Browse Algebra problems in the Studdy Learning Bank!

Problem 4601

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

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Problem 4602

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

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Problem 4603

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

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Problem 4604

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

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Problem 4605

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 4606

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 4607

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

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Problem 4608

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

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Problem 4609

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

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Problem 4610

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

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Problem 4611

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 4612

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

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Problem 4613

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

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Problem 4614

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 4615

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

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Problem 4616

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 4617

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 4618

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

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Problem 4619

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

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Problem 4620

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

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Problem 4621

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

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Problem 4622

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

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Problem 4623

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

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Problem 4624

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

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Problem 4625

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

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Problem 4626

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

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Problem 4627

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 4628

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 4629

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 4630

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

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Problem 4631

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 4632

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 4633

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

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Problem 4634

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 4635

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

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Problem 4636

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 4637

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 4638

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 4639

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

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Problem 4640

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

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Problem 4641

Find the equation of the linear function passing through the point $(x, y) = (-4, 6)$ with slope $2$ .

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Problem 4642

Solve for the value of $v$ given the equation $v-\frac{3}{8}=-\frac{3}{4}$ .

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Problem 4643

Describe the translation from $y=2(x-15)^{2}+3$ to $y=2(x-11)^{2}+3$ : 4 units to the left

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Problem 4644

Solve the linear equation $2+r=7+6r$ for the unknown variable $r$ .

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Problem 4645

Encuentra la solución de la ecuación $y=-\frac{5}{7} x+7$ cuando $x=7$ .

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Problem 4646

Find values of x that satisfy the inequality $17 > -2x + 11$ . Circle all applicable options: $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3 \frac{4}{9}$ .

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Problem 4647

Find the value of $x$ that satisfies the equation $(1+7)(4+1x) = 15 - 2.5(x+1)$ , rounded to two decimal places.

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Problem 4648

Find the missing value in the given expression: $3 \times 2^{2} \times 8 = 3 \times \square \times 8 = \square \times 8 = \square$ .

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Problem 4649

Start with 3, multiply by 3 to find the next 3 numbers in the pattern. Find $3 \times 3, 3 \times 3 \times 3, 3 \times 3 \times 3 \times 3$ .

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Problem 4650

Find the function representing the direct variation between $x$ and $y$ given that $y=14$ when $x=6$ .

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Problem 4651

Solve the inequality $4x-5<0$ for real values of $x$ .

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Problem 4652

Find the value of $p(0)$ when $p(z)=2z^3-5z$ .

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Problem 4653

Solve the inequality $5x + 10 > 30$ and select the correct solution.

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Problem 4654

Identify the starting value and rate of change of the linear equation $y=7x-2$ .

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Problem 4655

Find the number(s) $x$ such that $2x^2 - 12 = -5x$ .

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Problem 4656

Find the x-intercept of the trend line $y=-0.13x+11.2$ . Determine if the x-intercept is plausible in a real-world scenario and explain.

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Problem 4657

Find the value of $x$ that satisfies the equation $4x=124$ .

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Problem 4658

Describe the graph of the geometric sequence $640, 160, 40, 10, \ldots$ . Select two: (1) Graph shows exponential growth, (2) Graph appears linear, (3) Domain is natural numbers, (4) Range is natural numbers, (5) Graph shows exponential decay.

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Problem 4659

Evaluate the expression $\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 8$ and provide the value.

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Problem 4660

Solve the equation $-2(x+11)=-8$ to find the value of $x$ .

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Problem 4661

Solve the linear equation $y-5=0$ for the value of $y$ .

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Problem 4662

Solve the equation $0.7^{3}=n$ for the value of $n$ .

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Problem 4663

Find an equation for a number plus 5.1 equals 8.8, using variable $n$ .

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Problem 4664

Solve for $y$ in the linear equation $3y - 8y = 25$ .

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Problem 4665

Solve the equation $3.5(2.25+x)=14$ for $x$ .

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Problem 4666

Determine the properties of the polynomial $1+7x^2$ , including the constant term, leading term, and leading coefficient.

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Problem 4667

Solve for $m$ in the equation $-64=m^{3}$ . Express the solution in simplest radical form.

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Problem 4668

Solve the equation $2^{(x-1)(x+2)(x-7)(x+8)}=1$ .

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Problem 4669

Drag the points on the line to show the ordered pairs that satisfy $y = -3x + 2$ .

