Browse Math problems in the Studdy Learning Bank!

Problem 2601

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

See Solution

Problem 2602

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

See Solution

Problem 2603

Find the value of $x$ if $\ln(x) - \ln(\sqrt{x}) = \frac{1}{2}$ .

See Solution

Problem 2604

Solve for t in the equation $h = 7 + 35t - 16t^2$ , given that $h = 25$ .

See Solution

Problem 2605

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

See Solution

Problem 2606

Evaluate the integral $\int_{-\frac{\pi}{3}}^{\frac{\pi}{4}} 3 \cos(4x) \, dx$ .

See Solution

Problem 2607

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

See Solution

Problem 2608

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

See Solution

Problem 2609

Find the value of $k$ where the interior angles of a triangle are $k^{\circ}, 27^{\circ}$ , and $10^{\circ}$ . $k=\square^{\circ}$

See Solution

Problem 2610

Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.
$A \cup B$ is: a. $\{3,4,5\}$ b. $\{3\}$ c. $\{1,2,3,4,5,6\}$ d. $\{2,3,4,5\}$

See Solution

Problem 2611

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

See Solution

Problem 2612

Mix black and white paint to make gray. Avery uses 5 cups black, 6 cups white. Grayson uses 4 cups black, 5 cups white. Calculate the percent of white paint to determine whose gray will be lighter.
Avery percent of white paint (to nearest whole number) $=54\%$ Grayson percent of white paint (to nearest whole number) $=56\%$ Grayson's gray paint will be lighter.

See Solution

Problem 2613

Simplify the expression $2.5 \times 1.29$ .

See Solution

Problem 2614

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?

See Solution

Problem 2615

Find the composite function $f(r(x))$ where $f(x)=19x^2$ and $r(x)=\sqrt{18x}$ .

See Solution

Problem 2616

Find $z$ using Cramer's rule and a calculator for the system: $4x-y+5z=1, -x+2y+z=0, 5x-2y+2z=-4$ .

See Solution

Problem 2617

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) $t \geq-84$ .

See Solution

Problem 2618

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

See Solution

Problem 2619

Find the value of the fraction $9 / 24$ .

See Solution

Problem 2620

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

See Solution

Problem 2621

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

See Solution

Problem 2622

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

See Solution

Problem 2623

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. $r=S-800$

See Solution

Problem 2624

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 $(0,80)$ .

See Solution

Problem 2625

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

See Solution

Problem 2626

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.

See Solution

Problem 2627

Solve the simple equation $27+0=27$ .

See Solution

Problem 2628

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

See Solution

Problem 2629

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

See Solution

Problem 2630

Find the area of a square with sides of length $28.1$ in. Round the area to the nearest hundredth.

See Solution

Problem 2631

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

See Solution

Problem 2632

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

See Solution

Problem 2633

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 $\left(\frac{3}{4}\right)^{3} \times\left(\frac{3}{4}\right)^{3}$ .

See Solution

Problem 2634

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.

See Solution

Problem 2635

Find the value of $-9.4 \cdot 2.7$ .

See Solution

Problem 2636

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

See Solution

Problem 2637

Determine if the number $97$ is divisible by $2, 3, 4, 5, 6, 8, 9$ , and/or $10$ . If not, answer "None".

See Solution

Problem 2638

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

See Solution

Problem 2639

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

See Solution

Problem 2640

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

See Solution

Problem 2641

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

See Solution

Problem 2642

Find the volume in mL to administer 23 mg of valium given a 10 mL bottle containing 100 mg of solution.

See Solution

Problem 2643

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

See Solution

Problem 2644

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

See Solution

Problem 2645

Find products of fractions and whole numbers. Determine if fraction-based statements are true or false. Calculate miles ridden and explain equivalence of fraction multiplication and division.
1a) $\frac{1}{4}$ of $6=1.5$ 1b) $\frac{1}{5} \times 30=6$ 1c) $\frac{1}{3}$ of $27=9$ 1d) $\frac{3}{4}$ of $6=4.5$ 1e) $\frac{4}{5} \times 30=24$ 1f) $\frac{2}{3} \times 27=18$
2a) $\frac{1}{4} \times 9=2.25$ (False) 2b) $\frac{3}{5}$ of $25=15$ (True) 2c) $\frac{2}{5}$ of $15=6$ (False) 2d) $18 \times \frac{1}{5}=3.6$ (False) 2e) $\frac{2}{6} \times 24=8$ (True) 2f) $17 \times \frac{1}{3}=\frac{17}{3}$ (True)
3) Pete rode $\frac{2}{3}$ of 150 miles, which is 100 miles.
4) Kim is correct. $\frac{1}{4} \times 12=3$ , which is the same as dividing 12 by 4.

