Browse Algebra problems in the Studdy Learning Bank!

Problem 3801

Find the value of $x$ such that $h(x) = 1 - 3x$ equals -2.

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Problem 3802

Find the value of $m$ such that $2^m = \frac{1}{4}$ .

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Problem 3803

Find the value of $a b^{2}$ when $a = -5i$ and $b = -5x$ , in simplified form.

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Problem 3804

Find the value of $x$ where $f(g(x))$ is undefined, given $f(x)=\frac{1}{(5-|x|)^{1 / 4}}$ and $g(x)=\sqrt{28-x}$ .

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Problem 3805

Find the value of $q$ in the equation $0.5q = 6.25$ . Round the answer to the nearest tenth.

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Problem 3806

Solve the linear equation $x + 9 = 17x$ for the value of $x$ .

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Problem 3807

Solve the linear equation $18=x+2$ for the unknown variable $x$ .

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Problem 3808

Solve the quadratic equation $v^2 - 22v - 77 = -2$ by completing the square.

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Problem 3809

Encuentra el valor de $x$ si un número es 8 menos que el doble de $x$ y la suma de los números es 40.

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Problem 3810

Find the number of solutions to the linear equation $-6-h=-h+4-2h$ .

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Problem 3811

Evaluate the expression $3+6 \div\left(-1 \frac{3}{4}+-2\right)$ and write the answer as a fraction or whole/mixed number.

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Problem 3812

Find the value of $p$ in the equation $7+p=16$ .

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Problem 3813

Find two consecutive odd integers whose product is 323.

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Problem 3814

Solve the linear equation $30.52 + 6x = 4.42$ for the unknown variable $x$ .

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Problem 3815

Solve $2^{2 b-3}=32$ to find the value of $b$ .

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Problem 3816

Find the linear correlation coefficient for the ordered pairs $(5,39)$ , $(7,36)$ , $(9,33)$ , and $(11,30)$ .

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Problem 3817

Graph the inverse of the linear function $f(x) = \frac{2}{3}x - 1$ . Plot the original function in red and its inverse in blue.

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Problem 3818

Solve the equation $-7x + x^2 + 6 = -6x + 3 + x^2$ either algebraically or graphically. Options: A) $x = -11$ , B) $x = 3$ , C) no solution, D) $x = -5$ .

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Problem 3819

Find the values of $v$ that solve the equation $-5v-16=4$ .

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Problem 3820

Solve the linear equation $13.5 + 55x = 244$ for the unknown variable $x$ .

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Problem 3821

Determine if the equation $0=-9d+9d$ is an identity.

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Problem 3822

Find the zeros and valid $x$ values for the rocket's path equation $y = -3x^2 + 11x + 4$ .

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Problem 3823

Determine if $-46$ is a solution to the equation $\frac{x+1}{5}=-8$ .

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Problem 3824

Find the roots of the equation $\frac{b+3}{4}=\frac{b-1}{2}$ .

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Problem 3825

Resuelve la ecuación cuadrática $13x - 9x^2 = 4$ .

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Problem 3826

Find the 4th term in the sequence: $2, 5, 10, 17, \ldots$

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Problem 3827

Solve the quadratic equations: $x^{2}+3 x-12=6$ , $18 x^{2}+45 x-27=0$ , $90 x^{2}-84 x=-18$ , $x^{2}+8 x=-15$ .

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Problem 3828

Solve for $x$ in the equation $9=25\left(\frac{x+3}{25}\right)^2$ .

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Problem 3829

Find values of $m$ and $n$ so that the polynomial $3m-63x^9 + (7-42n)x + 15$ is constant.

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Problem 3830

Solve for $y$ in the equation $-7=\frac{y}{1.2}$ .

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Problem 3831

Solve $(-2)(-5)(-3)(-4)$ and choose the correct result: (A) 120, (B) 36, (C) -36, or (D) -120.

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Problem 3832

Solve the linear equation $1 / 2 y = -12$ for the variable $y$ .

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Problem 3833

Find the value of the linear function $f(x) = 23.2x + 2.5$ when $x = -4.2$ .

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Problem 3834

Find the value of $m(6)$ for the linear function $m(x) = 4x + 5$ .

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Problem 3835

Solve for $d$ . Round your answer to the nearest hundredth. The opposite of a power is a root.

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Problem 3836

Find the missing number in the equation: $75 + 1,000 = (3 + 40)$

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Problem 3837

Find the sum of the arithmetic series with $a_{1}=12$ , $d=4$ , and $n=30$ .

