Math Statement

Problem 15401

Add or subtract these measurements, ensuring the correct significant digits:
8.700 g + 1.37 g = \square g 16.600 g - 0.70 g = \square g 7.827 g - 1.2 g = \square g

See Solution

Problem 15402

Calculate the following volumes: 1) $7.57 \mathrm{~mL} + 11.7 \mathrm{~mL} = \square \mathrm{mL}$ 2) $19.5 \mathrm{~mL} + 9.977 \mathrm{~mL} = \square \mathrm{mL}$ 3) $17.500 \mathrm{~mL} - 9.8 \mathrm{~mL} = \square \mathrm{mL}$

See Solution

Problem 15403

Calculate: 20.94 g/mL × 33 mL = ? g and 496.3 m ÷ 0.90 s = ? m/s.

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Problem 15404

Multiply or divide these measurements, ensuring correct significant digits:
1. $2.094 \mathrm{~cm} \times 1.10 \mathrm{~cm} = \square \mathrm{cm}^{2}$
2. $20.94 \frac{\mathrm{g}}{\mathrm{mL}} \times 33 \mathrm{mL} = \square \mathrm{g}$
3. $496.3 \mathrm{~m} \div 0.90 \mathrm{~s} = \square \frac{\mathrm{m}}{\mathrm{s}}$

See Solution

Problem 15405

Calculate: 405.36 g ÷ 0.57 mL = $\square$ g/mL; 7.808 g/mL × 0.6 mL = $\square$ g; 269.58 g ÷ 0.86 mL = $\square$ g/mL.

See Solution

Problem 15406

Calculate the following: 78.08 cm × 50 cm = $\square$ cm², 792.4 g ÷ 43.37 mL = $\square$ g/mL, 0.93 g/mL × 4.925 mL = $\square$ g.

See Solution

Problem 15407

Multiply or divide these measurements with correct significant digits:
1. $7.81 \frac{\mathrm{mol}}{\mathrm{L}} \times 4.525 \mathrm{~L}=\square \mathrm{mol}$
2. $215.0 \mathrm{~mol} \div 0.85 \mathrm{~L}=\square \frac{\mathrm{mol}}{\mathrm{L}}$
3. $578.36 \mathrm{~m} \div 0.41 \mathrm{~s}=\square \frac{\mathrm{m}}{\mathrm{s}}$

See Solution

Problem 15408

Find the corner points of the following inequalities: $3x - 2y \leq 6$ , $x + y \geq -5$ , $y \geq 4$ .

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Problem 15409

Solve the inequality: $21 x - 18 \leq 5 x + 14$ . Subtract $5 x$ and simplify.

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Problem 15410

Solve the inequality by subtracting $5x$ from both sides: $21x - 18 \leq 5x + 14$ .

See Solution

Problem 15411

Solve the inequality: $-\frac{13}{4} < x < -\frac{5}{2}$ .

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Problem 15412

Solve the inequality: $21 x - 18 \leq 5 x + 14$ by simplifying both sides.

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Problem 15413

Simplify the expression $\left(\frac{a+1}{a-1}+\frac{a-1}{a+1}\right) \div\left(\frac{a+1}{a-1}-\frac{a-1}{a+1}\right)$ .

See Solution

Problem 15414

Identify which function is continuous for all $x$ in the interval $(-\infty, \infty)$ from the given options.

See Solution

Problem 15415

Divide and multiply these measurements, ensuring correct significant digits:
173.39 mol ÷ 0.61 L = \square mol/L 7.8084 mol/L × 2.3 L = \square mol 714.4 m ÷ 39.05 s = \square m/s

See Solution

Problem 15416

Divide or multiply these measurements, ensuring correct significant digits:
213.30 mol ÷ 85.1 L = $\square$ mol/L 7.808 mol/L × 3.1 L = $\square$ mol 248.6 mol ÷ 0.46 L = $\square$ mol/L

See Solution

Problem 15417

Factoriza $a^{4}+a^{2}-2$ .

