from the given expressions: $f(x)=-2 x^{2}+5$ , $f(x)=5 x$ , $f(x)=-5 x^{5}-2 x^{3}+4 x$ , $f(x)=2 x^{3}+3 x^{2}+4 x+3$ , $f(x)=-3 x^{3}+6 x$ .

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Problem 1668

Solve the linear equation $7x = 9x + 3$ for the value of $x$ .

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Problem 1669

Solve for x in the equation $3=\frac{x}{18.75}$ .

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Problem 1670

Find the values of a, b, and c in the equation $\frac{9 x^{17} y^{a}}{3 x^{b} y^{2}}=c x^{5} y^{7}$ .

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Problem 1671

Solve the equation $-17=-2v-13$ and express the solution as an integer, simplified fraction, or decimal rounded to two decimal places.

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Problem 1672

Express $\left(\frac{2}{7}\right)^{4}$ as a division of two powers.

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Problem 1673

Find the solutions to the quadratic equation $(t+7)(t-9)=0$ . The solution set is $-7, 9$ .

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Problem 1674

Find $z$ when $x=5$ if $z$ varies directly as $x^{2}$ and $z=8$ when $x=2$ .

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Problem 1675

Solve the linear equation $-y-8 \frac{2}{7}=0$ for the unknown variable $y$ .

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Problem 1676

Find the least common denominator (LCD) to solve the linear equation $\frac{1}{5}x + \frac{1}{2}x = \frac{1}{3}$ .

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Problem 1677

Identify the error in Henry's steps to solve an equation: $-5(-x-1)+4x-1=49$ .

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Problem 1678

Find the difference of two polynomial expressions and write the result in standard form. $(7x^4 + 6x^5 - 11x) - (12x + 4x^4 - 2x^5)$

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Problem 1679

Solve the quadratic equation $2c^2 - 5c - 14 = -5$ for all real solutions in simplest form.

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Problem 1680

Find the value(s) of $z$ that satisfy the equation $3=\frac{z+4}{3}$ .

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Problem 1681

Find the difference of two functions $p(x) = x^2 - 9x$ and $c(x) = -2x + 3$ as a simplified polynomial or rational function.

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Problem 1682

Find the range of the function with domain $\{-5, -4, -2, 0, 2\}$ and codomain $\{-9, -5, -4, -3, -2, 0, 2, 5, 7\}$ .

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Problem 1683

Find the value of $x$ when $-x-4=9$ .

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Problem 1684

A band writes $87.5\%$ more songs than they expect to put on a $CD$ with $16$ songs. After editing, $30\%$ of songs are removed. How many songs will be on the final $CD$ ?
There will be $\lfloor 16 \cdot (1 + 0.875) \cdot (1 - 0.3) \rfloor$ songs on the final $CD$ .

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Problem 1685

Rewrite the expression as a single fraction. $(\frac{1}{5})^{3}=\frac{1}{125}$

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Problem 1686

Find the factors of the trinomial $x^{2}-4x-5$ . Options: $x-5$ , $x-2$ , $x-1$ , $x+1$ , $x+2$ , $x+5$ .

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Problem 1687

Evaluate $2c-3b$ when $c=8$ and $b=3.5$ . Then, find the values of $10.5$ , $2$ , $13$ , and $-5.5$ .

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Problem 1688

Find the values of $x$ where $3x^2 - 19x - 14 > 0$ .

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Problem 1689

Find the integer solution to the equation $(x+4)(5x+6)=0$ .

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Problem 1690

Write a quadratic function $f(m) = m^2 + bm + c$ with roots at 18 and $P$ .

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Problem 1691

Solve the linear equation $5x + 3.5 = -1.5$ .

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Problem 1692

Solve for $p$ in the linear equation $2.6(5.5p-12.4)=127.92$ . Use distributive, addition, and division properties to find $p=\frac{160.16}{14.3}$ .

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Problem 1693

Solve the quadratic equation $2x(3x-1) = 2x-4$ for $x$ .

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Problem 1694

Solve for $y$ in the equation $\frac{y}{7} - 1 = 8$ .

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Problem 1695

Solve for the value of $x$ given the equation $15=9+\sqrt{x}$ .

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Problem 1696

Rewrite the confidence interval $0.22 < p < 0.72$ using plus/minus notation and interval notation.
(a) plus/minus notation: $p = 0.47 \pm 0.25$ (b) interval notation: $(0.22, 0.72)$

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Problem 1697

Find the y-intercept of the linear equation $y=\frac{3}{2}x-4$ . Enter the value that correctly fills the blank.

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Problem 1698

Find the value of $c$ , where $c = \sqrt[3]{-20}^3$ .

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Problem 1699

Solve for the value of $b$ in the equation $-76 = -3b - 49$ .