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Problem 3838

Encuentra el valor de $r$ que satisface la desigualdad $-19r < 19$ .

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Problem 3839

Solve the equation $0.8x - 0.3 = 0.5x$ for $x$ .

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Problem 3840

Find the inverse function $f^{-1}(28)$ if $f(19)=28$ and $f$ is one-to-one.

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Problem 3841

Evaluate the sum $\sum_{k=1}^{7}(2-3k)$ . Options: A. -69, B. -77, C. -70, D. -140.

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Problem 3842

Find the value of $\frac{|x|}{x^{2}}$ when $x=-5$ .

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Problem 3843

Find the value of $x$ given the expression $15^2 - 5^2$ .

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Problem 3844

Solve for $u$ in the equation $x = \frac{7}{8u} + 2$ .

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Problem 3845

Solve for the value of $x$ in the equation $14 x-3(2 x-4)=-8 x-4$ .

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Problem 3846

Find two numbers whose difference is 108, and where the smaller number multiplied by 6 is 7 more than the larger number.

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Problem 3847

Does the point ( $6,46$ ) satisfy the equation $y = -7x + 4$ ? Yes or no?

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Problem 3848

Find the value of $u$ that satisfies the equation $8(u-6)=16$ .

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Problem 3849

Solve for the value of $u$ given the equation $-3=u-2$ .

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Problem 3850

Simplify radical expression: $\sqrt{36} \cdot \sqrt{b^{2}} \cdot \sqrt{c^{2}} \cdot \sqrt{2ab}$ . Choose the correct step.

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Problem 3851

Find the value of $x$ that satisfies the equation $2x - 4 = 24$ .

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Problem 3852

Solve the linear equation $12[2+(x+2)]=5(x-2)+2$ for the unknown variable $x$ .

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Problem 3853

Simplify the mathematical expression $3 x(x+2)$ by factoring.

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Problem 3854

Solve the equation $9 = -k + 2(4k + 7)$ .

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Problem 3855

Evaluate the expression $(2-7)^{2} + \sqrt[3]{6(8-5)+9}$ .

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Problem 3856

Solve for $y$ in the equation $289=236-y$ .

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Problem 3857

Finden Sie die Wurzeln des Polynoms $f(x) = 0.25 \cdot (x-3)^{2}(x+2)$ und erläutern Sie die Schritte.

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Problem 3858

Annie charges $75 plus$ 35 per hour for tutoring. The linear equation is $y=75+35x$ . The independent variable is the time Annie tutors, and the dependent variable is the amount she earns. The y-intercept is $75, and the slope is$ 35.

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Problem 3859

Solve the inequality $3x - 1 < 8$ for real number $x$ .

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Problem 3860

Find the score $y$ on a 100-point test with 5 points per question, given the number of incorrect answers $x$ , where $y=100-5x$ .

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Problem 3861

Determine scholarship allocation among 340 English, 292 Psychology, and 401 Graphic Design majors using the Jefferson method.
Simplified problem statement: Allocate $18$ scholarships among $340$ English, $292$ Psychology, and $401$ Graphic Design majors using the Jefferson method.

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Problem 3862

Find the value of $x$ given the linear function $h(x) = 7x - 3$ and $h(x) = 11$ .

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Problem 3863

Find the values of $x$ that make $f(x)=\frac{2-x}{x^{2}-25}$ undefined.

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Problem 3864

Find the values of n that make the inequality $\frac{n}{-8} > 7$ true. Write the equivalent inequality in terms of n.

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Problem 3865

Find two real numbers with sum $2$ and product $-24$ using a quadratic equation.

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Problem 3866

Find the sum of $4 \sqrt[3]{x^{10}}+5 x^{3} \sqrt[3]{8 x}$ when $x \neq 0$ , in simplest form.

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Problem 3867

Find the value of $z$ that satisfies the equation $11011=z-7286$ .

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Problem 3868

Sketch a graph to solve the inequality $x^2 - 9x + 18 > 0$ .

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Problem 3869

Find the values of $x$ and $y$ that satisfy the equation $12x - 10y = 18$ . Reduce all fractions to lowest terms.

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Problem 3870

Find the value of 'c' to make the given quadratic expressions perfect squares. Express the equations in vertex form by completing the square.
1. (a) $x^{2}+14 x+c$ , (b) $x^{2}-9 x+c$ , (c) $x^{2}-\frac{7}{6} x+c$
2. Express the equations in vertex form by completing the square.

