Math Statement

Problem 16201

For the function $f(x)=5 x-1$ , find each of the following. (a) $f(p)$ $f(p)=5 p-1$ (Simplify your answer.) (b) $f(-r)$ $f(-r)=-5 r-1$ (Simplify your answer.) (c) $f(m-2)$ $f(m-2)=$ $\square$ (Simplify your answer.)

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Problem 16202

Use any convenient method to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form. $\left\{\begin{array}{rr} -3 x+3 y+6 z= & -12 \\ x+7 y-z= & 27 \\ 4 x+4 y-7 z= & 39 \end{array}\right.$

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Problem 16203

3) Evaluate $\int_{4}^{12} \frac{1}{\sqrt[3]{x-4}} d x$

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Problem 16204

Use a sum-to-product formula to find the exact value. Write your answer as a simplified fraction and rationalize the denominator, if nece $\sin 165^{\circ}-\sin 75^{\circ}=$ $\square$ $\sqrt{\text { 延 }}$

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Problem 16205

Difference of S Ex: Factor $x^{2}-16=x^{2}+0 x-16$

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Problem 16206

Simplify. $\left(v^{-6}\right)^{-6}$
Write your answer without using negative exponents.

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Problem 16207

Factor by grouping. $6 x^{3}-12 x^{2}-7 x+14$

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Problem 16208

2 . In Exercises 23-28, graph three periods of the function. Use your understanding of transformations, not your grapher. Be sure to show the scale on both axes.
23. $y=5 \sin 2 x$
24. $y=3 \cos \frac{x}{2}$
25. $y=0.5 \cos 3 x$
26. $y=20 \sin 4 x$

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Problem 16209

Simplify. $\sqrt{v^{14}}$
Assume that the variable represents a positive real number.

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Problem 16210

Factor. $128 c^{2}-50$

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Problem 16211

$-\left(\frac{-8}{2}\right)^{2}+1-(-3)^{2}$

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Problem 16212

Write an equivalent expression $-6)^{4}(y-4) 1$
Select all that apply A. $-6(4 y-4)$ B $-6\left(x_{y}-16\right)$ C. $-24 y+96$ D. $-6 y=$ vel E. $-24 y-96$

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Problem 16213

Evaluate the expressions. $\begin{array}{r} -2\left(\frac{2}{3}\right)^{0}= \\ -(4)^{0}= \end{array}$

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Problem 16214

Rewrite the following without an exponent. $(-3)^{-2}$

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Problem 16215

isentity whichic expressions are equivalent to the given expression $2(2 y+2)$
Which of the following is equivalent to the expression $2(2 y+2)$ ? Select all that apply. A. $4 y+6$ - 2 - $+2=2$ y C. $4 y+4$

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Problem 16216

$\begin{array}{c}-(8)^{2}= \\ -(-6)^{3}=\end{array}$

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Problem 16217

[EX1] Simplify each rational expres (1) $\frac{5 x}{6}+\frac{3-x}{4}$

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Problem 16218

18 Write the equation of the line in slope-intercept form with the following slope and y-intercept: $\mathrm{m}=\frac{5}{2}$ $y$ -intercept $=(0,-2)$ $\square$

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Problem 16219

Solve the equation $(x-3)^{2 / 3}+(x-3)^{1 / 3}-6=0$ .

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Problem 16220

Solve for $x$ in the equation $a \sec x = 3$ .

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Problem 16221

Solve for $x$ if $\sec x=3$ .

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Problem 16222

Evaluate $\frac{3-4 i}{5 i}$ and express the result as $a + b i$ .

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Problem 16223

Calculate the result of the complex division: $(-38+135 i) \div(11-10 i)$ .

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Problem 16224

Divide $\frac{-3-4 i}{2 i}$ and express the answer as $a + bi$ .

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Problem 16225

Simplify $\frac{\sqrt{-1}}{\sqrt{-9} \sqrt{-7}}$ and express it as $a + bi$ .

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Problem 16226

Calculate the product of $(-6-4i)$ and its conjugate $(-6+4i)$ .

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Problem 16227

Factor the trinomial $42 x^{2}-53 x+15$ .

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Problem 16228

Factor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

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Problem 16229

Solve the equation $x^{2}-24 x+143=0$ .