See Solution

Problem 15418

Multiply or divide these measurements with proper significant digits:
1. $20.947 \frac{\mathrm{g}}{\mathrm{mL}} \times 32 \mathrm{mL} = \square \mathrm{g}$
2. $914.4 \mathrm{g} \div 0.65 \mathrm{mL} = \square \frac{\mathrm{g}}{\mathrm{mL}}$
3. $0.934 \mathrm{cm} \times 1.125 \mathrm{cm} = \square \mathrm{cm}^{2}$

See Solution

Problem 15419

Find the six trigonometric functions for the angle $-\frac{5 \pi}{4}$ without using a calculator.

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Problem 15420

Find the values of the six trigonometric functions for the angle $\frac{\pi}{4}$ without using a calculator.

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Problem 15421

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

See Solution

Problem 15422

Solve the equation: $\frac{x}{5}-4=\frac{x}{4}-6$ .

See Solution

Problem 15423

Solve the equation: $\frac{4}{x-4}=\frac{-4}{x+3}+\frac{12}{(x-4)(x+3)}$

See Solution

Problem 15424

Solve for $x$ in the equation $\frac{3}{x}+3=\frac{3}{5 x}+\frac{31}{10}$ .

See Solution

Problem 15425

Find the exact value of $\sin(13 \pi)$ without using a calculator.

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Problem 15426

Find the exact value of $\tan(11 \pi)$ without using a calculator.

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Problem 15427

Find the exact value of $\cos (-2 \pi)$ without using a calculator.

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Problem 15428

Find the six trigonometric functions for the angle $\frac{3 \pi}{4}$ . State "not defined" if applicable.

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Problem 15429

Find the exact value of $\cot \frac{3 \pi}{2} - \cos \frac{3 \pi}{2}$ without a calculator.

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Problem 15430

Find the equation of the line passing through the point $(-4,5)$ with a slope of $m=\frac{1}{2}$ .

See Solution

Problem 15431

Find the exact values of the six trigonometric functions for the angle $\theta$ with the point (4, -5) on its terminal side.

See Solution

Problem 15432

Convert $2x + 5y = 12$ to slope-intercept form, $y = mx + b$ .

See Solution

Problem 15433

Find the exact values of the six trigonometric functions of $t$ for the point $P=\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)$ on the unit circle.

See Solution

Problem 15434

Calculate the value of $\cos 90^{\circ} + \cot 45^{\circ}$ without using a calculator.

See Solution

Problem 15435

Calculate the exact value of $\sin 46^{\circ} - \cos 44^{\circ}$ without a calculator.

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Problem 15436

Calculate the value of $\sin 90^{\circ} + \tan 45^{\circ}$ without a calculator.

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Problem 15437

Calculate the value of $2 \cos \frac{\pi}{3} - 6 \tan \frac{\pi}{6}$ without using a calculator.

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Problem 15438

Find the value of $\cot \frac{3 \pi}{2} + \cos \frac{3 \pi}{2}$ without a calculator.

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Problem 15439

Find the exact value of $\sin 29^{\circ} - \cos 61^{\circ}$ without a calculator.

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Problem 15440

Find the midpoint of the segment with endpoints $(9,5)$ and $(1,1)$ .

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Problem 15441

Find the midpoint between the points $(8,7)$ and $(2,10)$ .

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Problem 15442

Find the range of values of $p$ such that both $3x^{2}+2px+3=0$ and $x^{2}+4x-p=0$ have real roots.

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Problem 15443

Find the equations of lines through $(-2,3)$ : one parallel to $y=-2x+4$ and one perpendicular to it.

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Problem 15444

Find the distance between the points (6,9) and (-3,7) in simplest radical form: $d = \sqrt{(6 - (-3))^2 + (9 - 7)^2}$

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Problem 15445

Calculate the distance between the points (3,0) and (-3,-8) in simplest radical form.

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Problem 15446

Define the function $f$ : $f(x) = -3x + 4$ for $x < 1$ and $f(x) = 4x - 3$ for $x \geq 1$ . Find its domain, intercepts, graph, and range.