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Problem 3871

Solve for $x$ in the equation $5+2x=25$ and provide a justification for each step.

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Problem 3872

Write the quadratic equation with roots $3 - 2i$ and $3 + 2i$ .

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Problem 3873

Factorize the quadratic equation $3x^2 - 6x - 24 = 0$ and find the missing coefficients.

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Problem 3874

Use the transitive property to find the relationship between $a$ and $c$ given $a=b$ and $b=c$ .

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Problem 3875

Rewrite $x^2 - 2x - 6$ in $(x+c)^2 + d$ form. Find $c$ and $d$ . Then solve $x^2 - 2x - 6 = 0$ in $x = f \pm \sqrt{g}$ form.

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Problem 3876

Solve an expression using order of operations to find the value of 1.

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Problem 3877

Rewrite linear inequality $15x + 5y \leq -7$ in slope-intercept form $y \leq \frac{-15x - 7}{5}$ .

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Problem 3878

Solve the equation $\frac{1}{3}(x+5)=2x+10$ and find the values of $x$ .

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Problem 3879

A county park system has 19 golf courses of varying difficulty. There are 4 gold courses and twice as many bronze as silver courses. How many selections are possible if a golfer decides to play a round at a silver or gold course? $\square$ possible selection(s).

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Problem 3880

Rewrite the inequality $13x + y \leq 11$ in slope-intercept form, with y first and an inequality symbol.

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Problem 3881

Solve for the value of $x$ in the equation $-\frac{3}{8} x-18=-24$ .

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Problem 3882

Solve the equation $-72 = -3f$ .

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Problem 3883

Solve for the missing values in the given equations: $\frac{-5}{2^{2}}=\square$ and $\left(-\frac{2}{3}\right)^{3}=\square$ .

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Problem 3884

Find the value of $\frac{x}{25}$ given the equation $75=24x$ .

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Problem 3885

Factor and graph the quadratic equation $y = -x^2 - 8x - 19$ .

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Problem 3886

Solve $x^2 - x = 56$ for $x$ , showing all steps. Determine equation type.

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Problem 3887

Find the solutions to the equation $(x+13)(x-6)=0$ . Options: (A) $x=6, x=13$ (B) $x=-13, x=6$ (C) $x=-6, x=13$ (D) $x=-13, x=-6$

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Problem 3888

Solve for the value of $b$ given the equation $1.5b = 3$ .

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Problem 3889

Find the roots of the polynomial equation $6 x^{3}-8 x^{2}-54 x+72=0$ .

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Problem 3890

Find the profit function for a product where revenue is $R=580x$ and cost is $C=15,000+40x+x^2$ . Determine the number of units that maximizes profit and the maximum profit.
a. $P(x)=580x-(15,000+40x+x^2)$ b. Find $x$ that maximizes $P(x)$ c. Evaluate $P(x)$ at the optimal $x$ to find the maximum profit.

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Problem 3891

Solve for $x$ given the equation $10x=120$ .

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Problem 3892

Find the shortest distance from (0,0) to the line $x + 2y - 5 = 0$ .

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Problem 3893

Solve $5x - 9 = 0$ and select the correct solution: A) $x = \square$ , B) $(-\infty, \infty)$ , C) No solution.

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Problem 3894

Solve for $w$ in the equation $-7w + 11w + 5 = 2w + 31$ , and simplify the answer $w = \square$ .

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Problem 3895

Solve for $u$ where $5.12=4u$ .

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Problem 3896

Find the solution set for $5x^2 + 3x = 6 - 4x$ . Options: A. $\{-2, 3/5\}$ , B. $\{-3/5, 0\}$ , C. $\{3/5\}$ , D. No real solution.

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Problem 3897

Solve the linear equation $4x = 2x + 14$ for the value of $x$ .

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Problem 3898

Find the real and imaginary parts ( $a$ and $b$ ) of the square of the complex number $z=8-3i$ . $a=64$ and $b=-48$ .

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Problem 3899

Determine the highest degree for which the quadratic formula can solve an equation: $A. 1, B. 3, C. 0, D. 2$

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Problem 3900

Find the lengths of the major and minor axes of the ellipse given by the equation $9x^2 + 16y^2 - 90x + 128y + 337 = 0$ , rounded to the nearest tenth.

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Algebra

Problem 3801

Find the value of xxx such that h(x)=1−3xh(x) = 1 - 3xh(x)=1−3x equals -2.

Problem 3802

Find the value of mmm such that 2m=142^m = \frac{1}{4}2m=41​.