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Problem 16230

Prove that $\frac{1+\sin x}{\cos x}+\frac{\cos x}{1+\sin x} \equiv 2 \sec x$ .

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Problem 16231

Solve the equation: $p^{2}-144=0$ . Enter your integer or reduced fraction answers separated by commas.

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Problem 16232

Prove that $\frac{1-\cos ^{2} x}{\sec ^{2} x-1} = 1-\sin ^{2} x$ .

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Problem 16233

Show that $\frac{\sin x}{1-\cos^{2} x} = \operatorname{cosec} x$ .

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Problem 16234

Factor and solve the equation $6 a^{2}-21 a-12=0$ . List your answers separated by a comma.

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Problem 16235

Prove that $\sec ^{4} \theta - \sec ^{2} \theta = \tan ^{2} \theta + \tan ^{4} \theta$ .

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Problem 16236

Prove that $\frac{1+\sin x}{1-\sin x} \equiv(\tan x+\sec x)^{2}$ .

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Problem 16237

Solve the equation $-2x^2 - 20x - 42 = 0$ by first dividing by $-2$ .

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Problem 16238

Solve $2x^2 + 5x - 12 = 0$ using the quadratic formula. List the solutions, separated by commas.

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Problem 16239

Prove that $\left(\frac{1+\sin x}{\cos x}\right)^{2}+\left(\frac{1-\sin x}{\cos x}\right)^{2} = 2 \sec ^{2} x+2 \tan ^{2} x$ .

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Problem 16240

Rewrite the equation $x^{2}+2x-99=0$ by completing the square and solve for $x$ .

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Problem 16241

Solve the equation $4 w^{2}+w-7=0$ using the quadratic formula. List solutions, separated by commas.

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Problem 16242

Solve the equation by completing the square: $x^{2}-8 x+26=5$ . Find the roots.

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Problem 16243

Solve for $x$ using the quadratic formula for the equation $4x^{2} + 12x + 12 = 0$ .

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Problem 16244

Solve the equation $2 z^{2}+3 z-1=0$ and provide simplified answers, separated by commas.

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Problem 16245

Solve the equation $4 w^{2}+3 w+12=2$ and simplify your answer, including non-real solutions. $w=$

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Problem 16246

Solve for $x$ in the equation $\log _{2}(x+4)=3$ .

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Problem 16247

Solve $9 \cot ^{2} \frac{1}{2} x=4$ for $-180^{\circ} \leq x \leq 180^{\circ}$ .

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Problem 16248

Solve $2 \operatorname{cosec}(2 x-1)=3$ for $-\pi \leq x \leq \pi$ .

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Problem 16249

Find the value of $\mathrm{c}$ if the line $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ passes through the origin.

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Problem 16250

Find the orientation, center, vertices, conjugate axis ends, foci, and lengths of the axes for $\frac{y^{2}}{16}-x^{2}=1$ . Graph it.

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Problem 16251

Determine the center, vertices, foci, and axis of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and graph it.

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Problem 16252

Graph the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and determine its asymptotes.

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Problem 16253

Determine the transverse and conjugate axes of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and sketch its graph.

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Problem 16254

Convert the hyperbola equation $-16x^{2}+y^{2}+128x-272=0$ to standard form and graph it.

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Problem 16255

Calculate the integral $\int_{1}^{5}\left(x+\frac{2}{x^{2}}\right) d x$ using the trapezium rule at $x=1,2,3,4,5$ , rounded to two decimal places.

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Problem 16256

Convert the hyperbola equation $16x^{2}-9y^{2}+32x-18y-137=0$ to standard form and graph it.

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Problem 16257

Find the limit as $x$ approaches -2 for $\frac{x^{3}+8}{x+2}$ .

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Problem 16258

Analyze the function $f\left(x_{1}, x_{2}\right)=x_{1}^{2} x_{2}^{2}$ . Is it constant, increasing, or decreasing returns to scale?

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Problem 16259

Solve for $x$ : $\frac{x+1}{x}+\frac{3}{4}=\frac{-3}{x}$ . What is $x$ ?

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Problem 16260

Solve for $x$ in the equation $\frac{7}{2} x=\frac{4}{3} x-\frac{1}{6}$ .

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Problem 16261

Solve $\frac{7}{x}=\frac{2}{3 x}-10$ for $x$ . What is $x$ ?

