Math Statement

Problem 13301

Factor out the greatest common factor from $4 \cot x + 20$ .

See Solution

Problem 13302

Factor $\tan^{2} x + 9 \tan x + 20$ .

See Solution

Problem 13303

Simplify $(\cos x+\sin x)^{2}$ .

See Solution

Problem 13304

Factor the expression $25 - x^{2}$ completely over the integers.

See Solution

Problem 13305

Factor the expression $4 - \sin^2 \theta$ completely over the integers.

See Solution

Problem 13306

Solve for $\theta$ using the substitution $y=9 \cos \theta$ in the equation $\sqrt{81-y^{2}}$ .

See Solution

Problem 13307

Multiply and simplify: $\frac{5}{22} \cdot \frac{5}{8} \cdot \frac{2}{25}$ .

See Solution

Problem 13308

Simplify $\sqrt{4-x^{2}}$ using the substitution $x=2 \sin \theta$ .

See Solution

Problem 13309

Simplify: $\frac{x-3}{x^{2}-9}$ . Note: $x \neq 3$ and $x \neq -3$ .

See Solution

Problem 13310

In a right triangle, if $a=2$ (opposite angle $A$ ) and $b=7$ (hypotenuse), find $\sin(A)$ , $\cos(A)$ , $\tan(A)$ , $\sec(A)$ , $\csc(A)$ , $\cot(A)$ .

See Solution

Problem 13311

Calculate: $-\frac{2}{3}+\frac{3}{5} \times 1 \frac{5}{8}-\frac{3}{5}$ .

See Solution

Problem 13312

Simplify the expression by substituting exact values: $(2 \cos(60^{\circ}))^{2}$ and provide the exact answer.

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Problem 13313

Simplify these expressions using exact values: a) $\frac{\tan(60^{\circ})}{\tan(45^{\circ})$ b) $\sin(30^{\circ}) \cos(60^{\circ}) - \cos(30^{\circ}) \sin(60^{\circ})$ c) $\sin^{2}(45^{\circ}) - 2\sin(45^{\circ})\cos(45^{\circ}) + \cos^{2}(45^{\circ})$ d) $\tan^{2}(60^{\circ}) - \tan^{2}(45^{\circ})$

See Solution

Problem 13314

Simplify: $80 \div 2^{3} \times 5$

See Solution

Problem 13315

Calculate $34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}$ .

See Solution

Problem 13316

Simplify the expression: $80 \div 2^{3} \times 5$ . List the steps.

See Solution

Problem 13317

Calculate $3(15-9)^{2}+2 \cdot 5$ .

See Solution

Problem 13318

Hitung nilai $P_{31}$ dari $P=3\begin{bmatrix}-1 & -2 \\ 2 & 4 \\ 1 & 5\end{bmatrix}$ .

See Solution

Problem 13319

Find the value of $k$ for which the system $-12x + 4y = 40$ and $Ax - 2y = -20$ has no solution.

See Solution

Problem 13320

Find the value of $k$ for which the system $-12x + 4y = 40$ and $Ax - 2y = -20$ has no solution.

See Solution

Problem 13321

Find the value of $a$ for the system of equations with infinite solutions: $\frac{1}{2} x+\frac{1}{3} y=\frac{1}{6}$ and $a x+y=c$ .

See Solution

Problem 13322

Determine if the statement "No irrational numbers are real numbers" is True or False.

See Solution

Problem 13323

All integers can be expressed as fractions, confirming they are rational numbers.

See Solution

Problem 13324

Calculate the value of $\frac{10-6 \times 2+8}{(4-7)^{2}-3(4+8)}$ .

See Solution

Problem 13325

Solve the inequality: $\frac{3}{4} x+\frac{1}{2} \leq \frac{5}{4}$ .

