Math Statement

Problem 21801

Solve $\frac{a \sqrt{a}}{\sqrt[3]{a^{2}}}=a^{k}$ for the value of $k$ .

See Solution

Problem 21802

Find the exact value of $\tan 20^{\circ}-\frac{\cos 70^{\circ}}{\cos 20^{\circ}}$ without a calculator.

See Solution

Problem 21803

Find $\cos \theta$ given $\tan \theta=\frac{1}{3}$ and $\csc \theta<0$ . Simplify your answer.

See Solution

Problem 21804

Find the domain of the function $F(x)=\frac{6 x(x-7)}{6 x^{2}-41 x-7}$ . Is it A: $x \neq \square$ or B: all real numbers?

See Solution

Problem 21805

Calculate the value of $\sin \frac{\pi}{3} - \cos \frac{\pi}{6}$ without a calculator. Options: 0, $\sqrt{3}$ , $\frac{\sqrt{3}-1}{2}$ , 1.

See Solution

Problem 21806

Find the domain of the function $R(x)=\frac{x}{x^{3}+216}$ . Is it A: $\{x \mid \square\}$ or B: all real numbers?

See Solution

Problem 21807

Find the vertex and y-intercept of the function $f(x)=-4x^{2}+8x+3$ .

See Solution

Problem 21808

Find $\cos \theta$ if $\tan \theta=\frac{4}{3}$ . Options: $\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{5}{3}$ , $\frac{4}{5}$ .

See Solution

Problem 21809

Find $f(-2)$ if $f(x)=9 x^{2}+5 x-8$ . Choices: A. -54 B. -18 C. 18 D. 36 E. 38

See Solution

Problem 21810

Multiply $6 \frac{1}{2}$ by $1 \frac{8}{13}$ and simplify to a mixed number.

See Solution

Problem 21811

Solve for $x$ in the equation $\frac{x+7}{-3}=1$ .

See Solution

Problem 21812

Find the exact value of $\sec \frac{\pi}{3}$ . Options: 2, $\sqrt{2}$ , $\frac{2 \sqrt{3}}{3}$ , $\frac{\sqrt{3}}{2}$ .

See Solution

Problem 21813

Solve for $x$ : $\frac{x-1}{-4}=-6$

See Solution

Problem 21814

Find $\tan \theta$ given $\sin \theta=\frac{\sqrt{3}}{2}$ . Choices: $\frac{2 \sqrt{3}}{3}$ , $\sqrt{3}$ , $\frac{\sqrt{3}}{3}$ .

See Solution

Problem 21815

Solve for $x$ in the equation $\frac{2 x}{3}=12$ .

See Solution

Problem 21816

Find the number of solutions for the equation $3(x+4)=3x+4$ . A) no solution B) one solution C) two solutions D) infinitely many solutions

See Solution

Problem 21817

Calculate $k$ using the formula: $k=2(-2)^{2}+8(-2)+7$ .

See Solution

Problem 21818

Solve: $3(2x - 5) = 6x - 15$

See Solution

Problem 21819

Find the exact value of $\sin \frac{25 \pi}{3}$ using a coterminal angle. Options: $-\frac{1}{2}$ , $-\frac{\sqrt{3}}{2}$ , $\frac{1}{2}$ , $\frac{\sqrt{3}}{2}$ .

See Solution

Problem 21820

Find the vertex and y-intercept of the equation $y=-4x^{2}+8x+3$ .

See Solution

Problem 21821

Find the exact value of $\cot 720^{\circ}$ using a coterminal angle without a calculator. Options: 0, -1, 1, undefined.

See Solution

Problem 21822

Round 576.558 to the nearest tenths place: 576.6, 580, 576.56, or 576.5?

See Solution

Problem 21823

Find the exact value of $\sin 390^{\circ}$ using a coterminal angle without a calculator.

See Solution

Problem 21824

Find the intersection point of $f(x)$ and its inverse $f^{-1}(x)$ on the coordinate plane.

See Solution

Problem 21825

Describe how the function $j(x)=\frac{1}{3}(x-6)^{2}$ is transformed from its parent function.