See Solution

Problem 2646

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

See Solution

Problem 2647

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

See Solution

Problem 2648

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.

See Solution

Problem 2649

Find the equation of the line passing through the point $(4,-3)$ and parallel to the line $y = -\frac{1}{6}x - 1$ .

See Solution

Problem 2650

Find the product of -1 and -7.

See Solution

Problem 2651

Find the secant of $\pi$ and simplify the result, using integers or fractions. If the expression is undefined, select the corresponding choice.

See Solution

Problem 2652

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

See Solution

Problem 2653

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

See Solution

Problem 2654

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

See Solution

Problem 2655

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

See Solution

Problem 2656

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

See Solution

Problem 2657

Solve the system $A \mathbf{x}=\mathbf{b}$ using the given factorization $A=P^{\top} L U$ , where $\mathbf{b}=\begin{bmatrix}1 \\ 1 \\ 7\end{bmatrix}$ and $\mathbf{x}=\begin{bmatrix}2 \\ 3 \\ 2\end{bmatrix}$ .

See Solution

Problem 2658

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.

See Solution

Problem 2659

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

See Solution

Problem 2660

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

See Solution

Problem 2661

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

See Solution

Problem 2662

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

See Solution

Problem 2663

Differentiate the given functions: $f(x)=x^{2}+4x$ , $f(x)=5x^{3}-2x^{4}$ , $f(x)=x^{5}-7x^{4}+3x^{3}$ , $g(x)=\frac{1}{2}x^{4}-\frac{1}{x}$ , $g(x)=(2x-3)^{2}$ , $g(x)=\frac{1}{9}x^{-3}-\frac{1}{6}x^{-2}$ , $y=\frac{1}{3}\sqrt{x}-\frac{2}{\sqrt{x}}$ , $y=6\sqrt[4]{x}-3\sqrt[3]{x}+\frac{10}{\sqrt[5]{x}}$ , $y=(x^{2}-2x)^{3}$ .

See Solution

Problem 2664

Identify the domain and graph the function $f(x)=\sqrt{x-2}$ .

See Solution

Problem 2665

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

See Solution

Problem 2666

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

See Solution

Problem 2667

Find the value of $x$ that satisfies the equation $\ln(3x) = 2x - 5$ .

See Solution

Problem 2668

Find the inverse cosine of -0.8 and express the result in radians, rounded to two decimal places.

See Solution

Problem 2669

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

See Solution

Problem 2670

Find the absolute value of $x$ when $x=15$ and $x=-15$ . The absolute value of both 15 and -15 is 15.

See Solution

Problem 2671

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

See Solution

Problem 2672

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

See Solution

Problem 2673

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

See Solution

Problem 2674

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

See Solution

Problem 2675

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

See Solution

Problem 2676

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

See Solution

Problem 2677

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

See Solution

Problem 2678

Find the cube root of $64$ .

See Solution

Problem 2679

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

See Solution

Problem 2680

Find the power series for the indefinite integral $\int \frac{e^{8x} - 1}{7x} dx$ , and give the first 5 nonzero terms.
$f(x) = C + \frac{8x}{7} + \frac{64x^2}{7 \cdot 2!} + \frac{512x^3}{7 \cdot 3!} + \frac{4096x^4}{7 \cdot 4!} + \frac{32768x^5}{7 \cdot 5!} + \cdots$

See Solution

Problem 2681

Find the P-value for a right-tailed test with test statistic $z=0.52$ . Use a 0.05 significance level to determine if the null hypothesis should be rejected or failed to be rejected.

See Solution

Problem 2682

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

See Solution

Problem 2683

Solve for $y$ in terms of $x$ , given the equation $\ln(y-9) - \ln 4 = x + \ln x$ .