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Problem 16262

Solve for $x$ in the equation $\frac{1}{x+4}=\frac{4}{x-4}$ . What is $x$ ?

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Problem 16263

Solve for $x$ in the equation $x^{3 / 7}=27$ .

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Problem 16264

Divide 72 by 5, then divide that result by 7. What is the final answer?

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Problem 16265

Solve for $x$ : $(5x + 4)^{5/7} = 32$ ; find $x = \square$ .

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Problem 16266

Solve the equation $|6x + 7| = 49$ . List all solutions separated by commas.

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Problem 16267

Solve for $x$ : $(x+5)^{3/7} = 8$ . What is the value of $x$ ?

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Problem 16268

Find the value of $k$ for each case:
19. $2^{4 k}=16^{2}$ ,
20. $2^{8-3 k}=0.5$ ,
21. $19^{5 k-3}=\frac{1}{19^{k-3}}$ ,
22. $\left(\frac{1}{6^{k}}\right)^{2}=216^{2}$ .

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Problem 16269

Solve the equation: $|5x - 8| = 32$ . List all solutions, separated by commas.

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Problem 16270

Solve for $x$ : $-3 + 7|4x - 8| = -38$ . If multiple solutions, separate with commas; if none, enter DNE.

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Problem 16271

Solve for $x$ in the equation $|x-9|=4$ . Separate your answers with a comma.

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Problem 16272

Solve for $x$ : $-5 + 6|4x - 6| = 31$ . If multiple solutions, separate with commas.

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Problem 16273

Solve for $x$ : $\sqrt{x-9}=9$ . What is $x$ ?

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Problem 16274

Solve $\sqrt{x+1}+5=8$ for $x$ .

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Problem 16275

Calculate $29 \cdot 40$ and then find $29 \cdot 40 \div 12$ .

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Problem 16276

Solve the equation $\sqrt{5 x-8}=\sqrt{x+2}$ . Find the value of $x$ .

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Problem 16277

Convert these numbers to scientific notation: 0.00000056, -193.47, $0.0531 \times 10^{8}$ , $-3671 \times 10^{5}$ .

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Problem 16278

Calculate $29 \cdot 40 \div 12$ .

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Problem 16279

Solve for $x$ : $\sqrt{4x+3}=\sqrt{3x+11}$ . If no solution, write DNE. $x=$

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Problem 16280

Convert these numbers to scientific notation: 0.00000056, -193.47, $0.0531 \times 10^{8}$ , $-3671 \times 10^{5}$ . Also, simplify: $2.9 \times 10^{5}$ , $56 \times 10^{-4}$ .

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Problem 16281

Solve: $\sqrt{x+2}-\sqrt{x-2}=6$ . Find $x=$ (integers or fractions, or DNE if no solutions).

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Problem 16282

Solve for $x$ : $\sqrt{56-x}=x$ . If no solution, write DNE.

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Problem 16283

Does Lagrange's mean value theorem apply to $f(x)=x^{1/3}$ on $[-1, 1]$ ? What can we conclude?

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Problem 16284

Solve the equation $x - 3\sqrt{x} - 4 = 0$ for real solutions. Use exact answers with fractions and roots.

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Problem 16285

Convert the following numbers to integers or decimals: 1) $2.9 \times 10^{5}$ , 2) $56 \times 10^{-4}$ , 3) $0.274 \times 10^{8}$ , 4) $0.00338 \times 10^{-3}$ .

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Problem 16286

Solve $12(5x-2)^{2}-5(5x-2)-2=0$ and list solutions as $x_1,x_2$ .

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Problem 16287

Evaluate the following without a calculator and express in scientific notation:
1. $0.0025 \times 10^{7}-1.07 \times 10^{5}$
2. $9 \times 10^{6}+2.4 \times 10^{7}$
3. $(0.0034)(2.5 \times 10^{-7})$
4. $1.44 \times 10^{-8} \div 0.000024$

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Problem 16288

Calculate $(187-88)+1-(130-31)$ .

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Problem 16289

Evaluate these expressions without a calculator and express answers in scientific notation:
1. $0.0025 \times 10^{7}-1.07 \times 10^{5}$
2. $9 \times 10^{6}+2.4 \times 10^{7}$
3. $(0.0034)(2.5 \times 10^{-7})$
4. $1.44 \times 10^{-8} \div 0.000024$

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Problem 16290

Calculate $8.12 \times 10^{6} \times 4.7 \times 10^{3}$ using scientific notation. Give your answer with correct significant figures.