See Solution

Problem 21826

Find $(c \cdot d)(x)$ for $c(x)=4x-2$ and $d(x)=x^2+5x$ .

See Solution

Problem 21827

Explain the transformation of the function $h(x)=-(x+5)^{2}+7$ .

See Solution

Problem 21828

Find the new vertices of $\triangle A B C$ after these translations: 1. $T_{\langle-2,3\rangle}$ , 2. $T_{\langle-4,-1\rangle}$ , 3. $T_{(4,6)}$ .

See Solution

Problem 21829

Convert $88^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$ using ${ }^{\circ} \mathrm{F}=\left({ }^{\circ} \mathrm{C} \times 9 / 5\right)+32$ .

See Solution

Problem 21830

Convert 20°C to °F using the formula °F = (°C × 9/5) + 32.

See Solution

Problem 21831

Identify the transformation from $f(x)=(2 x-3)^{3}$ to $g(x)=(-2 x-3)^{3}$ : A. vertical reflection B. horizontal reflection C. vertical shift D. horizontal shift.

See Solution

Problem 21832

Find the value of $\cos \left(-\frac{\pi}{4}\right)$ without a calculator. A. $\cos \left(-\frac{\pi}{4}\right)=$ (simplify) B. undefined.

See Solution

Problem 21833

Determine if the function $f(x)=x^{6}+10 x^{4}-11 x^{2}+19$ is even, odd, or neither. Choices: A, B, C, D.

See Solution

Problem 21834

Find the limit as x approaches 1: $\lim_{{x \to 1}} \frac{\sqrt{2 x^{3}+x+1}-2 x}{x-1}$

See Solution

Problem 21835

Find the direction of the parabola given by $y=-2 x^{2}+4 x+3$ . Does it open up or down?

See Solution

Problem 21836

Find the vertex of the parabola defined by $y=-2 x^{2}-4 x-5$ . What are the coordinates?

See Solution

Problem 21837

Identify the vertex, AOS, min/max value, domain, and range of $y=(x+1)^{2}+7$ .

See Solution

Problem 21838

Convert the function $y=6(x+1)^{2}-15$ into standard form.

See Solution

Problem 21839

Find the vertex of the parabola given by $y=-2 x^{2}+4 x+3$ . What are the coordinates of the vertex?

See Solution

Problem 21840

Find the vertex and y-intercept of the function $y=-x^{2}+14x-30$ .

See Solution

Problem 21841

Find the vertex and y-intercept of $y=2x^{2}+20x-5$ .

See Solution

Problem 21842

Find the limits: 1. $\lim _{x \rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}$ , 2. $\lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{\sin x-\cos x}$ . Also, find $\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}-x$ and $f(x)=\frac{1}{x+3}$ .

See Solution

Problem 21843

Find the axis of symmetry for the parabola $y=-2 x^{2}+4 x+3$ . Write your answer as an equation.

See Solution

Problem 21844

Determine the direction the parabola $y=-2 x^{2}+4 x+1$ opens: up or down?

See Solution

Problem 21845

Identify the common factor in the polynomial $2x^{3} - 4x^{2} + x + 1$ .

See Solution

Problem 21846

Calculate the product of -23 and 40: $(-23) \cdot 40$ .

See Solution

Problem 21847

Find the $x$ -intercept and $y$ -intercept of $f(x)=4x+12$ . Choose the correct option from A, B, C, or D.

See Solution

Problem 21848

Simplify: $-8 - 1 + 4 \cdot 2$

See Solution

Problem 21849

Check if sets $A=\{0,-1,4,5,6\}$ and $B=\{0,-1,6,5,4\}$ are equal or not. Determine if $A=B$ or $A \neq B$ .

See Solution

Problem 21850

Determine if the sets $A$ and $B$ are equal:
$A=\left\{\frac{1}{2}, 0,-\frac{1}{2},-\frac{1}{8}\right\}, \quad B=\left\{\frac{1}{2}, 0, \frac{1}{3}, \frac{1}{8}\right\}$
Is $A=B$ or $A \neq B$ ?

See Solution

Problem 21851

Calculate $\left(\frac{1}{3}\right)^{5}$ . Choose from: $\frac{5}{3}$ , $\frac{1}{81}$ , $\frac{1}{27}$ , $\frac{1}{243}$ .