See Solution

Problem 13326

Calculate the sum: $\frac{4}{9} + \frac{1}{3} =$

See Solution

Problem 13327

Calculate the product: $\left(\frac{4}{5}\right)\left(\frac{1}{6}\right)=$

See Solution

Problem 13328

Simplify the following expressions and show your work (2 points each):
19. $1000^{\frac{2}{3}}$ ,
22. $125^{\frac{2}{3}}$ ,
25. $(-16)^{\frac{3}{2}}$ ,
20. $9^{\frac{5}{2}}$ ,
23. $25^{\frac{3}{2}}$ ,
26. $-125^{\frac{2}{3}}$ ,
18. $(-343)^{\frac{4}{3}}$ ,
21. $64^{\frac{3}{2}}$ ,
24. $16^{\frac{3}{2}}$ ,
27. $36^{\frac{3}{2}}$ .

See Solution

Problem 13329

Solve for x: $\frac{x}{4}=7$

See Solution

Problem 13330

Calculate $(-343)^{\frac{4}{3}}$ .

See Solution

Problem 13331

Calculate $1000^{\frac{2}{3}}$ .

See Solution

Problem 13332

Solve for $x$ in the equation $\frac{32}{x}=\frac{5}{8}$ .

See Solution

Problem 13333

Solve for $x$ in the equation $\frac{2}{5} x - 7 = 10$ .

See Solution

Problem 13334

Solve the equation: $3 x - (x + 9) = 4 x + 15 + 2(x - 8)$ .

See Solution

Problem 13335

Calculate $125^{\frac{2}{3}}$ .

See Solution

Problem 13336

Solve the equation: $3 x - 6 = 5 x + 8$

See Solution

Problem 13337

Solve the equation: $\frac{15}{u}=3$ for $u$ .

See Solution

Problem 13338

Calculate the expression $-49 / (-9 - -2)$ .

See Solution

Problem 13339

1. What is $123 / -41$ ?

See Solution

Problem 13340

Calculate $-49 / (-9 - -2)$ .

See Solution

Problem 13341

Calculate the value of $\frac{3^{4} \cdot 2^{-3} \cdot 5^{2} \cdot 2^{-3}}{5 \cdot(-3)^{-2} \cdot 3 \cdot(-3)^{3}}$ .

See Solution

Problem 13342

Calculate $\frac{3}{7} \div \frac{4}{9} + \left(\frac{3}{7} - \frac{7}{9}\right)$ .

See Solution

Problem 13343

Convert $222 \div 9$ into a mixed number.

See Solution

Problem 13344

Convert $222 \div 9$ into a mixed number.

See Solution

Problem 13345

Find $f(-2)$ , $f(-\frac{2}{5})$ , and $f(4)$ for the piecewise function $f(x)$ defined as: $f(x)=\begin{cases} 2x-3 & -5 \leq x \leq -2 \\ x^2 & -2 < x \leq 2 \\ -\frac{3}{2}x + \frac{7}{2} & 2 < x \leq 5 \end{cases}$

See Solution

Problem 13346

Solve for $a$ in the equation $a^{\frac{2}{5}}=2$ .

See Solution

Problem 13347

Convert $67 / 8$ to a fraction that is greater than 1.

See Solution

Problem 13348

Convert the complex number $\frac{3+i}{1+2 i}$ to standard form $(a+b i)$ .

See Solution

Problem 13349

Simplify: $4 - \left[\left(4b^{3} - 25b^{2} + 14b - 2\right) \div (4b - 1)\right] - \square b^{2} + b$

See Solution

Problem 13350

Find the slope of the tangent line for $r=3 \cos \theta$ at $\theta=\frac{\pi}{3}$ .

See Solution

Problem 13351

Solve the equations: $2s - \frac{1}{3}t = 10$ and $5s = t + 12 - s$ . Choose the correct statement about solutions.

See Solution

Problem 13352

Calculate the product of the complex numbers $z_{1}=5-4 i$ and $z_{2}=5+4 i$ : find $z_{1} z_{2}$ .

See Solution

Problem 13353

Solve for $x$ : $2|3 x-4|+15=43$

See Solution

Problem 13354

Find the value of $b$ if the graph of $y=\log _{b} x$ passes through $(8, 2)$ . Choices: a. 10, b. 2, c. $2\sqrt{2}$ , d. $2\sqrt{3}$ .