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Problem 15447

Check if 7264 is divisible by 2 and 3. Answers: a. Yes/No, b. Yes/No.

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Problem 15448

Solve the system of equations: $x - \frac{y}{7} = -1$ and $-\frac{x}{2} + \frac{y}{16} = \frac{1}{4}$ .

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Problem 15449

Find the values of $x$ and $y$ that satisfy the equation $2x + 3y = 12$ for the point $(3,1)$ .

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Problem 15450

Define the function $f(x)$ as: $f(x)=x$ if $x<0$ and $f(x)=x^{2}$ if $x \geq 0$ . Find its domain, intercepts, graph, and range.

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Problem 15451

Find the sum function $(f+g)(x)$ for $f(x)=5x+4$ if $x<2$ and $x^2+4x$ if $x \geq 2$ , and $g(x)=-3x+1$ if $x \leq 0$ and $g(x)=x-7$ if $x > 0$ .

See Solution

Problem 15452

Find the values of $m$ such that $2x - 2m + (x + m)^{2} > 0$ for all real $x$ .

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Problem 15453

Identify the types of functions $f(x)=x^{3}+x^{2}-3 x+4$ and $g(x)=2^{x}-4$ . What do they have in common?

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Problem 15454

Find the slope of the line given by the equation $2x + 3y = 12$ .

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Problem 15455

Calculate the wind chill $W$ for $t=10^{\circ}C$ and $v=1 \text{ m/s}$ using the given formula. Round to the nearest degree.

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Problem 15456

Find the prime factors of the number 105. What is its prime factorization? $105 =$

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Problem 15457

Solve $(x+1)(x-2)=3$ and express your answers in surd form.

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Problem 15458

Find the coordinates of the point $(x,y)$ that satisfies the equation $3x - 5y = 15$ at the point $(6,1)$ .

See Solution

Problem 15459

Find the prime factorization of 76 using exponents for repeated factors. $76=$

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Problem 15460

Find the roots of $2 x = -5 + 3 x^{2}$ and the values of $c$ for which $3 x^{2} + 5 x + c > 0$ .

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Problem 15461

Find the prime factorization of 225, using exponents for repeated factors.

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Problem 15462

Find the GCD of 84 and 56. The GCD of 84 and 56 is $$.

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Problem 15463

Find the GCD of 99 and 66. The GCD of 99 and 66 is $$.

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Problem 15464

Find the least common multiple (LCM) of 84 and 24. The LCM is $\text{lcm}(84, 24)$ .

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Problem 15465

Find the LCM of 90 and 20. The LCM of 90 and 20 is $$.

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Problem 15466

Find the prime factorization of 44 using exponents for repeated factors. $44 =$

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Problem 15467

Determine the number of significant figures in $20.00_{3}$ .

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Problem 15468

Calculate the product of 3.15, 2.5, and 4.00 with the correct significant figures: $3.15 \times 2.5 \times 4.00 =$

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Problem 15469

Find the result of $313.0 - (1.2 \times 10^{3})$ with the correct significant figures.

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Problem 15470

Calculate $(4.123 \times 0.12) + 24.2$ and give the result with the right significant figures.

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Problem 15471

Calculate $(17.103 + 2.03) \times 1.02521$ with the correct number of significant figures.

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Problem 15472

Find the value of $k$ for the function $f(x)=\left\{\begin{array}{ll}\frac{\sqrt{x+3}-\sqrt{3 x-1}}{x-2} & x \neq 2 \\ k & x=2\end{array}\right.$ to be continuous.

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Problem 15473

Identify the correct half-equation for the oxidation of ethanol to ethanoic acid from the options provided.

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Problem 15474

Rewrite the equation $x^{2}-14 x-1$ as $(x+ a)^2 + b$ with integers $a$ and $b$ .

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Problem 15475

Find the roots of $x^{2}-24x+5$ by rewriting it as $(x+a)^2=b$ with integers $a$ and $b$ .

See Solution

Problem 15476

Rewrite $x^{2}+10 x+8$ as $(x+a)^{2}+b$ with integers $a$ and $b$ .