See Solution

Problem 21852

Find the limit as $h$ approaches 0 for the difference quotient of: 1. $f(x)=x^{2}-x$ , 2. $f(x)=\frac{1}{x+3}$ .

See Solution

Problem 21853

Calculate $11^3$ . Options: 33, 121, 1,331, 177,144.

See Solution

Problem 21854

Identify the base and exponent for $n \cdot n \cdot n \cdot n$ . Options: $n^{4}$ , $4 n^{4}$ , $4 n$ , $\frac{n}{4}$ .

See Solution

Problem 21855

Solve the compound inequality: $-4 x \leq -16$ or $4 x - 12 \geq 8$ . What is the solution?

See Solution

Problem 21856

If $H$ is a linear function, what is $H(11)-H(5)$ equivalent to? (A) $H(11)+H(5)$ (B) $\frac{H(11)-H(5)}{6}$ (C) $H(14)-H(8)$ (D) $H(11-5)$

See Solution

Problem 21857

Determine if sets $A$ and $B$ are equal: $A=\{3.1,-1.1,1.8,-2.8\}$ and $B=\{-1.1,1.8,3.1\}$ .

See Solution

Problem 21858

Convert 952 g to mg. What is the value? Use the conversion: $1 \mathrm{~g} = 1000 \mathrm{~mg}$ .

See Solution

Problem 21859

Convert 0.574 m to cm. What is the value in cm?

See Solution

Problem 21860

Calculate $13^2$ . Choices: 169, 26, 8192, 24.

See Solution

Problem 21861

Solve the compound inequality $x<2$ and $x>-3$ . Graph the solution and write it in interval notation.

See Solution

Problem 21862

Convert $5.287 \mathrm{~L}$ to milliliters ( $\mathrm{mL}$ ).

See Solution

Problem 21863

Simplify: $72 \div 9 + 7^{2}$

See Solution

Problem 21864

Convert $785.3 \mathrm{~km}$ to meters.

See Solution

Problem 21865

Is $B$ a subset of $A$ ? A = {-2, -4, -6, -8}, B = {-2, 4, -6, -8}. Answer Yes or No.

See Solution

Problem 21866

Select a base and exponent: $(-8) \cdot (-8)$ , $(-8)^{2}$ , $-8(-8)^{2}$ , $8^{2}$ , $64^{2}$ .

See Solution

Problem 21867

Calculate $(-2)^{8}$ . Choose from: -128, 256, -16.

See Solution

Problem 21868

Find the solution set for $x<2$ and $x>-3$ . A. The solution set is $(>k<3)$ .

See Solution

Problem 21869

מה הגבול של $\left(\sqrt[3]{x^{3}+x^{2}}-x\right)$ כש- $x$ מתקרב למינוס אינסוף?

See Solution

Problem 21870

Find the exact values of the other trigonometric functions for $\theta$ given that $\tan \theta=\frac{12}{5}$ and $\sin \theta<0$ .

See Solution

Problem 21871

Find the domain of the rational function $R(x)=\frac{7\left(x^{2}-2 x-3\right)}{8\left(x^{2}-9\right)}$ .

See Solution

Problem 21872

Evaluate the piecewise function $f$ at $x=3$ to check if it's continuous and differentiable. What is true about $f$ at $x=3$ ?

See Solution

Problem 21873

Calculate $7^{2}+10 \cdot 5^{2}+10$ .

See Solution

Problem 21874

Find the unknown product X in the reaction ${}_{12}^{26} \mathrm{Mg}+{}_{1}^{1} \mathrm{p} \rightarrow{}_{2}^{4} \alpha+\mathrm{X}$ , conserving atomic number and mass.

See Solution

Problem 21875

Solve for $b$ in the equation: $3(b-8)=-3$ . What is the value of $b$ ?

See Solution

Problem 21876

Solve for $d$ in the equation $4=\frac{d+9}{3}$ . What is $d$ ?

See Solution

Problem 21877

Solve for $j$ in the equation: $19j - 18j = 12$ . What is the value of $j$ ?