See Solution

Problem 13355

Calculate $\pm \sqrt{64+36}$ .

See Solution

Problem 13356

Identify the function for a geometric sequence: A. $A(n)=P+(n-1) i \cdot P$ B. $A(n)=n+(i-1) \cdot P$ C. $A(n)=(n-1)(P \cdot n)^{i}$ D. $A(n)=P(1+i)^{n-1}$

See Solution

Problem 13357

Identify the number set for $-\sqrt{49}$ using N, W, Z, Q, or T.

See Solution

Problem 13358

Solve for $z$ in the equation: $4x + 8z = 2$ .

See Solution

Problem 13359

Explain why $\overline{B D} \cong \overline{B D}$ in the proof of $\angle A \simeq \angle C$ in $\triangle A B C$ .

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Problem 13360

Divide the number 6670657365686665686362656468686674666471 by 20.

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Problem 13361

Identify $\mathrm{OH}^-$ as the conjugate base, acid, or conjugate acid in the reaction: $\mathrm{CH}_{3} \mathrm{NH}_{2} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} + \mathrm{OH}^{-}$ .

See Solution

Problem 13362

Calculate the distance between points $P(2,8)$ and $Q(5,3)$ . Options: A. 9 B. $\sqrt{18}$ C. $\sqrt{34}$ D. $\sqrt{170}$

See Solution

Problem 13363

Find the range of $f(x)=2^{x}-10$ for integers $x$ from -1 to 3. Which values are in the range? Options: -12, -10, -9, -6, -2.

See Solution

Problem 13364

Find the equivalent ratio to $3:5$ from these options: $6:18$ , $9:15$ , $12:15$ , $15:20$ .

See Solution

Problem 13365

Solve for $x$ in the equation: $\frac{1}{3} x+\frac{1}{4}=\frac{5}{12}$ .

See Solution

Problem 13366

Solve the equation $2x + 1 = 2(x + 1)$ .

See Solution

Problem 13367

Solve for $x$ in the equation: $-x + 21 = 44$ .

See Solution

Problem 13368

Simplify the expression using the distributive property: $\frac{1}{6}\left(\frac{3}{5} x+18\right)$ .

See Solution

Problem 13369

Find the values of $x$ that satisfy the equation $x^{2}=1$ .

See Solution

Problem 13370

Future Amount $=[30](1+0.20)$

See Solution

Problem 13371

Find the value of $1+7$ based on the pattern: $2+3=25$ , $4+5=45$ , $0+8=40$ .

See Solution

Problem 13372

Calculate the Future Amount using $=30(1+0.20)^{3}$ . Evaluate the expression inside the parentheses first.

See Solution

Problem 13373

Solve for $3-a$ given the equations $3+a=4-b$ and $4+b=7+a$ .

See Solution

Problem 13374

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

See Solution

Problem 13375

Find $(A \cup B) \cup C$ for sets $A=\{1,2,3,4,5,6,7,8\}$ , $B=\{2,4,6,10,12,14\}$ , and $C=\{5,7,9,11,13,15\}$ .

See Solution

Problem 13376

Calculate $3.2 - (-5.7)$ . What is the result?

See Solution

Problem 13377

Calculate $-50 \frac{1}{2} + (-12.3)$ .

See Solution

Problem 13378

求解方程 $8^{a+9}=9^{a+8}$ ，找出 $a$ 的值。

See Solution

Problem 13379

Solve for ? in the equation: $-50 ? + 123 = 0$ .

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Problem 13380

Rewrite the function $f(x)=\frac{1}{x-3}+1$ into standard polynomial form.

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Problem 13381

Find $V_{2}$ in the equation $P_{1} V_{1}=P_{2} V_{2}$ .

See Solution

Problem 13382

Find $\Delta \mathrm{T}$ from the equation: $q = m \times \Delta T \times C$ .

See Solution

Problem 13383

Simplify the expression: $\frac{15 x+36}{\frac{2}{x+2}+\frac{3}{x+3}}$ ?