See Solution

Problem 15477

Calculate $1000 + (140 + 160)$ .

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Problem 15478

Rewrite the equation $x^{2}-24 x+5$ as $(x+a)^2 + b$ by completing the square, with $a$ and $b$ as integers.

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Problem 15479

Find the unit price $p$ that maximizes revenue $r(p) = -9p^2 + 27,000p$ and determine the maximum revenue.

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Problem 15480

Find the unit price $p$ that maximizes revenue given $r(p)=-9p^2+36,000p$ . What is the maximum revenue?

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Problem 15481

Minimize marginal cost for $C(x) = x^{2} - 140x + 7700$ . Find optimal $x$ and minimum cost.

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Problem 15482

Monthly revenue is $R(x)=79x-0.2x^2$ and cost is $C(x)=30x+1600$ . Find wristwatches for max revenue and profit. Explain differences.

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Problem 15483

Find $\lim _{x \rightarrow 0} \frac{\cos 2 x}{3}$ . Choose from: A) 0 B) $\frac{1}{3}$ C) $\frac{2}{3}$ D) does not exist.

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Problem 15484

A shot put's height is given by $F(x)=-0.02x^2+1.2x+5.3$ .
a. Confirm if the max height is 23.3 feet.
b. Find the max horizontal distance of the throw.

See Solution

Problem 15485

Which inequality is true: A. $\frac{3}{4}<\frac{5}{9}$ , B. $\frac{17}{20}>\frac{4}{5}$ , C. $\frac{5}{6}<\frac{11}{14}$ , D. $\frac{7}{12}>\frac{16}{25}$ ?

See Solution

Problem 15486

An athlete releases a shot modeled by $f(x)=-0.01 x^{2}+0.7 x+5.4$ . Find the maximum height and its distance from release.

See Solution

Problem 15487

Solve the inequality: $\frac{x+3}{x-1}>2$

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Problem 15488

Find the equivalent expression for the profit $0.5(200 + 32s)$ and calculate profit for $s = 30$ .

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Problem 15489

An athlete releases a shot modeled by $f(x)=-0.02 x^{2}+1.7 x+5.7$ . Find the max height and distance from release.

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Problem 15490

Solve the equation $-\frac{1}{3} x = 9$ . What is the value of $x$ ?

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Problem 15491

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+0.6 x+6$ . Find its max height and distance from release.

See Solution

Problem 15492

Find the weekly profit function $P(x)$ from cost $C(x)=565.00+0.65x$ and revenue $R(x)=-0.001x^2+3x$ .

See Solution

Problem 15493

Find the maximum height of the ball described by $f(x)=-0.3 x^{2}+2.1 x+6$ and its distance from the throw point.

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Problem 15494

Find the limit: $271 \lim _{x \rightarrow+\infty} \frac{4 x-1}{2 x+1}$ . What is the result?

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Problem 15495

Find the limit as $x$ approaches infinity for $\frac{4x - 1}{2x + 1}$ .

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Problem 15496

Solve the inequality $4|t+3| \geq 8$ .

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Problem 15497

Which point is on the graph of the piecewise function $f(x)$ defined as: $f(x)=-9$ for $x<-6$ , $f(x)=1$ for $x=-6$ , and $f(x)=7x-1$ for $x>-6$ ? Options: $(-6,-9)$ , $(-6,-43)$ , $(1,-6)$ , $(0,-9)$ , $(-5,-36)$ , or None.

See Solution

Problem 15498

A ball is thrown from 6 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.8 x+6$ . Find the max height and distance from release.