Problem 3803

Find the value of ab2a b^{2}ab2 when a=−5ia = -5ia=−5i and b=−5xb = -5xb=−5x, in simplified form.

Problem 3804

Find the value of xxx where f(g(x))f(g(x))f(g(x)) is undefined, given f(x)=1(5−∣x∣)1/4f(x)=\frac{1}{(5-|x|)^{1 / 4}}f(x)=(5−∣x∣)1/41​ and g(x)=28−xg(x)=\sqrt{28-x}g(x)=28−x​.

Problem 3805

Find the value of qqq in the equation 0.5q=6.250.5q = 6.250.5q=6.25. Round the answer to the nearest tenth.

Problem 3806

Solve the linear equation x+9=17xx + 9 = 17xx+9=17x for the value of xxx.

Problem 3807

Solve the linear equation 18=x+218=x+218=x+2 for the unknown variable xxx.

Problem 3808

Solve the quadratic equation v2−22v−77=−2v^2 - 22v - 77 = -2v2−22v−77=−2 by completing the square.

Problem 3809

Encuentra el valor de xxx si un número es 8 menos que el doble de xxx y la suma de los números es 40.

Problem 3810

Find the number of solutions to the linear equation −6−h=−h+4−2h-6-h=-h+4-2h−6−h=−h+4−2h.

Problem 3811

Evaluate the expression 3+6÷(−134+−2)3+6 \div\left(-1 \frac{3}{4}+-2\right)3+6÷(−143​+−2) and write the answer as a fraction or whole/mixed number.

Problem 3812

Find the value of ppp in the equation 7+p=167+p=167+p=16.

Problem 3813

Find two consecutive odd integers whose product is 323.

Problem 3814

Solve the linear equation 30.52+6x=4.4230.52 + 6x = 4.4230.52+6x=4.42 for the unknown variable xxx.

Problem 3815

Solve 22b−3=322^{2 b-3}=3222b−3=32 to find the value of bbb.

Problem 3816

Find the linear correlation coefficient for the ordered pairs (5,39)(5,39)(5,39), (7,36)(7,36)(7,36), (9,33)(9,33)(9,33), and (11,30)(11,30)(11,30).

Problem 3817

Graph the inverse of the linear function f(x)=23x−1f(x) = \frac{2}{3}x - 1f(x)=32​x−1. Plot the original function in red and its inverse in blue.

Problem 3818

Solve the equation −7x+x2+6=−6x+3+x2-7x + x^2 + 6 = -6x + 3 + x^2−7x+x2+6=−6x+3+x2 either algebraically or graphically. Options: A) x=−11x = -11x=−11, B) x=3x = 3x=3, C) no solution, D) x=−5x = -5x=−5.

Problem 3819

Find the values of vvv that solve the equation −5v−16=4-5v-16=4−5v−16=4.

Problem 3820

Solve the linear equation 13.5+55x=24413.5 + 55x = 24413.5+55x=244 for the unknown variable xxx.

Problem 3821

Determine if the equation 0=−9d+9d0=-9d+9d0=−9d+9d is an identity.

Problem 3822

Find the zeros and valid xxx values for the rocket's path equation y=−3x2+11x+4y = -3x^2 + 11x + 4y=−3x2+11x+4.

Problem 3823

Determine if −46-46−46 is a solution to the equation x+15=−8\frac{x+1}{5}=-85x+1​=−8.

Problem 3824

Find the roots of the equation b+34=b−12\frac{b+3}{4}=\frac{b-1}{2}4b+3​=2b−1​.

Problem 3825

Resuelve la ecuación cuadrática 13x−9x2=413x - 9x^2 = 413x−9x2=4.

Problem 3826

Find the 4th term in the sequence: 2,5,10,17,…2, 5, 10, 17, \ldots2,5,10,17,…

Problem 3827

Solve the quadratic equations: x2+3x−12=6x^{2}+3 x-12=6x2+3x−12=6, 18x2+45x−27=018 x^{2}+45 x-27=018x2+45x−27=0, 90x2−84x=−1890 x^{2}-84 x=-1890x2−84x=−18, x2+8x=−15x^{2}+8 x=-15x2+8x=−15.

Problem 3828

Solve for xxx in the equation 9=25(x+325)29=25\left(\frac{x+3}{25}\right)^29=25(25x+3​)2.

Problem 3829

Find values of mmm and nnn so that the polynomial 3m−63x9+(7−42n)x+153m-63x^9 + (7-42n)x + 153m−63x9+(7−42n)x+15 is constant.