See Solution

Problem 13384

If $BD$ bisects $\angle ABC$ , find $m \angle ABD$ , $m \angle CBD$ , and $m \angle ABC$ with $m \angle ABC = (25x+34)^\circ$ and $m \angle CBD = (11x+22)^\circ$ .

See Solution

Problem 13385

Find an equivalent expression for $-3(y-4)$ . A. $-3 y-4$ B. $-3 y+4$ C. $-3 y-12$ D. $-3 y+12$

See Solution

Problem 13386

Find the value of $(-1)^{-1}$ .

See Solution

Problem 13387

Find $a$ so that $\lim_{{x \rightarrow \infty}} \frac{ax^{3}+4x^{2}-x-1}{3x^{3}+x^{2}-9} = -5$ .

See Solution

Problem 13388

Choose the correct expanded form of 4.012: (A) $4+0.1+0.02$ (B) $4+0.1+0.002$ (C) $4+0.01+0.02$ (D) $4+0.01+0.002$

See Solution

Problem 13389

Prove that if $m \angle \mathrm{A}+m \angle \mathrm{B}=m \angle \mathrm{B}+m \angle \mathrm{C}$ , then $m \angle \mathrm{C}=m \angle \mathrm{A}$ . Write a paragraph proof.

See Solution

Problem 13390

Determine the domain of the function $q(x)=\sqrt{7-x}$ .

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Problem 13391

Plot the piecewise function $g(x) = \begin{cases} -6 & \text{if } x < -2 \\ (x+1)^{2} & \text{if } x \geq -2 \end{cases}$ and identify where it increases or decreases.

See Solution

Problem 13392

Find the formula for one exterior angle of a polygon with $n$ sides.

See Solution

Problem 13393

Find the formula for one interior angle of a polygon with $n$ sides. Use the formula $\frac{(n-2) \cdot 180}{n}$ .

See Solution

Problem 13394

Find the domain of the function $g(x)=\frac{2}{3} x^{2}-\frac{1}{6} \times \frac{3}{4}$ .

See Solution

Problem 13395

A bacterium triples every hour. Start with 90. Find the count at hour 5 using $a(n)=90 \cdot 3^{n-1}$ . Options: A. 21,870 B. 810 C. 7290 D. 1350

See Solution

Problem 13396

Which function represents the simple interest formula? A. $A(n)=(n-1)(P \cdot i)^{n}$ B. $A(n)=P(1+i)^{n-1}$ C. $A(n)=P+(n-1) i \cdot P$ D. $A(n)=n+(P-1) i \cdot P$

See Solution

Problem 13397

774 divided by 24 equals what? Options: 750, 36 R 10, 32, 32 R 6.

See Solution

Problem 13398

Graph the piecewise function $f(x)=\left\{\begin{array}{r}x \text { if } x \leq-3 \\ -2 x+1 \text { if } x>-3\end{array}\right.$ and find its domain $D$ and range $R$ .

See Solution

Problem 13399

Solve for x in the equation: $211 = 10x + 10 + 21$ .

See Solution

Problem 13400

Calculate $225,000 \div 900$ . What is the result? Choose from: 250, 2,500, 25,000, 224,100.

See Solution

1 ...131 132 133 134 135 136 137 ...270

Math Statement

Problem 13301

Factor out the greatest common factor from 4cot⁡x+204 \cot x + 204cotx+20.

Problem 13302

Factor tan⁡2x+9tan⁡x+20\tan^{2} x + 9 \tan x + 20tan2x+9tanx+20.

Problem 13303

Simplify (cos⁡x+sin⁡x)2(\cos x+\sin x)^{2}(cosx+sinx)2.

Problem 13304

Factor the expression 25−x225 - x^{2}25−x2 completely over the integers.

Problem 13305

Factor the expression 4−sin⁡2θ4 - \sin^2 \theta4−sin2θ completely over the integers.

Problem 13306

Solve for θ\thetaθ using the substitution y=9cos⁡θy=9 \cos \thetay=9cosθ in the equation 81−y2\sqrt{81-y^{2}}81−y2​.