See Solution

Problem 15499

8) $\frac{1}{2} x+3=\frac{1}{4} x+5$

See Solution

Problem 15500

Verify the product law for differentiation, $(\mathbf{A B})^{\prime}=\mathbf{A}^{\prime} \mathbf{B}+\mathbf{A} \mathbf{B}^{\prime}$ where $\mathbf{A}(t)=\left[\begin{array}{rr}3 t & 3 t-1 \\ t^{3} & \frac{1}{t}\end{array}\right]$ and $\mathbf{B}(t)=\left[\begin{array}{rr}1-t & 1+t \\ 2 t^{2} & 3 t^{3}\end{array}\right]$ .
To calculate $(\mathbf{A B})^{\prime}$ , first calculate $\mathbf{A B}$ . $A B=$ $\square$ Now take the derivative of $A B$ to find $(A B)^{\prime}$ . $(A B)^{\prime}=$ $\square$ To calculate $\mathbf{A}^{\prime} \mathbf{B}+\mathbf{A B ^ { \prime }}$ , first calculate $\mathbf{A}^{\prime}$ . $A^{\prime}=$ $\square$ Now find $\mathbf{A}^{\prime} \mathbf{B}$ . $A^{\prime} B=$ $\square$ Now find $\mathbf{B}^{\prime}$ . $\mathbf{B}^{\prime}=\square$ $\square$ Now calculate $\mathbf{A B}^{\prime}$ . $\mathbf{A B}^{\prime}=\square$ $\square$ Finally, find $\mathbf{A}^{\prime} \mathbf{B}+\mathbf{A B} \mathbf{B}^{\prime}$ . $A^{\prime} B+A B^{\prime}=$ $\square$

See Solution

1 ...152 153 154 155 156 157 158 ...270

Math Statement

Problem 15401

Add or subtract these measurements, ensuring the correct significant digits: 8.700 g + 1.37 g = \square g 16.600 g - 0.70 g = \square g 7.827 g - 1.2 g = \square g

Problem 15402

Problem 15403

Calculate: 20.94 g/mL × 33 mL = ? g and 496.3 m ÷ 0.90 s = ? m/s.

Problem 15404

Problem 15405

Calculate: 405.36 g ÷ 0.57 mL = □\square□ g/mL; 7.808 g/mL × 0.6 mL = □\square□ g; 269.58 g ÷ 0.86 mL = □\square□ g/mL.

Problem 15406

Calculate the following: 78.08 cm × 50 cm = □\square□ cm², 792.4 g ÷ 43.37 mL = □\square□ g/mL, 0.93 g/mL × 4.925 mL = □\square□ g.

Problem 15407

Problem 15408

Find the corner points of the following inequalities: 3x−2y≤63x - 2y \leq 63x−2y≤6, x+y≥−5x + y \geq -5x+y≥−5, y≥4y \geq 4y≥4.

Problem 15409

Solve the inequality: 21x−18≤5x+1421 x - 18 \leq 5 x + 1421x−18≤5x+14. Subtract 5x5 x5x and simplify.

Problem 15410

Solve the inequality by subtracting 5x5x5x from both sides: 21x−18≤5x+1421x - 18 \leq 5x + 1421x−18≤5x+14.

Problem 15411

Solve the inequality: −134<x<−52-\frac{13}{4} < x < -\frac{5}{2}−413​<x<−25​.

Problem 15412

Solve the inequality: 21x−18≤5x+1421 x - 18 \leq 5 x + 1421x−18≤5x+14 by simplifying both sides.

Problem 15413

Simplify the expression (a+1a−1+a−1a+1)÷(a+1a−1−a−1a+1)\left(\frac{a+1}{a-1}+\frac{a-1}{a+1}\right) \div\left(\frac{a+1}{a-1}-\frac{a-1}{a+1}\right)(a−1a+1​+a+1a−1​)÷(a−1a+1​−a+1a−1​).

Problem 15414

Identify which function is continuous for all xxx in the interval (−∞,∞)(-\infty, \infty)(−∞,∞) from the given options.

Problem 15415

Divide and multiply these measurements, ensuring correct significant digits: 173.39 mol ÷ 0.61 L = \square mol/L 7.8084 mol/L × 2.3 L = \square mol 714.4 m ÷ 39.05 s = \square m/s

Problem 15416

Divide or multiply these measurements, ensuring correct significant digits: 213.30 mol ÷ 85.1 L = □\square□ mol/L 7.808 mol/L × 3.1 L = □\square□ mol 248.6 mol ÷ 0.46 L = □\square□ mol/L

Problem 15417

Factoriza a4+a2−2a^{4}+a^{2}-2a4+a2−2.