See Solution

Problem 21878

Solve for $a$ : $-27=-12+a$

See Solution

Problem 21879

Given $g(x)$ is differentiable at $x=-3$ with $g(-3)=9$ and $g'(-3)=0$ , which statements are true?

See Solution

Problem 21880

Solve for $y$ in the equation $11y - 8y - 2 = 10$ . Find $y = \square$ .

See Solution

Problem 21881

Solve for $b$ : $\frac{b - 4}{4} = 4$

See Solution

Problem 21882

Calculate the expression $(10 + 2 - 2) \cdot 6^{2} - 1$ .

See Solution

Problem 21883

Calculate the expression: $(10+2-2) \cdot 6^{2}-1$ .

See Solution

Problem 21884

False. Perpendicular lines intersect at one point.

See Solution

Problem 21885

Is it true or false that a line extends infinitely in both directions?

See Solution

Problem 21886

Is it true or false that the intersection of three planes can be a line segment?

See Solution

Problem 21887

Solve the system: $a - 3b = 24$ and $a + 2b = -16$ .

See Solution

Problem 21888

Is it true or false that the intersection of a plane and a line can be a ray?

See Solution

Problem 21889

Find the domain of $h(x)=\frac{5}{\sqrt{2 x+10}}$ in set builder notation.

See Solution

Problem 21890

Calculate $\frac{49}{7} \cdot \frac{60^{2}}{2 \cdot 5}$ .

See Solution

Problem 21891

Is this statement true or false? A plane is two-dimensional. true or false?

See Solution

Problem 21892

Find values of $a$ and $b$ for the piecewise function to be continuous and differentiable everywhere:
$f(x)=\left\{\begin{array}{ll} -x-8, & x<1 \\ \frac{2}{3} x^{2}+a x+b, & x \geq 1 \end{array}\right.$
Answer: $a=$ and $b=$

See Solution

Problem 21893

Is this true or false? A plane is one-dimensional. true false

See Solution

Problem 21894

Is it true or false that a plane and a line segment can intersect as a line segment?

See Solution

Problem 21895

Is it true or false that two lines can intersect at a point? true false

See Solution

Problem 21896

For the function $F(x)=-4+\frac{1}{x}$ , identify its domain and asymptotes. Choose the correct graph from options given.

See Solution

Problem 21897

Find the domain and range of $f(x) = -4 + \frac{1}{x}$ . Choose the correct options for each.

See Solution

Problem 21898

Find $a$ and $b$ for the function $f(x)=\begin{cases} 2x+2, & x<-4 \\ \frac{1}{6}x^2+ax+b, & x \geq -4 \end{cases}$ to be continuous and differentiable.

See Solution

Problem 21899

Find the range and vertical asymptote of the function $f(x)=-4+\frac{1}{x}$ .

See Solution

Problem 21900

Find $a$ and $b$ for the piecewise function to be continuous and differentiable: $f(x)=\begin{cases} 2x+2, & x<-4 \\ \frac{1}{6}x^2 + ax + b, & x \geq -4 \end{cases}$

See Solution

1 ...216 217 218 219 220 221 222 ...269

Math Statement

Problem 21801

Solve aaa23=ak\frac{a \sqrt{a}}{\sqrt[3]{a^{2}}}=a^{k}3a2​aa​​=ak for the value of kkk.

Problem 21802

Find the exact value of tan⁡20∘−cos⁡70∘cos⁡20∘\tan 20^{\circ}-\frac{\cos 70^{\circ}}{\cos 20^{\circ}}tan20∘−cos20∘cos70∘​ without a calculator.

Problem 21803

Find cos⁡θ\cos \thetacosθ given tan⁡θ=13\tan \theta=\frac{1}{3}tanθ=31​ and csc⁡θ<0\csc \theta<0cscθ<0. Simplify your answer.

Problem 21804

Find the domain of the function F(x)=6x(x−7)6x2−41x−7F(x)=\frac{6 x(x-7)}{6 x^{2}-41 x-7}F(x)=6x2−41x−76x(x−7)​. Is it A: x≠□x \neq \squarex=□ or B: all real numbers?