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Problem 16291

Convert 41 and 21 from decimal to binary: 41 and $21_{10}$ .

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Problem 16292

Find the maximum height of the ball given the function $f(x)=-0.7 x^{2}+2.7 x+5$ and its distance from the throw point.

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Problem 16293

A ball is thrown from 5 ft high. Its height is modeled by $f(x)=-0.1 x^{2}+0.8 x+5$ . Find the max height and distance.

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Problem 16294

Calculate the limit: $\lim _{x \rightarrow+\infty} \frac{2-x}{3}(x^{3}-1)$ .

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Problem 16295

Solve the system:
y = x + 2
5x² + y² = 4
List all solutions as ordered pairs or state if there are none.

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Problem 16296

Solve the system: $2x^{2}+y^{2}=5$ and $x^{2}-2y^{2}+12=0$ . List all solutions or state if none exist.

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Problem 16297

Solve the system of equations:
1. $x^{2}-3y^{2}+8=0$
2. $6x^{2}+y^{2}=28$ .
List all solutions as ordered pairs or state if there are no solutions.

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Problem 16298

Simplify $4^{7}, 8^{5}, 2^{16}, 64^{3}$ and the expressions in problems 44 and 45 with positive indices.

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Problem 16299

Express $\left(\frac{1}{125}\right)^{600}$ as $5^{n}$ for some integer $n$ .

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Problem 16300

Express $4^{x+1}+12(4^{x})$ as a power of $4$ . Then simplify $\frac{(4^{3 x})(5^{6 x})}{10^{4 x}}$ as a power of $10$ .

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1 ...160 161 162 163 164 165 166 ...270

Math Statement

Problem 16201

Problem 16202

Problem 16203

3) Evaluate ∫4121x−43dx\int_{4}^{12} \frac{1}{\sqrt[3]{x-4}} d x∫412​3x−4​1​dx

Problem 16204

Use a sum-to-product formula to find the exact value. Write your answer as a simplified fraction and rationalize the denominator, if nece sin⁡165∘−sin⁡75∘=\sin 165^{\circ}-\sin 75^{\circ}=sin165∘−sin75∘= □\square□ 延 \sqrt{\text { 延 }} 延 ​

Problem 16205

Difference of S Ex: Factor x2−16=x2+0x−16x^{2}-16=x^{2}+0 x-16x2−16=x2+0x−16

Problem 16206

Simplify. (v−6)−6\left(v^{-6}\right)^{-6}(v−6)−6Write your answer without using negative exponents.

Problem 16207

Factor by grouping. 6x3−12x2−7x+146 x^{3}-12 x^{2}-7 x+146x3−12x2−7x+14

Problem 16208

Problem 16209

Simplify. v14\sqrt{v^{14}}v14​Assume that the variable represents a positive real number.

Problem 16210

Factor. 128c2−50128 c^{2}-50128c2−50

Problem 16211

−(−82)2+1−(−3)2-\left(\frac{-8}{2}\right)^{2}+1-(-3)^{2}−(2−8​)2+1−(−3)2

Problem 16212

Write an equivalent expression −6)4(y−4)1-6)^{4}(y-4) 1−6)4(y−4)1Select all that apply A. −6(4y−4)-6(4 y-4)−6(4y−4) B −6(xy−16)-6\left(x_{y}-16\right)−6(xy​−16) C. −24y+96-24 y+96−24y+96 D. −6y=-6 y=−6y= vel E. −24y−96-24 y-96−24y−96

Problem 16213

Evaluate the expressions. −2(23)0=−(4)0=\begin{array}{r} -2\left(\frac{2}{3}\right)^{0}= \\ -(4)^{0}= \end{array}−2(32​)0=−(4)0=​

Problem 16214

Rewrite the following without an exponent. (−3)−2(-3)^{-2}(−3)−2

Problem 16215

isentity whichic expressions are equivalent to the given expression 2(2y+2)2(2 y+2)2(2y+2)Which of the following is equivalent to the expression 2(2y+2)2(2 y+2)2(2y+2) ? Select all that apply. A. 4y+64 y+64y+6 - 2 - +2=2+2=2+2=2 y C. 4y+44 y+44y+4