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Problem 1700

Find $y$ when $x$ is inversely proportional to $\sqrt{x}$ and $y=79$ when $x=625$ , given $x=390625$ . (Round to nearest hundredth)

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Algebra

Problem 1601

Solve the equation x+1=11x+1=11x+1=11 and find all real solutions.

Problem 1602

Divide the polynomial (x2−4)\left(x^{2}-4\right)(x2−4) by (x−2)(x-2)(x−2) using factoring.

Problem 1603

Solve the linear equation 2(5x+4)=4(x+3)+4+2x2(5x+4) = 4(x+3) + 4 + 2x2(5x+4)=4(x+3)+4+2x and select the correct solution.

Problem 1604

Find aaa and bbb such that P(x)=(2a−b)x2+(b−6)x+a−3P(x) = (2a - b)x^2 + (b - 6)x + a - 3P(x)=(2a−b)x2+(b−6)x+a−3 is the zero polynomial.

Problem 1605

Determine if the equation y2=3x−2y^{2}=3x-2y2=3x−2 represents a function.

Problem 1606

Find the value of the expression 6526\frac{6^{\frac{5}{2}}}{6}6625​​.

Problem 1607

Solve for www in the quadratic equation 4w2=−11w−64 w^{2} = -11 w - 64w2=−11w−6. If there are multiple solutions, list them separately.

Problem 1608

Find the expression equivalent to 5.8÷1.155.8 \div 1.155.8÷1.15.

Problem 1609

Find the value of ccc given the equation −0.1=−10c-0.1 = -10c−0.1=−10c.

Problem 1610

Graph the linear function y=−2xy = -2xy=−2x.

Problem 1611

Describe the linear relationship between xxx and yyy. Write the equation x+12=yx + 12 = yx+12=y. Find the flower's height after 9 days.

Problem 1612

Expand the expression (2x+6)(2x+5)(2x+6)(2x+5)(2x+6)(2x+5) and express the result as a trinomial.

Problem 1613

Solve the quadratic equation b(b−1)=2+b2b(b-1) = 2 + b^{2}b(b−1)=2+b2 for bbb.

Problem 1614

Find the possible values of xxx and yyy for two distinct points, (5,−2)(5, -2)(5,−2) and (x,y)(x, y)(x,y), to represent a function.

Problem 1615

Redefine the problem: Skateboard shop gets 92 wheels, puts 4 per board. Write a function g(x)g(x)g(x) to describe the number of wheels left after assembling xxx boards.

Problem 1616

Solve the equation 8∣ln⁡x∣−16=08|\ln x|-16=08∣lnx∣−16=0. The solution set is {e2,e−2}\{e^{2}, e^{-2}\}{e2,e−2}.

Problem 1617

Find the value of xxx in the equation y12=y2xy^{12} = y^{2x}y12=y2x.

Problem 1618

Rewrite the equation y=94x5y = \frac{9}{4x^5}y=4x59​ to not be a fraction.

Problem 1619

Trouver l'ordonnée à l'origine de la fonction y=5xy=5^{x}y=5x.

Problem 1620

Solve the equation 32−32x=(6x+4)(x−1)32-32x = (6x+4)(x-1)32−32x=(6x+4)(x−1) by factoring. The solution set is {−4,1}\{-4, 1\}{−4,1}.

Problem 1621

Solve for uuu in the equation 9=u−89=u-89=u−8.

Problem 1622

Problem 1623

Find the equation equivalent to 2x+180=2x22x + 180 = 2x^22x+180=2x2. Options: 2x2+2x+180=02x^2 + 2x + 180 = 02x2+2x+180=0, 2x2−2x+180=02x^2 - 2x + 180 = 02x2−2x+180=0, 2x2+2x−180=02x^2 + 2x - 180 = 02x2+2x−180=0, 2x2−2x−180=02x^2 - 2x - 180 = 02x2−2x−180=0.

Problem 1624

Find the other factor in the denominator when x=−3x = -3x=−3 is a restricted value for f(x)=anythingnot zerof(x) = \frac{\text{anything}}{\text{not zero}}f(x)=not zeroanything​.

Problem 1625

Hani maximizes utility with goods XXX and YYY given prices $5\$ 5$5 and $8\$ 8$8 and income $120\$ 120$120. What are the optimal units of XXX and YYY?

Problem 1626

Solve for www where 39=w12\frac{3}{9}=\frac{w}{12}93​=12w​. Simplify the solution www as much as possible.

Problem 1627

Determine why the equation y=−x2+1y=-x^{2}+1y=−x2+1 does not represent a line.

Problem 1628

Solve the system of linear equations y=5y=5y=5 and −3x+4y=8-3x+4y=8−3x+4y=8.

Problem 1629

Solve the equation 14t−6=−4\frac{1}{4}t-6=-441​t−6=−4 for ttt.