Problem 21805

Calculate the value of sin⁡π3−cos⁡π6\sin \frac{\pi}{3} - \cos \frac{\pi}{6}sin3π​−cos6π​ without a calculator. Options: 0, 3\sqrt{3}3​, 3−12\frac{\sqrt{3}-1}{2}23​−1​, 1.

Problem 21806

Find the domain of the function R(x)=xx3+216R(x)=\frac{x}{x^{3}+216}R(x)=x3+216x​. Is it A: {x∣□}\{x \mid \square\}{x∣□} or B: all real numbers?

Problem 21807

Find the vertex and y-intercept of the function f(x)=−4x2+8x+3f(x)=-4x^{2}+8x+3f(x)=−4x2+8x+3.

Problem 21808

Find cos⁡θ\cos \thetacosθ if tan⁡θ=43\tan \theta=\frac{4}{3}tanθ=34​. Options: 35\frac{3}{5}53​, 34\frac{3}{4}43​, 53\frac{5}{3}35​, 45\frac{4}{5}54​.

Problem 21809

Find f(−2)f(-2)f(−2) if f(x)=9x2+5x−8f(x)=9 x^{2}+5 x-8f(x)=9x2+5x−8. Choices: A. -54 B. -18 C. 18 D. 36 E. 38

Problem 21810

Multiply 6126 \frac{1}{2}621​ by 18131 \frac{8}{13}1138​ and simplify to a mixed number.

Problem 21811

Solve for xxx in the equation x+7−3=1\frac{x+7}{-3}=1−3x+7​=1.

Problem 21812

Find the exact value of sec⁡π3\sec \frac{\pi}{3}sec3π​. Options: 2, 2\sqrt{2}2​, 233\frac{2 \sqrt{3}}{3}323​​, 32\frac{\sqrt{3}}{2}23​​.

Problem 21813

Solve for xxx: x−1−4=−6\frac{x-1}{-4}=-6−4x−1​=−6

Problem 21814

Find tan⁡θ\tan \thetatanθ given sin⁡θ=32\sin \theta=\frac{\sqrt{3}}{2}sinθ=23​​. Choices: 233\frac{2 \sqrt{3}}{3}323​​, 3\sqrt{3}3​, 33\frac{\sqrt{3}}{3}33​​.

Problem 21815

Solve for xxx in the equation 2x3=12\frac{2 x}{3}=1232x​=12.

Problem 21816

Find the number of solutions for the equation 3(x+4)=3x+43(x+4)=3x+43(x+4)=3x+4. A) no solution B) one solution C) two solutions D) infinitely many solutions

Problem 21817

Calculate kkk using the formula: k=2(−2)2+8(−2)+7k=2(-2)^{2}+8(-2)+7k=2(−2)2+8(−2)+7.

Problem 21818

Solve: 3(2x−5)=6x−153(2x - 5) = 6x - 153(2x−5)=6x−15

Problem 21819

Find the exact value of sin⁡25π3\sin \frac{25 \pi}{3}sin325π​ using a coterminal angle. Options: −12-\frac{1}{2}−21​, −32-\frac{\sqrt{3}}{2}−23​​, 12\frac{1}{2}21​, 32\frac{\sqrt{3}}{2}23​​.

Problem 21820

Find the vertex and y-intercept of the equation y=−4x2+8x+3y=-4x^{2}+8x+3y=−4x2+8x+3.

Problem 21821

Find the exact value of cot⁡720∘\cot 720^{\circ}cot720∘ using a coterminal angle without a calculator. Options: 0, -1, 1, undefined.

Problem 21822

Round 576.558 to the nearest tenths place: 576.6, 580, 576.56, or 576.5?

Problem 21823

Find the exact value of sin⁡390∘\sin 390^{\circ}sin390∘ using a coterminal angle without a calculator.

Problem 21824

Find the intersection point of f(x)f(x)f(x) and its inverse f−1(x)f^{-1}(x)f−1(x) on the coordinate plane.

Problem 21825

Describe how the function j(x)=13(x−6)2j(x)=\frac{1}{3}(x-6)^{2}j(x)=31​(x−6)2 is transformed from its parent function.

Problem 21826

Find (c⋅d)(x)(c \cdot d)(x)(c⋅d)(x) for c(x)=4x−2c(x)=4x-2c(x)=4x−2 and d(x)=x2+5xd(x)=x^2+5xd(x)=x2+5x.