See Solution

Problem 2684

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

See Solution

Problem 2685

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 $CD$ .

See Solution

Problem 2686

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

See Solution

Problem 2687

Which limit definition represents the derivative of $f(x)$ ? Options: $\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$ , $\lim_{x\to a} \frac{f(x)-f(a)}{x-a}$

See Solution

Problem 2688

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

See Solution

Problem 2689

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

See Solution

Problem 2690

Find the tax on a $930,000 property given a$ 620,000 property is taxed $9,300 and tax rates are proportional.

See Solution

Problem 2691

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

See Solution

Problem 2692

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

See Solution

Problem 2693

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

See Solution

Problem 2694

Find the matrix $X$ that satisfies the equation $A(X + 5B) = C$ .

See Solution

Problem 2695

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

See Solution

Problem 2696

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

See Solution

Problem 2697

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

See Solution

Problem 2698

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

See Solution

Problem 2699

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

See Solution

Problem 2700

Find the percent of Container A that is full after pumping water into Container B until it is completely full. Container A has radius 13 ft and height 18 ft. Container B has radius 11 ft and height 20 ft.

See Solution

Math

Problem 2601

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

Problem 2602

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

Problem 2603

Find the value of xxx if ln⁡(x)−ln⁡(x)=12\ln(x) - \ln(\sqrt{x}) = \frac{1}{2}ln(x)−ln(x​)=21​.

Problem 2604

Solve for t in the equation h=7+35t−16t2h = 7 + 35t - 16t^2h=7+35t−16t2, given that h=25h = 25h=25.

Problem 2605

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

Problem 2606

Evaluate the integral ∫−π3π43cos⁡(4x) dx\int_{-\frac{\pi}{3}}^{\frac{\pi}{4}} 3 \cos(4x) \, dx∫−3π​4π​​3cos(4x)dx.

Problem 2607

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

Problem 2608

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 2609

Find the value of kkk where the interior angles of a triangle are k∘,27∘k^{\circ}, 27^{\circ}k∘,27∘, and 10∘10^{\circ}10∘. k=□∘ k=\square^{\circ} k=□∘

Problem 2610

Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.A∪BA \cup BA∪B is: a. {3,4,5}\{3,4,5\}{3,4,5} b. {3}\{3\}{3} c. {1,2,3,4,5,6}\{1,2,3,4,5,6\}{1,2,3,4,5,6} d. {2,3,4,5}\{2,3,4,5\}{2,3,4,5}

Problem 2611

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 2612

Problem 2613

Simplify the expression 2.5×1.292.5 \times 1.292.5×1.29.

Problem 2614

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 2615

Find the composite function f(r(x))f(r(x))f(r(x)) where f(x)=19x2f(x)=19x^2f(x)=19x2 and r(x)=18xr(x)=\sqrt{18x}r(x)=18x​.

Problem 2616

Find zzz using Cramer's rule and a calculator for the system: 4x−y+5z=1,−x+2y+z=0,5x−2y+2z=−44x-y+5z=1, -x+2y+z=0, 5x-2y+2z=-44x−y+5z=1,−x+2y+z=0,5x−2y+2z=−4.

Problem 2617

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 2618

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 2619

Find the value of the fraction 9/249 / 249/24.

Problem 2620

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

Problem 2621

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

Problem 2622

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

Problem 2623

Find the equation that correctly expresses rrr as the subject of S=800(1−r)S=800(1-r)S=800(1−r).A. r=800−S800r=\frac{800-S}{800}r=800800−S​ B. r=S−800800r=\frac{S-800}{800}r=800S−800​ C. r=800−Sr=800-Sr=800−S D. r=S−800r=S-800r=S−800

Problem 2624

The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation 3x+4y=2403x + 4y = 2403x+4y=240 represents this relationship. The graph of this equation is a line through the points (60,0)(60,0)(60,0) and (0,80)(0,80)(0,80).

Problem 2625

Solve the inequality 2(3x−1)<22(3x-1)<22(3x−1)<2 for real values of xxx.

Problem 2626

Solve the system of linear equations with constants bbb and ccc. If b=c−12b = c - \frac{1}{2}b=c−21​, determine which statement about xxx and yyy is true.

Problem 2627

Solve the simple equation 27+0=2727+0=2727+0=27.