Problem 1630

Solve for mmm in the equation 2(−3m−9)=542(-3 m-9)=542(−3m−9)=54.

Problem 1631

Solve the system by graphing: x−y=5x-y=5x−y=5 and y=−2y=-2y=−2.

Problem 1632

Solve the linear equation 7=−10s−37 = -10s - 37=−10s−3 for the unknown variable sss.

Problem 1633

Find the missing value in the solution to the linear equation 4x+y=104x + y = 104x+y=10, given the point (,−6)(\quad, -6)(,−6).

Problem 1634

Solve 2(g−h)=b+42(g-h)=b+42(g−h)=b+4 for ggg. Options: (A) g=b+h+4g=b+h+4g=b+h+4 (B) g=b+2h+4g=b+2h+4g=b+2h+4 (C) g=b+h+2g=b+h+2g=b+h+2 g=b2+h+2g=\frac{b}{2}+h+2g=2b​+h+2

Problem 1635

Scientists study distant planet's temperature yyy (°C) and height xxx (km). The equation is −7x+38=y-7x + 38 = y−7x+38=y. What is the temperature change per kilometer?

Problem 1636

Find the solution set for the inequality −6t7≤72\frac{-6 t}{7} \leq 727−6t​≤72. Options: a) t≤−62t \leq-62t≤−62, b) t≥−62t \geq-62t≥−62, c) t≤−84t \leq-84t≤−84, d) t≥−84t \geq-84t≥−84.

Problem 1637

Solve for the value of ddd that satisfies the equation (d−7)(5d−2)=0(d-7)(5d-2)=0(d−7)(5d−2)=0.

Problem 1638

Simplify the expression −4(3+9)-4(3+9)−4(3+9) and select the correct answer.

Problem 1639

Write inequality 10x+10y<−1010x + 10y < -1010x+10y<−10 in slope-intercept form.

Problem 1640

Rewrite the product (x+3)(x−3)(x+3)(x-3)(x+3)(x−3) as a difference of two squares.

Solve the equation $x+1=11$ and find all real solutions.

Divide the polynomial $\left(x^{2}-4\right)$ by $(x-2)$ using factoring.

Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

Find $a$ and $b$ such that $P(x) = (2a - b)x^2 + (b - 6)x + a - 3$ is the zero polynomial.

Determine if the equation $y^{2}=3x-2$ represents a function.

Find the value of the expression $\frac{6^{\frac{5}{2}}}{6}$ .

Solve for $w$ in the quadratic equation $4 w^{2} = -11 w - 6$ . If there are multiple solutions, list them separately.

Find the expression equivalent to $5.8 \div 1.15$ .

Find the value of $c$ given the equation $-0.1 = -10c$ .

Graph the linear function $y = -2x$ .

Describe the linear relationship between $x$ and $y$ . Write the equation $x + 12 = y$ . Find the flower's height after 9 days.

Expand the expression $(2x+6)(2x+5)$ and express the result as a trinomial.

Solve the quadratic equation $b(b-1) = 2 + b^{2}$ for $b$ .

Find the possible values of $x$ and $y$ for two distinct points, $(5, -2)$ and $(x, y)$ , to represent a function.

Redefine the problem: Skateboard shop gets 92 wheels, puts 4 per board. Write a function $g(x)$ to describe the number of wheels left after assembling $x$ boards.

Solve the equation $8|\ln x|-16=0$ . The solution set is $\{e^{2}, e^{-2}\}$ .

Find the value of $x$ in the equation $y^{12} = y^{2x}$ .

Rewrite the equation $y = \frac{9}{4x^5}$ to not be a fraction.

Trouver l'ordonnée à l'origine de la fonction $y=5^{x}$ .

Solve the equation $32-32x = (6x+4)(x-1)$ by factoring. The solution set is $\{-4, 1\}$ .

Solve for $u$ in the equation $9=u-8$ .

Find the equation equivalent to $2x + 180 = 2x^2$ . Options: $2x^2 + 2x + 180 = 0$ , $2x^2 - 2x + 180 = 0$ , $2x^2 + 2x - 180 = 0$ , $2x^2 - 2x - 180 = 0$ .

Find the other factor in the denominator when $x = -3$ is a restricted value for $f(x) = \frac{\text{anything}}{\text{not zero}}$ .

Hani maximizes utility with goods $X$ and $Y$ given prices $\$ 5$ and $\$ 8$ and income $\$ 120$ . What are the optimal units of $X$ and $Y$ ?

Solve for $w$ where $\frac{3}{9}=\frac{w}{12}$ . Simplify the solution $w$ as much as possible.

Determine why the equation $y=-x^{2}+1$ does not represent a line.

Solve the system of linear equations $y=5$ and $-3x+4y=8$ .

Solve the equation $\frac{1}{4}t-6=-4$ for $t$ .