Problem 21827

Explain the transformation of the function h(x)=−(x+5)2+7h(x)=-(x+5)^{2}+7h(x)=−(x+5)2+7.

Problem 21828

Find the new vertices of △ABC\triangle A B C△ABC after these translations: 1. T⟨−2,3⟩T_{\langle-2,3\rangle}T⟨−2,3⟩​, 2. T⟨−4,−1⟩T_{\langle-4,-1\rangle}T⟨−4,−1⟩​, 3. T(4,6)T_{(4,6)}T(4,6)​.

Problem 21829

Convert 88∘F88^{\circ} \mathrm{F}88∘F to ∘C{ }^{\circ} \mathrm{C}∘C using ∘F=(∘C×9/5)+32{ }^{\circ} \mathrm{F}=\left({ }^{\circ} \mathrm{C} \times 9 / 5\right)+32∘F=(∘C×9/5)+32.

Problem 21830

Convert 20°C to °F using the formula °F = (°C × 9/5) + 32.

Problem 21831

Identify the transformation from f(x)=(2x−3)3f(x)=(2 x-3)^{3}f(x)=(2x−3)3 to g(x)=(−2x−3)3g(x)=(-2 x-3)^{3}g(x)=(−2x−3)3: A. vertical reflection B. horizontal reflection C. vertical shift D. horizontal shift.

Problem 21832

Find the value of cos⁡(−π4)\cos \left(-\frac{\pi}{4}\right)cos(−4π​) without a calculator. A. cos⁡(−π4)=\cos \left(-\frac{\pi}{4}\right)=cos(−4π​)= (simplify) B. undefined.

Problem 21833

Determine if the function f(x)=x6+10x4−11x2+19f(x)=x^{6}+10 x^{4}-11 x^{2}+19f(x)=x6+10x4−11x2+19 is even, odd, or neither. Choices: A, B, C, D.

Problem 21834

Find the limit as x approaches 1: lim⁡x→12x3+x+1−2xx−1\lim_{{x \to 1}} \frac{\sqrt{2 x^{3}+x+1}-2 x}{x-1}limx→1​x−12x3+x+1​−2x​

Problem 21835

Find the direction of the parabola given by y=−2x2+4x+3y=-2 x^{2}+4 x+3y=−2x2+4x+3. Does it open up or down?

Problem 21836

Find the vertex of the parabola defined by y=−2x2−4x−5y=-2 x^{2}-4 x-5y=−2x2−4x−5. What are the coordinates?

Problem 21837

Identify the vertex, AOS, min/max value, domain, and range of y=(x+1)2+7y=(x+1)^{2}+7y=(x+1)2+7.

Problem 21838

Convert the function y=6(x+1)2−15y=6(x+1)^{2}-15y=6(x+1)2−15 into standard form.

Problem 21839

Find the vertex of the parabola given by y=−2x2+4x+3y=-2 x^{2}+4 x+3y=−2x2+4x+3. What are the coordinates of the vertex?

Problem 21840

Solve $\frac{a \sqrt{a}}{\sqrt[3]{a^{2}}}=a^{k}$ for the value of $k$ .

Find the exact value of $\tan 20^{\circ}-\frac{\cos 70^{\circ}}{\cos 20^{\circ}}$ without a calculator.

Find $\cos \theta$ given $\tan \theta=\frac{1}{3}$ and $\csc \theta<0$ . Simplify your answer.

Find the domain of the function $F(x)=\frac{6 x(x-7)}{6 x^{2}-41 x-7}$ . Is it A: $x \neq \square$ or B: all real numbers?

Calculate the value of $\sin \frac{\pi}{3} - \cos \frac{\pi}{6}$ without a calculator. Options: 0, $\sqrt{3}$ , $\frac{\sqrt{3}-1}{2}$ , 1.

Find the domain of the function $R(x)=\frac{x}{x^{3}+216}$ . Is it A: $\{x \mid \square\}$ or B: all real numbers?

Find the vertex and y-intercept of the function $f(x)=-4x^{2}+8x+3$ .