Problem 3830

Solve for yyy in the equation −7=y1.2-7=\frac{y}{1.2}−7=1.2y​.

Problem 3831

Solve (−2)(−5)(−3)(−4)(-2)(-5)(-3)(-4)(−2)(−5)(−3)(−4) and choose the correct result: (A) 120, (B) 36, (C) -36, or (D) -120.

Problem 3832

Solve the linear equation 1/2y=−121 / 2 y = -121/2y=−12 for the variable yyy.

Problem 3833

Find the value of the linear function f(x)=23.2x+2.5f(x) = 23.2x + 2.5f(x)=23.2x+2.5 when x=−4.2x = -4.2x=−4.2.

Problem 3834

Find the value of m(6)m(6)m(6) for the linear function m(x)=4x+5m(x) = 4x + 5m(x)=4x+5.

Problem 3835

Solve for ddd. Round your answer to the nearest hundredth. The opposite of a power is a root.

Problem 3836

Find the missing number in the equation: 75+1,000=(3+40)75 + 1,000 = (3 + 40)75+1,000=(3+40)

Problem 3837

Find the sum of the arithmetic series with a1=12a_{1}=12a1​=12, d=4d=4d=4, and n=30n=30n=30.

Problem 3838

Encuentra el valor de rrr que satisface la desigualdad −19r<19-19r < 19−19r<19.

Problem 3839

Solve the equation 0.8x−0.3=0.5x0.8x - 0.3 = 0.5x0.8x−0.3=0.5x for xxx.

Problem 3840

Find the value of $x$ such that $h(x) = 1 - 3x$ equals -2.

Find the value of $m$ such that $2^m = \frac{1}{4}$ .

Find the value of $a b^{2}$ when $a = -5i$ and $b = -5x$ , in simplified form.

Find the value of $x$ where $f(g(x))$ is undefined, given $f(x)=\frac{1}{(5-|x|)^{1 / 4}}$ and $g(x)=\sqrt{28-x}$ .

Find the value of $q$ in the equation $0.5q = 6.25$ . Round the answer to the nearest tenth.

Solve the linear equation $x + 9 = 17x$ for the value of $x$ .

Solve the linear equation $18=x+2$ for the unknown variable $x$ .

Solve the quadratic equation $v^2 - 22v - 77 = -2$ by completing the square.

Encuentra el valor de $x$ si un número es 8 menos que el doble de $x$ y la suma de los números es 40.

Find the number of solutions to the linear equation $-6-h=-h+4-2h$ .

Evaluate the expression $3+6 \div\left(-1 \frac{3}{4}+-2\right)$ and write the answer as a fraction or whole/mixed number.

Find the value of $p$ in the equation $7+p=16$ .

Solve the linear equation $30.52 + 6x = 4.42$ for the unknown variable $x$ .

Solve $2^{2 b-3}=32$ to find the value of $b$ .

Find the linear correlation coefficient for the ordered pairs $(5,39)$ , $(7,36)$ , $(9,33)$ , and $(11,30)$ .

Graph the inverse of the linear function $f(x) = \frac{2}{3}x - 1$ . Plot the original function in red and its inverse in blue.

Solve the equation $-7x + x^2 + 6 = -6x + 3 + x^2$ either algebraically or graphically. Options: A) $x = -11$ , B) $x = 3$ , C) no solution, D) $x = -5$ .

Find the values of $v$ that solve the equation $-5v-16=4$ .

Solve the linear equation $13.5 + 55x = 244$ for the unknown variable $x$ .

Determine if the equation $0=-9d+9d$ is an identity.

Find the zeros and valid $x$ values for the rocket's path equation $y = -3x^2 + 11x + 4$ .

Determine if $-46$ is a solution to the equation $\frac{x+1}{5}=-8$ .

Find the roots of the equation $\frac{b+3}{4}=\frac{b-1}{2}$ .

Resuelve la ecuación cuadrática $13x - 9x^2 = 4$ .

Find the 4th term in the sequence: $2, 5, 10, 17, \ldots$

Solve the quadratic equations: $x^{2}+3 x-12=6$ , $18 x^{2}+45 x-27=0$ , $90 x^{2}-84 x=-18$ , $x^{2}+8 x=-15$ .

Solve for $x$ in the equation $9=25\left(\frac{x+3}{25}\right)^2$ .

Find values of $m$ and $n$ so that the polynomial $3m-63x^9 + (7-42n)x + 15$ is constant.