Solve for $m$ in the equation $2(-3 m-9)=54$ .

Solve the system by graphing: $x-y=5$ and $y=-2$ .

Solve the linear equation $7 = -10s - 3$ for the unknown variable $s$ .

Find the missing value in the solution to the linear equation $4x + y = 10$ , given the point $(\quad, -6)$ .

Solve $2(g-h)=b+4$ for $g$ . Options: (A) $g=b+h+4$ (B) $g=b+2h+4$ (C) $g=b+h+2$ $g=\frac{b}{2}+h+2$

Scientists study distant planet's temperature $y$ (°C) and height $x$ (km). The equation is $-7x + 38 = y$ . What is the temperature change per kilometer?

Find the solution set for the inequality $\frac{-6 t}{7} \leq 72$ . Options: a) $t \leq-62$ , b) $t \geq-62$ , c) $t \leq-84$ , d) $t \geq-84$ .

Solve for the value of $d$ that satisfies the equation $(d-7)(5d-2)=0$ .

Simplify the expression $-4(3+9)$ and select the correct answer.

Write inequality $10x + 10y < -10$ in slope-intercept form.

Rewrite the product $(x+3)(x-3)$ as a difference of two squares.

Find the equation that correctly expresses $r$ as the subject of $S=800(1-r)$ .
A. $r=\frac{800-S}{800}$ B. $r=\frac{S-800}{800}$ C. $r=800-S$ D. $r=S-800$

The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation $3x + 4y = 240$ represents this relationship. The graph of this equation is a line through the points $(60,0)$ and $(0,80)$ .

Solve the inequality $2(3x-1)<2$ for real values of $x$ .

Solve the system of linear equations with constants $b$ and $c$ . If $b = c - \frac{1}{2}$ , determine which statement about $x$ and $y$ is true.

Find the equation with solution $x=5$ . Possible equations: $8x+1=41$ $5x+7=35$ $9x-4=-41$ $4x+1=61$

Find the sum of the expressions $7x + 7$ and $3 - 3x$ .

Solve for $w$ where $w + 12 \geq 16$ .

Find equivalent rational expression with denominator $a^2 b^2 c^2$ for $\frac{8 + 7c}{a^2 b^2 c}$ .

Assemble $x$ chain saws and $y$ wood chippers to maximize profit, given 7 hours for chain saw and 2 hours for chipper, with 42 hours total.

Graph the absolute value function $y = -5|x|$ . Click to plot the vertex.

Simplify the quotient $\sqrt{16 x^{3}} \div \sqrt{8 x}$ when $x>0$ .

Construct a function that expresses the relationship between your test grade $P$ and study hours $s$ , where $P = k \cdot s$ .

Identify the ordered pair that does not solve the linear equation $5x + y = 10$ .

Find the value of $y$ when $x = -4$ , where $y = (x - 2)^2$ .

Kira made 6 hats, 3 times as many as Henry. Find the number of hats Henry made, $n$ , using the equation $6 = 3n$ .

Solve the equation $\sqrt{x^{3}-2}=5$ exactly, using an inverse function when appropriate.

Solve for variable $x$ in the equation $8x = -16$ . Express the solution in fraction form if applicable.

Solve the quadratic equation $x^{2} + x - 61 = -5$ for the real-valued solutions.

Distribute $3 x(x-7)$ and select the simplified answer.

Solve the linear equation $6b = -42$ for the variable $b$ .

Find the proportional coefficient for $2Y + 4X = 0$ .

Solve for a variable by rewriting the formula to $\text{isolate the variable on one side}$ .

Find the value of $w$ that satisfies the equation $-9=-8w+7$ . Express the solution as an integer, simplified fraction, or decimal rounded to two decimal places.

Identify the odd functions from the given expressions: $f(x)=-2 x^{2}+5$ , $f(x)=5 x$ , $f(x)=-5 x^{5}-2 x^{3}+4 x$ , $f(x)=2 x^{3}+3 x^{2}+4 x+3$ , $f(x)=-3 x^{3}+6 x$ .

Solve the linear equation $7x = 9x + 3$ for the value of $x$ .

Solve for x in the equation $3=\frac{x}{18.75}$ .

Find the values of a, b, and c in the equation $\frac{9 x^{17} y^{a}}{3 x^{b} y^{2}}=c x^{5} y^{7}$ .

Solve the equation $-17=-2v-13$ and express the solution as an integer, simplified fraction, or decimal rounded to two decimal places.

Express $\left(\frac{2}{7}\right)^{4}$ as a division of two powers.

Find the solutions to the quadratic equation $(t+7)(t-9)=0$ . The solution set is $-7, 9$ .

Find $z$ when $x=5$ if $z$ varies directly as $x^{2}$ and $z=8$ when $x=2$ .