Find $\cos \theta$ if $\tan \theta=\frac{4}{3}$ . Options: $\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{5}{3}$ , $\frac{4}{5}$ .

Find $f(-2)$ if $f(x)=9 x^{2}+5 x-8$ . Choices: A. -54 B. -18 C. 18 D. 36 E. 38

Multiply $6 \frac{1}{2}$ by $1 \frac{8}{13}$ and simplify to a mixed number.

Solve for $x$ in the equation $\frac{x+7}{-3}=1$ .

Find the exact value of $\sec \frac{\pi}{3}$ . Options: 2, $\sqrt{2}$ , $\frac{2 \sqrt{3}}{3}$ , $\frac{\sqrt{3}}{2}$ .

Solve for $x$ : $\frac{x-1}{-4}=-6$

Find $\tan \theta$ given $\sin \theta=\frac{\sqrt{3}}{2}$ . Choices: $\frac{2 \sqrt{3}}{3}$ , $\sqrt{3}$ , $\frac{\sqrt{3}}{3}$ .

Solve for $x$ in the equation $\frac{2 x}{3}=12$ .

Find the number of solutions for the equation $3(x+4)=3x+4$ . A) no solution B) one solution C) two solutions D) infinitely many solutions

Calculate $k$ using the formula: $k=2(-2)^{2}+8(-2)+7$ .

Solve: $3(2x - 5) = 6x - 15$

Find the exact value of $\sin \frac{25 \pi}{3}$ using a coterminal angle. Options: $-\frac{1}{2}$ , $-\frac{\sqrt{3}}{2}$ , $\frac{1}{2}$ , $\frac{\sqrt{3}}{2}$ .

Find the vertex and y-intercept of the equation $y=-4x^{2}+8x+3$ .

Find the exact value of $\cot 720^{\circ}$ using a coterminal angle without a calculator. Options: 0, -1, 1, undefined.

Find the exact value of $\sin 390^{\circ}$ using a coterminal angle without a calculator.

Find the intersection point of $f(x)$ and its inverse $f^{-1}(x)$ on the coordinate plane.

Describe how the function $j(x)=\frac{1}{3}(x-6)^{2}$ is transformed from its parent function.

Find $(c \cdot d)(x)$ for $c(x)=4x-2$ and $d(x)=x^2+5x$ .

Explain the transformation of the function $h(x)=-(x+5)^{2}+7$ .

Find the new vertices of $\triangle A B C$ after these translations: 1. $T_{\langle-2,3\rangle}$ , 2. $T_{\langle-4,-1\rangle}$ , 3. $T_{(4,6)}$ .

Convert $88^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$ using ${ }^{\circ} \mathrm{F}=\left({ }^{\circ} \mathrm{C} \times 9 / 5\right)+32$ .

Identify the transformation from $f(x)=(2 x-3)^{3}$ to $g(x)=(-2 x-3)^{3}$ : A. vertical reflection B. horizontal reflection C. vertical shift D. horizontal shift.

Find the value of $\cos \left(-\frac{\pi}{4}\right)$ without a calculator. A. $\cos \left(-\frac{\pi}{4}\right)=$ (simplify) B. undefined.

Determine if the function $f(x)=x^{6}+10 x^{4}-11 x^{2}+19$ is even, odd, or neither. Choices: A, B, C, D.

Find the limit as x approaches 1: $\lim_{{x \to 1}} \frac{\sqrt{2 x^{3}+x+1}-2 x}{x-1}$

Find the direction of the parabola given by $y=-2 x^{2}+4 x+3$ . Does it open up or down?

Find the vertex of the parabola defined by $y=-2 x^{2}-4 x-5$ . What are the coordinates?

Identify the vertex, AOS, min/max value, domain, and range of $y=(x+1)^{2}+7$ .

Convert the function $y=6(x+1)^{2}-15$ into standard form.

Find the vertex of the parabola given by $y=-2 x^{2}+4 x+3$ . What are the coordinates of the vertex?

Find the vertex and y-intercept of the function $y=-x^{2}+14x-30$ .

Find the vertex and y-intercept of $y=2x^{2}+20x-5$ .