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Problem 4670

Find the number $x$ such that $-3x - 5 > 125$ . Which inequality represents the solution set for $x$ ?

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Problem 4671

Analyze the end behavior of $f(x) = 12x + 144 - 6x^2$ as $x \rightarrow \pm \infty$ .

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Problem 4672

Find the solutions to the absolute value equation $|x| + 10 = 1$ .

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Problem 4673

Find the ratio of $x$ to $y$ given the equation $3x = 7y$ .

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Problem 4674

Determine which equation is in standard form: a. $x+3=-5y$ , b. $5-y=x$ , c. $y=3x+6$ , d. $-8x+3y=12$ .

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Problem 4675

Choose the best term from the box to complete the vocabulary definitions: 1. $A(n)$ that contains numbers and at least one operation is a numerical expression. 2. A letter or symbol representing an unknown amount is a variable. 3. A number sentence using the $=$ symbol is an equation. 4. The answer to a multiplication problem is a product.

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Problem 4676

Solve the quadratic inequality $x^{2} - 4x + 3 \leq 0$ by graphing.

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Problem 4677

Simplify the expression $9 \sqrt{5} + \sqrt{45}$ .

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Problem 4678

Find the value of $w$ when $a=20$ , given $w=\frac{a}{4}+3$ .

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Problem 4679

Determine the number of light bulbs needed for 15 chandeliers given the function $b(n)=6n$ .

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Problem 4680

Solve for $x$ in the equation $x-4=-2x+9$ . Round to the nearest tenth if necessary.

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Problem 4681

Solve the absolute value equation $|b+4|-2=4$ .

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Problem 4682

Solve for $y$ in the equation $-6=-\frac{4}{3}y$ .

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Problem 4683

Solve for $x$ in the linear equation $8x + 3 = 6x - 9$ , then evaluate $3x - 2$ .

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Problem 4684

Solve the equation $9-|5x+1|=9$ and provide the solution(s) as a comma-separated list. If there is no solution, enter "NO SOLUTION".

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Problem 4685

Find the values of $y$ for $x = -2$ and $x = -1$ when $y = 2x$ .

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Problem 4686

Identify the property of real numbers in the equation: $-5[(-7y)+6y^2]=35y+(-30y^2)$ .

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Problem 4687

Solve the system of linear equations: $\frac{|4 x-2|}{5}=10$ and $-2|x-7|=-12$ .

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Problem 4688

Simplify the expression $(x+10)^{2}$ .

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Problem 4689

Solve the quadratic equation $0=-2(5 x-1)(3 x+4)$ for real values of $x$ .

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Problem 4690

Find the value of $A$ if $g(t) = \frac{2t - 9}{t - A}$ and $g(3) = 3$ . $A = \square$

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Problem 4691

Stopping distance of car at $30$ mph is $y=2(30)+15$ , where $y$ is stopping distance in feet. What is the stopping distance?

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Problem 4692

Solve the inequality $2|x-8|+4<13$ , and express the solution in the form $x<A$ or $x>B$ , where $A<x<B$ .

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Problem 4693

Find the value of $3x+5$ and $6+8x$ when $x=3$ .

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Problem 4694

Solve the linear equation $\frac{y}{5}-7=-2 x$ for $x$ and $y$ .

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Problem 4695

Find the equation where dividing both sides by 2 and then subtracting 10 is the correct order of steps. $10(x+2)=16$ , $2(x-10)=16$ , $2x+10=16$ , $2(x+10)=16$ .

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Problem 4696

Find the equivalent logarithmic equation for the exponential equation $12=5^{x}$ .

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Problem 4697

Solve linear equations with one or two variables. Find the value of an expression given a value for the variable.
a. Solve: $5x+2=10$ b. Find $5x+2$ when $x=-3$ c. Solve for $y: 5x+2y=10$ d. Solve for $x: 5x+2y=10$

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Problem 4698

Verify that $(6+4)+y=6+(4+y)$ is true when $y=5$ by substituting and simplifying both sides.

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Problem 4699

Find the original salary before a 9% raise, given the current salary of $50,031.

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Problem 4700

Find the equation of a parabola given its vertex at $(1, -3)$ and a point it passes through at $(0, \frac{7}{2})$ .

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Algebra

Problem 4601

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

Problem 4602

Find the upper bound of the inequality y≤x2+6x+4y \leq x^2 + 6x + 4y≤x2+6x+4.

Problem 4603

Find the equation of a line with y-intercept 999 and x-intercept −4-4−4.