Problem 13307

Multiply and simplify: 522⋅58⋅225\frac{5}{22} \cdot \frac{5}{8} \cdot \frac{2}{25}225​⋅85​⋅252​.

Problem 13308

Simplify 4−x2\sqrt{4-x^{2}}4−x2​ using the substitution x=2sin⁡θx=2 \sin \thetax=2sinθ.

Problem 13309

Simplify: x−3x2−9\frac{x-3}{x^{2}-9}x2−9x−3​. Note: x≠3x \neq 3x=3 and x≠−3x \neq -3x=−3.

Problem 13310

In a right triangle, if a=2a=2a=2 (opposite angle AAA) and b=7b=7b=7 (hypotenuse), find sin⁡(A)\sin(A)sin(A), cos⁡(A)\cos(A)cos(A), tan⁡(A)\tan(A)tan(A), sec⁡(A)\sec(A)sec(A), csc⁡(A)\csc(A)csc(A), cot⁡(A)\cot(A)cot(A).

Problem 13311

Calculate: −23+35×158−35-\frac{2}{3}+\frac{3}{5} \times 1 \frac{5}{8}-\frac{3}{5}−32​+53​×185​−53​.

Problem 13312

Simplify the expression by substituting exact values: (2cos⁡(60∘))2(2 \cos(60^{\circ}))^{2}(2cos(60∘))2 and provide the exact answer.

Problem 13313

Problem 13314

Simplify: 80÷23×580 \div 2^{3} \times 580÷23×5

Problem 13315

Calculate 34⋅(2541)⋅(1730)34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}34⋅(24​51​)⋅(13​70​).

Problem 13316

Simplify the expression: 80÷23×580 \div 2^{3} \times 580÷23×5. List the steps.

Problem 13317

Calculate 3(15−9)2+2⋅53(15-9)^{2}+2 \cdot 53(15−9)2+2⋅5.

Problem 13318

Hitung nilai P31P_{31}P31​ dari P=3[−1−22415]P=3\begin{bmatrix}-1 & -2 \\ 2 & 4 \\ 1 & 5\end{bmatrix}P=3⎣⎡​−121​−245​⎦⎤​.

Problem 13319

Find the value of kkk for which the system −12x+4y=40-12x + 4y = 40−12x+4y=40 and Ax−2y=−20Ax - 2y = -20Ax−2y=−20 has no solution.

Problem 13320

Find the value of kkk for which the system −12x+4y=40-12x + 4y = 40−12x+4y=40 and Ax−2y=−20Ax - 2y = -20Ax−2y=−20 has no solution.

Problem 13321

Find the value of aaa for the system of equations with infinite solutions: 12x+13y=16 \frac{1}{2} x+\frac{1}{3} y=\frac{1}{6} 21​x+31​y=61​ and ax+y=c a x+y=c ax+y=c.

Problem 13322

Determine if the statement "No irrational numbers are real numbers" is True or False.

Problem 13323

All integers can be expressed as fractions, confirming they are rational numbers.

Problem 13324

Calculate the value of 10−6×2+8(4−7)2−3(4+8)\frac{10-6 \times 2+8}{(4-7)^{2}-3(4+8)}(4−7)2−3(4+8)10−6×2+8​.

Problem 13325

Solve the inequality: 34x+12≤54\frac{3}{4} x+\frac{1}{2} \leq \frac{5}{4}43​x+21​≤45​.

Problem 13326

Calculate the sum: 49+13=\frac{4}{9} + \frac{1}{3} = 94​+31​=

Problem 13327

Calculate the product: (45)(16)=\left(\frac{4}{5}\right)\left(\frac{1}{6}\right)=(54​)(61​)=

Problem 13328

Problem 13329

Solve for x: x4=7\frac{x}{4}=74x​=7

Problem 13330

Calculate (−343)43(-343)^{\frac{4}{3}}(−343)34​.

Problem 13331

Calculate 1000231000^{\frac{2}{3}}100032​.