Problem 2628

Find the equation with solution x=5x=5x=5. Possible equations: 8x+1=418x+1=418x+1=41 5x+7=355x+7=355x+7=35 9x−4=−419x-4=-419x−4=−41 4x+1=614x+1=614x+1=61

Problem 2629

Find the sum of the expressions 7x+77x + 77x+7 and 3−3x3 - 3x3−3x.

Problem 2630

Find the area of a square with sides of length 28.128.128.1 in. Round the area to the nearest hundredth.

Problem 2631

Solve for www where w+12≥16w + 12 \geq 16w+12≥16.

Problem 2632

Find equivalent rational expression with denominator a2b2c2a^2 b^2 c^2a2b2c2 for 8+7ca2b2c\frac{8 + 7c}{a^2 b^2 c}a2b2c8+7c​.

Problem 2633

Problem 2634

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

Problem 2635

Find the value of −9.4⋅2.7-9.4 \cdot 2.7−9.4⋅2.7.

Problem 2636

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

Problem 2637

Determine if the number 979797 is divisible by 2,3,4,5,6,8,92, 3, 4, 5, 6, 8, 92,3,4,5,6,8,9, and/or 101010. If not, answer "None".

Problem 2638

Simplify the quotient 16x3÷8x\sqrt{16 x^{3}} \div \sqrt{8 x}16x3​÷8x​ when x>0x>0x>0.

Problem 2639

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

Problem 2640

Identify the ordered pair that does not solve the linear equation 5x+y=105x + y = 105x+y=10.

Problem 2641

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

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

Find the value of $x$ if $\ln(x) - \ln(\sqrt{x}) = \frac{1}{2}$ .

Solve for t in the equation $h = 7 + 35t - 16t^2$ , given that $h = 25$ .

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

Evaluate the integral $\int_{-\frac{\pi}{3}}^{\frac{\pi}{4}} 3 \cos(4x) \, dx$ .

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 $(\quad, -6)$ .

Find the value of $k$ where the interior angles of a triangle are $k^{\circ}, 27^{\circ}$ , and $10^{\circ}$ . $k=\square^{\circ}$

Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.
$A \cup B$ is: a. $\{3,4,5\}$ b. $\{3\}$ c. $\{1,2,3,4,5,6\}$ d. $\{2,3,4,5\}$

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

Simplify the expression $2.5 \times 1.29$ .

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 composite function $f(r(x))$ where $f(x)=19x^2$ and $r(x)=\sqrt{18x}$ .

Find $z$ using Cramer's rule and a calculator for the system: $4x-y+5z=1, -x+2y+z=0, 5x-2y+2z=-4$ .

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 $(d-7)(5d-2)=0$ .

Find the value of the fraction $9 / 24$ .

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.

Solve the simple equation $27+0=27$ .

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 $3 - 3x$ .

Find the area of a square with sides of length $28.1$ in. Round the area to the nearest hundredth.

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.

Find the value of $-9.4 \cdot 2.7$ .

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

Determine if the number $97$ is divisible by $2, 3, 4, 5, 6, 8, 9$ , and/or $10$ . If not, answer "None".

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.

Find the equation of the line passing through the point $(4,-3)$ and parallel to the line $y = -\frac{1}{6}x - 1$ .

Find the secant of $\pi$ and simplify the result, using integers or fractions. If the expression is undefined, select the corresponding choice.

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 $\text{isolate the variable on one side}$ .

Solve the system $A \mathbf{x}=\mathbf{b}$ using the given factorization $A=P^{\top} L U$ , where $\mathbf{b}=\begin{bmatrix}1 \\ 1 \\ 7\end{bmatrix}$ and $\mathbf{x}=\begin{bmatrix}2 \\ 3 \\ 2\end{bmatrix}$ .

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 $\frac{9 x^{17} y^{a}}{3 x^{b} y^{2}}=c x^{5} y^{7}$ .

Identify the domain and graph the function $f(x)=\sqrt{x-2}$ .

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 value of $x$ that satisfies the equation $\ln(3x) = 2x - 5$ .

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

Find the absolute value of $x$ when $x=15$ and $x=-15$ . The absolute value of both 15 and -15 is 15.

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

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

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

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