Solve for $y$ in the equation $-7=\frac{y}{1.2}$ .

Solve $(-2)(-5)(-3)(-4)$ and choose the correct result: (A) 120, (B) 36, (C) -36, or (D) -120.

Solve the linear equation $1 / 2 y = -12$ for the variable $y$ .

Find the value of the linear function $f(x) = 23.2x + 2.5$ when $x = -4.2$ .

Find the value of $m(6)$ for the linear function $m(x) = 4x + 5$ .

Solve for $d$ . Round your answer to the nearest hundredth. The opposite of a power is a root.

Find the missing number in the equation: $75 + 1,000 = (3 + 40)$

Find the sum of the arithmetic series with $a_{1}=12$ , $d=4$ , and $n=30$ .

Encuentra el valor de $r$ que satisface la desigualdad $-19r < 19$ .

Solve the equation $0.8x - 0.3 = 0.5x$ for $x$ .

Find the inverse function $f^{-1}(28)$ if $f(19)=28$ and $f$ is one-to-one.

Evaluate the sum $\sum_{k=1}^{7}(2-3k)$ . Options: A. -69, B. -77, C. -70, D. -140.

Find the value of $\frac{|x|}{x^{2}}$ when $x=-5$ .

Find the value of $x$ given the expression $15^2 - 5^2$ .

Solve for $u$ in the equation $x = \frac{7}{8u} + 2$ .

Solve for the value of $x$ in the equation $14 x-3(2 x-4)=-8 x-4$ .

Does the point ( $6,46$ ) satisfy the equation $y = -7x + 4$ ? Yes or no?

Find the value of $u$ that satisfies the equation $8(u-6)=16$ .

Solve for the value of $u$ given the equation $-3=u-2$ .

Simplify radical expression: $\sqrt{36} \cdot \sqrt{b^{2}} \cdot \sqrt{c^{2}} \cdot \sqrt{2ab}$ . Choose the correct step.

Find the value of $x$ that satisfies the equation $2x - 4 = 24$ .

Solve the linear equation $12[2+(x+2)]=5(x-2)+2$ for the unknown variable $x$ .

Simplify the mathematical expression $3 x(x+2)$ by factoring.

Solve the equation $9 = -k + 2(4k + 7)$ .

Evaluate the expression $(2-7)^{2} + \sqrt[3]{6(8-5)+9}$ .

Solve for $y$ in the equation $289=236-y$ .

Finden Sie die Wurzeln des Polynoms $f(x) = 0.25 \cdot (x-3)^{2}(x+2)$ und erläutern Sie die Schritte.

Annie charges $75 plus$ 35 per hour for tutoring. The linear equation is $y=75+35x$ . The independent variable is the time Annie tutors, and the dependent variable is the amount she earns. The y-intercept is $75, and the slope is$ 35.

Solve the inequality $3x - 1 < 8$ for real number $x$ .

Find the score $y$ on a 100-point test with 5 points per question, given the number of incorrect answers $x$ , where $y=100-5x$ .

Determine scholarship allocation among 340 English, 292 Psychology, and 401 Graphic Design majors using the Jefferson method.
Simplified problem statement: Allocate $18$ scholarships among $340$ English, $292$ Psychology, and $401$ Graphic Design majors using the Jefferson method.

Find the value of $x$ given the linear function $h(x) = 7x - 3$ and $h(x) = 11$ .

Find the values of $x$ that make $f(x)=\frac{2-x}{x^{2}-25}$ undefined.

Find the values of n that make the inequality $\frac{n}{-8} > 7$ true. Write the equivalent inequality in terms of n.

Find two real numbers with sum $2$ and product $-24$ using a quadratic equation.

Find the sum of $4 \sqrt[3]{x^{10}}+5 x^{3} \sqrt[3]{8 x}$ when $x \neq 0$ , in simplest form.

Find the value of $z$ that satisfies the equation $11011=z-7286$ .

Sketch a graph to solve the inequality $x^2 - 9x + 18 > 0$ .

Find the values of $x$ and $y$ that satisfy the equation $12x - 10y = 18$ . Reduce all fractions to lowest terms.

Solve for $x$ in the equation $5+2x=25$ and provide a justification for each step.

Write the quadratic equation with roots $3 - 2i$ and $3 + 2i$ .

Factorize the quadratic equation $3x^2 - 6x - 24 = 0$ and find the missing coefficients.

Use the transitive property to find the relationship between $a$ and $c$ given $a=b$ and $b=c$ .