Problem 4604

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

Problem 4605

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

Problem 4606

Solve the absolute value equations: ∣v−1∣=7|v-1|=7∣v−1∣=7, ∣y4∣=2\left|\frac{y}{4}\right|=2∣∣​4y​∣∣​=2, ∣−10k∣=30|-10 k|=30∣−10k∣=30, ∣n+8∣=1|n+8|=1∣n+8∣=1.

Problem 4607

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

Problem 4608

Solve the quadratic equation 2n2=27−15n2n^2 = 27 - 15n2n2=27−15n for the value of nnn.

Problem 4609

Find the value of the derivative fxf_{x}fx​ given the expression fx=7+2⋅3f_{x}=7+2 \cdot 3fx​=7+2⋅3.

Problem 4610

Solve the quadratic equation 3x2+5x=123x^2 + 5x = 123x2+5x=12 for real values of x.

Problem 4611

Helena earns $4\$ 4$4 per kid for babysitting. She needs to make at least $69\$ 69$69. Write the inequality 4x+53≥694x + 53 \geq 694x+53≥69 to find the minimum number of kids she needs to babysit, where xxx is the number of kids.

Problem 4612

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

Problem 4613

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

Problem 4614

Find the value of nnn in the equation 4n−3=54n-3=54n−3=5 by drawing a flowchart and using backtracking. (4 marks)

Problem 4615

Solve for xxx in the equation x+y3=5\frac{x+y}{3} = 53x+y​=5.

Problem 4616

Problem 4617

Find the first term u1u_1u1​ and the common difference ddd given u7=11u_7=11u7​=11 and u12=56u_{12}=56u12​=56 in an arithmetic sequence.

Problem 4618

Solve for xxx in the equation 7=x37=\frac{x}{3}7=3x​.

Problem 4619

Find the value of a+2bc3a\frac{a+2bc}{3a}3aa+2bc​ when a=4,b=−5,c=−7a=4, b=-5, c=-7a=4,b=−5,c=−7.

Problem 4620

Is the point (7,107, 107,10) a solution to the equation y=8x−7y = 8x - 7y=8x−7?

Problem 4621

Find the zero of 9x+2y=189x + 2y = 189x+2y=18 by setting 9x+2y=09x + 2y = 09x+2y=0 and solving for xxx.

Problem 4622

Solve the linear equation 4x−5=−x4x - 5 = -x4x−5=−x for the unknown variable xxx.

Problem 4623

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

Problem 4624

Solve the equation 4x+7=2\frac{4}{x+7}=2x+74​=2 and select the correct solution from the options provided.

Problem 4625

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

Problem 4626

Solve the cubic equation 5x−33−2=0\sqrt[3]{5x-3}-2=035x−3​−2=0 for xxx.

Problem 4627

Problem 4628

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

Problem 4629

Rewrite the expression x97x^{\frac{9}{7}}x79​. Select the correct answer: A. (1x)9\left(\frac{1}{\sqrt{x}}\right)^{9}(x​1​)9, B. xx27x \sqrt[7]{x^{2}}x7x2​, C. x79\sqrt[9]{x^{7}}9x7​, D. xx7x \sqrt[7]{x}x7x​.

Problem 4630

Find the value of 125z3y12125 z^{3} y^{12}125z3y12.

Problem 4631

Rewrite the equation y=2x2+8x+9y=2x^2+8x+9y=2x2+8x+9 in vertex form by completing the square, then graph the resulting function.

Problem 4632

Problem 4633

Find the value of aaa that satisfies the equation 3(a+1.5)=−1.53(a+1.5)=-1.53(a+1.5)=−1.5.

Problem 4634

Problem 4635

Solve for ggg given the equation f=17(g+h−k)f=\frac{1}{7}(g+h-k)f=71​(g+h−k).

Problem 4636

Find equivalent linear equations given 14x+7y=2114x + 7y = 2114x+7y=21. Options: y=2x+3y = 2x + 3y=2x+3, y+1=−2(x−2)y + 1 = -2(x - 2)y+1=−2(x−2), y=−2x+3y = -2x + 3y=−2x+3, y−1=2(x+2)y - 1 = 2(x + 2)y−1=2(x+2), y−3=−2xy - 3 = -2xy−3=−2x.