Problem 16216

−(8)2=−(−6)3=\begin{array}{c}-(8)^{2}= \\ -(-6)^{3}=\end{array}−(8)2=−(−6)3=​

Problem 16217

[EX1] Simplify each rational expres (1) 5x6+3−x4\frac{5 x}{6}+\frac{3-x}{4}65x​+43−x​

Problem 16218

18 Write the equation of the line in slope-intercept form with the following slope and y-intercept: m=52\mathrm{m}=\frac{5}{2}m=25​ yyy-intercept =(0,−2)=(0,-2)=(0,−2) □\square□

Problem 16219

Solve the equation (x−3)2/3+(x−3)1/3−6=0(x-3)^{2 / 3}+(x-3)^{1 / 3}-6=0(x−3)2/3+(x−3)1/3−6=0.

Problem 16220

Solve for xxx in the equation asec⁡x=3a \sec x = 3asecx=3.

Problem 16221

Solve for xxx if sec⁡x=3\sec x=3secx=3.

Problem 16222

Evaluate 3−4i5i\frac{3-4 i}{5 i}5i3−4i​ and express the result as a+bia + b ia+bi.

Problem 16223

Calculate the result of the complex division: (−38+135i)÷(11−10i)(-38+135 i) \div(11-10 i)(−38+135i)÷(11−10i).

Problem 16224

Divide −3−4i2i\frac{-3-4 i}{2 i}2i−3−4i​ and express the answer as a+bia + bia+bi.

Problem 16225

Simplify −1−9−7\frac{\sqrt{-1}}{\sqrt{-9} \sqrt{-7}}−9​−7​−1​​ and express it as a+bia + bia+bi.

Problem 16226

Calculate the product of (−6−4i)(-6-4i)(−6−4i) and its conjugate (−6+4i)(-6+4i)(−6+4i).

Problem 16227

Factor the trinomial 42x2−53x+1542 x^{2}-53 x+1542x2−53x+15.

Problem 16228

Factor the GCF from the polynomial: 25x6+5x4+35x325 x^{6}+5 x^{4}+35 x^{3}25x6+5x4+35x3.

Problem 16229

Solve the equation x2−24x+143=0x^{2}-24 x+143=0x2−24x+143=0.

Problem 16230

Prove that 1+sin⁡xcos⁡x+cos⁡x1+sin⁡x≡2sec⁡x\frac{1+\sin x}{\cos x}+\frac{\cos x}{1+\sin x} \equiv 2 \sec xcosx1+sinx​+1+sinxcosx​≡2secx.

Problem 16231

Solve the equation: p2−144=0p^{2}-144=0p2−144=0. Enter your integer or reduced fraction answers separated by commas.

Problem 16232

Prove that 1−cos⁡2xsec⁡2x−1=1−sin⁡2x\frac{1-\cos ^{2} x}{\sec ^{2} x-1} = 1-\sin ^{2} xsec2x−11−cos2x​=1−sin2x.

Problem 16233

Show that sin⁡x1−cos⁡2x=cosec⁡x\frac{\sin x}{1-\cos^{2} x} = \operatorname{cosec} x1−cos2xsinx​=cosecx.

Problem 16234

Factor and solve the equation 6a2−21a−12=06 a^{2}-21 a-12=06a2−21a−12=0. List your answers separated by a comma.

Problem 16235

Prove that sec⁡4θ−sec⁡2θ=tan⁡2θ+tan⁡4θ\sec ^{4} \theta - \sec ^{2} \theta = \tan ^{2} \theta + \tan ^{4} \thetasec4θ−sec2θ=tan2θ+tan4θ.

Problem 16236

Prove that 1+sin⁡x1−sin⁡x≡(tan⁡x+sec⁡x)2\frac{1+\sin x}{1-\sin x} \equiv(\tan x+\sec x)^{2}1−sinx1+sinx​≡(tanx+secx)2.

Problem 16237

Solve the equation −2x2−20x−42=0-2x^2 - 20x - 42 = 0−2x2−20x−42=0 by first dividing by −2-2−2.

Problem 16238

Solve 2x2+5x−12=02x^2 + 5x - 12 = 02x2+5x−12=0 using the quadratic formula. List the solutions, separated by commas.