Problem 13332

Solve for xxx in the equation 32x=58\frac{32}{x}=\frac{5}{8}x32​=85​.

Problem 13333

Solve for xxx in the equation 25x−7=10\frac{2}{5} x - 7 = 1052​x−7=10.

Problem 13334

Solve the equation: 3x−(x+9)=4x+15+2(x−8)3 x - (x + 9) = 4 x + 15 + 2(x - 8)3x−(x+9)=4x+15+2(x−8).

Problem 13335

Calculate 12523125^{\frac{2}{3}}12532​.

Problem 13336

Solve the equation: 3x−6=5x+83 x - 6 = 5 x + 83x−6=5x+8

Problem 13337

Solve the equation: 15u=3\frac{15}{u}=3u15​=3 for uuu.

Problem 13338

Calculate the expression −49/(−9−−2)-49 / (-9 - -2)−49/(−9−−2).

Problem 13339

1. What is 123/−41123 / -41123/−41?

Problem 13340

Calculate −49/(−9−−2)-49 / (-9 - -2)−49/(−9−−2).

Problem 13341

Factor out the greatest common factor from $4 \cot x + 20$ .

Factor $\tan^{2} x + 9 \tan x + 20$ .

Simplify $(\cos x+\sin x)^{2}$ .

Factor the expression $25 - x^{2}$ completely over the integers.

Factor the expression $4 - \sin^2 \theta$ completely over the integers.

Solve for $\theta$ using the substitution $y=9 \cos \theta$ in the equation $\sqrt{81-y^{2}}$ .

Multiply and simplify: $\frac{5}{22} \cdot \frac{5}{8} \cdot \frac{2}{25}$ .

Simplify $\sqrt{4-x^{2}}$ using the substitution $x=2 \sin \theta$ .

Simplify: $\frac{x-3}{x^{2}-9}$ . Note: $x \neq 3$ and $x \neq -3$ .

In a right triangle, if $a=2$ (opposite angle $A$ ) and $b=7$ (hypotenuse), find $\sin(A)$ , $\cos(A)$ , $\tan(A)$ , $\sec(A)$ , $\csc(A)$ , $\cot(A)$ .

Calculate: $-\frac{2}{3}+\frac{3}{5} \times 1 \frac{5}{8}-\frac{3}{5}$ .

Simplify the expression by substituting exact values: $(2 \cos(60^{\circ}))^{2}$ and provide the exact answer.

Simplify: $80 \div 2^{3} \times 5$

Calculate $34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}$ .

Simplify the expression: $80 \div 2^{3} \times 5$ . List the steps.

Calculate $3(15-9)^{2}+2 \cdot 5$ .

Hitung nilai $P_{31}$ dari $P=3\begin{bmatrix}-1 & -2 \\ 2 & 4 \\ 1 & 5\end{bmatrix}$ .

Find the value of $k$ for which the system $-12x + 4y = 40$ and $Ax - 2y = -20$ has no solution.

Find the value of $k$ for which the system $-12x + 4y = 40$ and $Ax - 2y = -20$ has no solution.

Find the value of $a$ for the system of equations with infinite solutions: $\frac{1}{2} x+\frac{1}{3} y=\frac{1}{6}$ and $a x+y=c$ .

Calculate the value of $\frac{10-6 \times 2+8}{(4-7)^{2}-3(4+8)}$ .

Solve the inequality: $\frac{3}{4} x+\frac{1}{2} \leq \frac{5}{4}$ .

Calculate the sum: $\frac{4}{9} + \frac{1}{3} =$

Calculate the product: $\left(\frac{4}{5}\right)\left(\frac{1}{6}\right)=$

Solve for x: $\frac{x}{4}=7$

Calculate $(-343)^{\frac{4}{3}}$ .

Calculate $1000^{\frac{2}{3}}$ .

Solve for $x$ in the equation $\frac{32}{x}=\frac{5}{8}$ .

Solve for $x$ in the equation $\frac{2}{5} x - 7 = 10$ .

Solve the equation: $3 x - (x + 9) = 4 x + 15 + 2(x - 8)$ .