Find the axis of symmetry for the parabola $y=-2 x^{2}+4 x+3$ . Write your answer as an equation.

Determine the direction the parabola $y=-2 x^{2}+4 x+1$ opens: up or down?

Identify the common factor in the polynomial $2x^{3} - 4x^{2} + x + 1$ .

Calculate the product of -23 and 40: $(-23) \cdot 40$ .

Find the $x$ -intercept and $y$ -intercept of $f(x)=4x+12$ . Choose the correct option from A, B, C, or D.

Simplify: $-8 - 1 + 4 \cdot 2$

Check if sets $A=\{0,-1,4,5,6\}$ and $B=\{0,-1,6,5,4\}$ are equal or not. Determine if $A=B$ or $A \neq B$ .

Determine if the sets $A$ and $B$ are equal:
$A=\left\{\frac{1}{2}, 0,-\frac{1}{2},-\frac{1}{8}\right\}, \quad B=\left\{\frac{1}{2}, 0, \frac{1}{3}, \frac{1}{8}\right\}$
Is $A=B$ or $A \neq B$ ?

Calculate $\left(\frac{1}{3}\right)^{5}$ . Choose from: $\frac{5}{3}$ , $\frac{1}{81}$ , $\frac{1}{27}$ , $\frac{1}{243}$ .

Find the limit as $h$ approaches 0 for the difference quotient of: 1. $f(x)=x^{2}-x$ , 2. $f(x)=\frac{1}{x+3}$ .

Calculate $11^3$ . Options: 33, 121, 1,331, 177,144.

Identify the base and exponent for $n \cdot n \cdot n \cdot n$ . Options: $n^{4}$ , $4 n^{4}$ , $4 n$ , $\frac{n}{4}$ .

Solve the compound inequality: $-4 x \leq -16$ or $4 x - 12 \geq 8$ . What is the solution?

If $H$ is a linear function, what is $H(11)-H(5)$ equivalent to? (A) $H(11)+H(5)$ (B) $\frac{H(11)-H(5)}{6}$ (C) $H(14)-H(8)$ (D) $H(11-5)$

Determine if sets $A$ and $B$ are equal: $A=\{3.1,-1.1,1.8,-2.8\}$ and $B=\{-1.1,1.8,3.1\}$ .

Convert 952 g to mg. What is the value? Use the conversion: $1 \mathrm{~g} = 1000 \mathrm{~mg}$ .

Calculate $13^2$ . Choices: 169, 26, 8192, 24.

Solve the compound inequality $x<2$ and $x>-3$ . Graph the solution and write it in interval notation.

Convert $5.287 \mathrm{~L}$ to milliliters ( $\mathrm{mL}$ ).

Simplify: $72 \div 9 + 7^{2}$

Convert $785.3 \mathrm{~km}$ to meters.

Is $B$ a subset of $A$ ? A = {-2, -4, -6, -8}, B = {-2, 4, -6, -8}. Answer Yes or No.

Select a base and exponent: $(-8) \cdot (-8)$ , $(-8)^{2}$ , $-8(-8)^{2}$ , $8^{2}$ , $64^{2}$ .

Calculate $(-2)^{8}$ . Choose from: -128, 256, -16.

Find the solution set for $x<2$ and $x>-3$ . A. The solution set is $(>k<3)$ .

מה הגבול של $\left(\sqrt[3]{x^{3}+x^{2}}-x\right)$ כש- $x$ מתקרב למינוס אינסוף?

Find the exact values of the other trigonometric functions for $\theta$ given that $\tan \theta=\frac{12}{5}$ and $\sin \theta<0$ .

Find the domain of the rational function $R(x)=\frac{7\left(x^{2}-2 x-3\right)}{8\left(x^{2}-9\right)}$ .

Evaluate the piecewise function $f$ at $x=3$ to check if it's continuous and differentiable. What is true about $f$ at $x=3$ ?

Calculate $7^{2}+10 \cdot 5^{2}+10$ .

Find the unknown product X in the reaction ${}_{12}^{26} \mathrm{Mg}+{}_{1}^{1} \mathrm{p} \rightarrow{}_{2}^{4} \alpha+\mathrm{X}$ , conserving atomic number and mass.