Problem 16239

Prove that (1+sin⁡xcos⁡x)2+(1−sin⁡xcos⁡x)2=2sec⁡2x+2tan⁡2x\left(\frac{1+\sin x}{\cos x}\right)^{2}+\left(\frac{1-\sin x}{\cos x}\right)^{2} = 2 \sec ^{2} x+2 \tan ^{2} x(cosx1+sinx​)2+(cosx1−sinx​)2=2sec2x+2tan2x.

Problem 16240

Rewrite the equation x2+2x−99=0x^{2}+2x-99=0x2+2x−99=0 by completing the square and solve for xxx.

Problem 16241

Solve the equation 4w2+w−7=04 w^{2}+w-7=04w2+w−7=0 using the quadratic formula. List solutions, separated by commas.

3) Evaluate $\int_{4}^{12} \frac{1}{\sqrt[3]{x-4}} d x$

Use a sum-to-product formula to find the exact value. Write your answer as a simplified fraction and rationalize the denominator, if nece $\sin 165^{\circ}-\sin 75^{\circ}=$ $\square$ $\sqrt{\text { 延 }}$

Difference of S Ex: Factor $x^{2}-16=x^{2}+0 x-16$

Simplify. $\left(v^{-6}\right)^{-6}$
Write your answer without using negative exponents.

Factor by grouping. $6 x^{3}-12 x^{2}-7 x+14$

Simplify. $\sqrt{v^{14}}$
Assume that the variable represents a positive real number.

Factor. $128 c^{2}-50$

$-\left(\frac{-8}{2}\right)^{2}+1-(-3)^{2}$

Write an equivalent expression $-6)^{4}(y-4) 1$
Select all that apply A. $-6(4 y-4)$ B $-6\left(x_{y}-16\right)$ C. $-24 y+96$ D. $-6 y=$ vel E. $-24 y-96$

Evaluate the expressions. $\begin{array}{r} -2\left(\frac{2}{3}\right)^{0}= \\ -(4)^{0}= \end{array}$

Rewrite the following without an exponent. $(-3)^{-2}$

isentity whichic expressions are equivalent to the given expression $2(2 y+2)$
Which of the following is equivalent to the expression $2(2 y+2)$ ? Select all that apply. A. $4 y+6$ - 2 - $+2=2$ y C. $4 y+4$

$\begin{array}{c}-(8)^{2}= \\ -(-6)^{3}=\end{array}$

[EX1] Simplify each rational expres (1) $\frac{5 x}{6}+\frac{3-x}{4}$

18 Write the equation of the line in slope-intercept form with the following slope and y-intercept: $\mathrm{m}=\frac{5}{2}$ $y$ -intercept $=(0,-2)$ $\square$

Solve the equation $(x-3)^{2 / 3}+(x-3)^{1 / 3}-6=0$ .

Solve for $x$ in the equation $a \sec x = 3$ .

Solve for $x$ if $\sec x=3$ .

Evaluate $\frac{3-4 i}{5 i}$ and express the result as $a + b i$ .

Calculate the result of the complex division: $(-38+135 i) \div(11-10 i)$ .

Divide $\frac{-3-4 i}{2 i}$ and express the answer as $a + bi$ .

Simplify $\frac{\sqrt{-1}}{\sqrt{-9} \sqrt{-7}}$ and express it as $a + bi$ .

Calculate the product of $(-6-4i)$ and its conjugate $(-6+4i)$ .

Factor the trinomial $42 x^{2}-53 x+15$ .

Factor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

Solve the equation $x^{2}-24 x+143=0$ .

Prove that $\frac{1+\sin x}{\cos x}+\frac{\cos x}{1+\sin x} \equiv 2 \sec x$ .

Solve the equation: $p^{2}-144=0$ . Enter your integer or reduced fraction answers separated by commas.

Prove that $\frac{1-\cos ^{2} x}{\sec ^{2} x-1} = 1-\sin ^{2} x$ .

Show that $\frac{\sin x}{1-\cos^{2} x} = \operatorname{cosec} x$ .

Factor and solve the equation $6 a^{2}-21 a-12=0$ . List your answers separated by a comma.

Prove that $\sec ^{4} \theta - \sec ^{2} \theta = \tan ^{2} \theta + \tan ^{4} \theta$ .