Problem 4637

Find f(−3)f(-3)f(−3) for the piecewise function f(x)={9x+4if x≤−5−12x+2if x>−5f(x) = \begin{cases} 9x+4 & \text{if } x \leq -5 \\ -\frac{1}{2}x+2 & \text{if } x > -5 \end{cases}f(x)={9x+4−21​x+2​if x≤−5if x>−5​.

Problem 4638

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

Problem 4639

Find the value of aaa when f(x)=2x3−9x2+7x+a=0f(x)=2x^3-9x^2+7x+a=0f(x)=2x3−9x2+7x+a=0 with x=2x=2x=2.

Problem 4640

Solve the linear equation x+10x=9\frac{x+10}{x}=9xx+10​=9 for xxx, where x≠0x \neq 0x=0.

Problem 4641

Find the equation of the linear function passing through the point (x,y)=(−4,6)(x, y) = (-4, 6)(x,y)=(−4,6) with slope 222.

Problem 4642

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

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

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

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

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. $x \sqrt[7]{x}$ .

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

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

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

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

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

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

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

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

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

Find the equation of the linear function passing through the point $(x, y) = (-4, 6)$ with slope $2$ .

Solve for the value of $v$ given the equation $v-\frac{3}{8}=-\frac{3}{4}$ .

Describe the translation from $y=2(x-15)^{2}+3$ to $y=2(x-11)^{2}+3$ : 4 units to the left

Solve the linear equation $2+r=7+6r$ for the unknown variable $r$ .

Encuentra la solución de la ecuación $y=-\frac{5}{7} x+7$ cuando $x=7$ .

Find values of x that satisfy the inequality $17 > -2x + 11$ . Circle all applicable options: $\frac{1}{11}$ , $-2 \frac{9}{17}$ , $-3 \frac{4}{9}$ .

Find the value of $x$ that satisfies the equation $(1+7)(4+1x) = 15 - 2.5(x+1)$ , rounded to two decimal places.

Find the missing value in the given expression: $3 \times 2^{2} \times 8 = 3 \times \square \times 8 = \square \times 8 = \square$ .

Start with 3, multiply by 3 to find the next 3 numbers in the pattern. Find $3 \times 3, 3 \times 3 \times 3, 3 \times 3 \times 3 \times 3$ .

Find the function representing the direct variation between $x$ and $y$ given that $y=14$ when $x=6$ .

Solve the inequality $4x-5<0$ for real values of $x$ .

Find the value of $p(0)$ when $p(z)=2z^3-5z$ .

Solve the inequality $5x + 10 > 30$ and select the correct solution.

Identify the starting value and rate of change of the linear equation $y=7x-2$ .

Find the number(s) $x$ such that $2x^2 - 12 = -5x$ .

Find the x-intercept of the trend line $y=-0.13x+11.2$ . Determine if the x-intercept is plausible in a real-world scenario and explain.

Find the value of $x$ that satisfies the equation $4x=124$ .

Describe the graph of the geometric sequence $640, 160, 40, 10, \ldots$ . Select two: (1) Graph shows exponential growth, (2) Graph appears linear, (3) Domain is natural numbers, (4) Range is natural numbers, (5) Graph shows exponential decay.

Evaluate the expression $\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 8$ and provide the value.

Solve the equation $-2(x+11)=-8$ to find the value of $x$ .

Solve the linear equation $y-5=0$ for the value of $y$ .

Solve the equation $0.7^{3}=n$ for the value of $n$ .

Find an equation for a number plus 5.1 equals 8.8, using variable $n$ .

Solve for $y$ in the linear equation $3y - 8y = 25$ .

Solve the equation $3.5(2.25+x)=14$ for $x$ .

Determine the properties of the polynomial $1+7x^2$ , including the constant term, leading term, and leading coefficient.

Solve for $m$ in the equation $-64=m^{3}$ . Express the solution in simplest radical form.

Solve the equation $2^{(x-1)(x+2)(x-7)(x+8)}=1$ .

Drag the points on the line to show the ordered pairs that satisfy $y = -3x + 2$ .

Find the number $x$ such that $-3x - 5 > 125$ . Which inequality represents the solution set for $x$ ?

Analyze the end behavior of $f(x) = 12x + 144 - 6x^2$ as $x \rightarrow \pm \infty$ .

Find the solutions to the absolute value equation $|x| + 10 = 1$ .

Find the ratio of $x$ to $y$ given the equation $3x = 7y$ .

Determine which equation is in standard form: a. $x+3=-5y$ , b. $5-y=x$ , c. $y=3x+6$ , d. $-8x+3y=12$ .