Calculate $125^{\frac{2}{3}}$ .

Solve the equation: $3 x - 6 = 5 x + 8$

Solve the equation: $\frac{15}{u}=3$ for $u$ .

Calculate the expression $-49 / (-9 - -2)$ .

1. What is $123 / -41$ ?

Calculate $-49 / (-9 - -2)$ .

Calculate the value of $\frac{3^{4} \cdot 2^{-3} \cdot 5^{2} \cdot 2^{-3}}{5 \cdot(-3)^{-2} \cdot 3 \cdot(-3)^{3}}$ .

Calculate $\frac{3}{7} \div \frac{4}{9} + \left(\frac{3}{7} - \frac{7}{9}\right)$ .

Convert $222 \div 9$ into a mixed number.

Convert $222 \div 9$ into a mixed number.

Solve for $a$ in the equation $a^{\frac{2}{5}}=2$ .

Convert $67 / 8$ to a fraction that is greater than 1.

Convert the complex number $\frac{3+i}{1+2 i}$ to standard form $(a+b i)$ .

Simplify: $4 - \left[\left(4b^{3} - 25b^{2} + 14b - 2\right) \div (4b - 1)\right] - \square b^{2} + b$

Find the slope of the tangent line for $r=3 \cos \theta$ at $\theta=\frac{\pi}{3}$ .

Solve the equations: $2s - \frac{1}{3}t = 10$ and $5s = t + 12 - s$ . Choose the correct statement about solutions.

Calculate the product of the complex numbers $z_{1}=5-4 i$ and $z_{2}=5+4 i$ : find $z_{1} z_{2}$ .

Solve for $x$ : $2|3 x-4|+15=43$

Find the value of $b$ if the graph of $y=\log _{b} x$ passes through $(8, 2)$ . Choices: a. 10, b. 2, c. $2\sqrt{2}$ , d. $2\sqrt{3}$ .

Calculate $\pm \sqrt{64+36}$ .

Identify the function for a geometric sequence: A. $A(n)=P+(n-1) i \cdot P$ B. $A(n)=n+(i-1) \cdot P$ C. $A(n)=(n-1)(P \cdot n)^{i}$ D. $A(n)=P(1+i)^{n-1}$

Identify the number set for $-\sqrt{49}$ using N, W, Z, Q, or T.

Solve for $z$ in the equation: $4x + 8z = 2$ .

Explain why $\overline{B D} \cong \overline{B D}$ in the proof of $\angle A \simeq \angle C$ in $\triangle A B C$ .

Identify $\mathrm{OH}^-$ as the conjugate base, acid, or conjugate acid in the reaction: $\mathrm{CH}_{3} \mathrm{NH}_{2} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} + \mathrm{OH}^{-}$ .

Calculate the distance between points $P(2,8)$ and $Q(5,3)$ . Options: A. 9 B. $\sqrt{18}$ C. $\sqrt{34}$ D. $\sqrt{170}$

Find the range of $f(x)=2^{x}-10$ for integers $x$ from -1 to 3. Which values are in the range? Options: -12, -10, -9, -6, -2.

Find the equivalent ratio to $3:5$ from these options: $6:18$ , $9:15$ , $12:15$ , $15:20$ .

Solve for $x$ in the equation: $\frac{1}{3} x+\frac{1}{4}=\frac{5}{12}$ .

Solve the equation $2x + 1 = 2(x + 1)$ .

Solve for $x$ in the equation: $-x + 21 = 44$ .

Simplify the expression using the distributive property: $\frac{1}{6}\left(\frac{3}{5} x+18\right)$ .

Find the values of $x$ that satisfy the equation $x^{2}=1$ .

Future Amount $=[30](1+0.20)$

Find the value of $1+7$ based on the pattern: $2+3=25$ , $4+5=45$ , $0+8=40$ .

Calculate the Future Amount using $=30(1+0.20)^{3}$ . Evaluate the expression inside the parentheses first.

Solve for $3-a$ given the equations $3+a=4-b$ and $4+b=7+a$ .

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