Prove that $\frac{1+\sin x}{1-\sin x} \equiv(\tan x+\sec x)^{2}$ .

Solve the equation $-2x^2 - 20x - 42 = 0$ by first dividing by $-2$ .

Solve $2x^2 + 5x - 12 = 0$ using the quadratic formula. List the solutions, separated by commas.

Prove that $\left(\frac{1+\sin x}{\cos x}\right)^{2}+\left(\frac{1-\sin x}{\cos x}\right)^{2} = 2 \sec ^{2} x+2 \tan ^{2} x$ .

Rewrite the equation $x^{2}+2x-99=0$ by completing the square and solve for $x$ .

Solve the equation $4 w^{2}+w-7=0$ using the quadratic formula. List solutions, separated by commas.

Solve the equation by completing the square: $x^{2}-8 x+26=5$ . Find the roots.

Solve for $x$ using the quadratic formula for the equation $4x^{2} + 12x + 12 = 0$ .

Solve the equation $2 z^{2}+3 z-1=0$ and provide simplified answers, separated by commas.

Solve the equation $4 w^{2}+3 w+12=2$ and simplify your answer, including non-real solutions. $w=$

Solve for $x$ in the equation $\log _{2}(x+4)=3$ .

Solve $9 \cot ^{2} \frac{1}{2} x=4$ for $-180^{\circ} \leq x \leq 180^{\circ}$ .

Solve $2 \operatorname{cosec}(2 x-1)=3$ for $-\pi \leq x \leq \pi$ .

Find the value of $\mathrm{c}$ if the line $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ passes through the origin.

Find the orientation, center, vertices, conjugate axis ends, foci, and lengths of the axes for $\frac{y^{2}}{16}-x^{2}=1$ . Graph it.

Determine the center, vertices, foci, and axis of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and graph it.

Graph the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and determine its asymptotes.

Determine the transverse and conjugate axes of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and sketch its graph.

Convert the hyperbola equation $-16x^{2}+y^{2}+128x-272=0$ to standard form and graph it.

Calculate the integral $\int_{1}^{5}\left(x+\frac{2}{x^{2}}\right) d x$ using the trapezium rule at $x=1,2,3,4,5$ , rounded to two decimal places.

Convert the hyperbola equation $16x^{2}-9y^{2}+32x-18y-137=0$ to standard form and graph it.

Find the limit as $x$ approaches -2 for $\frac{x^{3}+8}{x+2}$ .

Analyze the function $f\left(x_{1}, x_{2}\right)=x_{1}^{2} x_{2}^{2}$ . Is it constant, increasing, or decreasing returns to scale?

Solve for $x$ : $\frac{x+1}{x}+\frac{3}{4}=\frac{-3}{x}$ . What is $x$ ?

Solve for $x$ in the equation $\frac{7}{2} x=\frac{4}{3} x-\frac{1}{6}$ .

Solve $\frac{7}{x}=\frac{2}{3 x}-10$ for $x$ . What is $x$ ?

Solve for $x$ in the equation $\frac{1}{x+4}=\frac{4}{x-4}$ . What is $x$ ?

Solve for $x$ in the equation $x^{3 / 7}=27$ .

Solve for $x$ : $(5x + 4)^{5/7} = 32$ ; find $x = \square$ .

Solve the equation $|6x + 7| = 49$ . List all solutions separated by commas.

Solve for $x$ : $(x+5)^{3/7} = 8$ . What is the value of $x$ ?

Find the value of $k$ for each case:
19. $2^{4 k}=16^{2}$ ,
20. $2^{8-3 k}=0.5$ ,
21. $19^{5 k-3}=\frac{1}{19^{k-3}}$ ,
22. $\left(\frac{1}{6^{k}}\right)^{2}=216^{2}$ .

Solve the equation: $|5x - 8| = 32$ . List all solutions, separated by commas.

Solve for $x$ : $-3 + 7|4x - 8| = -38$ . If multiple solutions, separate with commas; if none, enter DNE.

Solve for $x$ in the equation $|x-9|=4$ . Separate your answers with a comma.

Solve for $x$ : $-5 + 6|4x - 6| = 31$ . If multiple solutions, separate with commas.

Solve for $x$ : $\sqrt{x-9}=9$ . What is $x$ ?

Solve $\sqrt{x+1}+5=8$ for $x$ .