Problem 15418

Problem 15419

Find the six trigonometric functions for the angle −5π4-\frac{5 \pi}{4}−45π​ without using a calculator.

Problem 15420

Find the values of the six trigonometric functions for the angle π4\frac{\pi}{4}4π​ without using a calculator.

Problem 15421

Solve for xxx in the equation xx+3=54\frac{x}{x+3}=\frac{5}{4}x+3x​=45​.

Problem 15422

Solve the equation: x5−4=x4−6\frac{x}{5}-4=\frac{x}{4}-65x​−4=4x​−6.

Problem 15423

Solve the equation: 4x−4=−4x+3+12(x−4)(x+3)\frac{4}{x-4}=\frac{-4}{x+3}+\frac{12}{(x-4)(x+3)}x−44​=x+3−4​+(x−4)(x+3)12​

Problem 15424

Solve for xxx in the equation 3x+3=35x+3110\frac{3}{x}+3=\frac{3}{5 x}+\frac{31}{10}x3​+3=5x3​+1031​.

Problem 15425

Find the exact value of sin⁡(13π)\sin(13 \pi)sin(13π) without using a calculator.

Problem 15426

Find the exact value of tan⁡(11π)\tan(11 \pi)tan(11π) without using a calculator.

Problem 15427

Find the exact value of cos⁡(−2π)\cos (-2 \pi)cos(−2π) without using a calculator.

Problem 15428

Find the six trigonometric functions for the angle 3π4\frac{3 \pi}{4}43π​. State "not defined" if applicable.

Problem 15429

Find the exact value of cot⁡3π2−cos⁡3π2\cot \frac{3 \pi}{2} - \cos \frac{3 \pi}{2}cot23π​−cos23π​ without a calculator.

Problem 15430

Find the equation of the line passing through the point (−4,5)(-4,5)(−4,5) with a slope of m=12m=\frac{1}{2}m=21​.

Problem 15431

Find the exact values of the six trigonometric functions for the angle θ\thetaθ with the point (4, -5) on its terminal side.

Problem 15432

Convert 2x+5y=122x + 5y = 122x+5y=12 to slope-intercept form, y=mx+by = mx + by=mx+b.

Problem 15433

Find the exact values of the six trigonometric functions of ttt for the point P=(223,−13)P=\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)P=(322​​,−31​) on the unit circle.

Problem 15434

Calculate the value of cos⁡90∘+cot⁡45∘\cos 90^{\circ} + \cot 45^{\circ}cos90∘+cot45∘ without using a calculator.

Problem 15435

Calculate the exact value of sin⁡46∘−cos⁡44∘\sin 46^{\circ} - \cos 44^{\circ}sin46∘−cos44∘ without a calculator.

Problem 15436

Calculate the value of sin⁡90∘+tan⁡45∘\sin 90^{\circ} + \tan 45^{\circ}sin90∘+tan45∘ without a calculator.

Problem 15437

Calculate the value of 2cos⁡π3−6tan⁡π62 \cos \frac{\pi}{3} - 6 \tan \frac{\pi}{6}2cos3π​−6tan6π​ without using a calculator.

Problem 15438

Find the value of cot⁡3π2+cos⁡3π2\cot \frac{3 \pi}{2} + \cos \frac{3 \pi}{2}cot23π​+cos23π​ without a calculator.

Problem 15439

Find the exact value of sin⁡29∘−cos⁡61∘\sin 29^{\circ} - \cos 61^{\circ}sin29∘−cos61∘ without a calculator.

Problem 15440

Find the midpoint of the segment with endpoints (9,5)(9,5)(9,5) and (1,1)(1,1)(1,1).

Problem 15441

Find the midpoint between the points (8,7)(8,7)(8,7) and (2,10)(2,10)(2,10).

Problem 15442

Add or subtract these measurements, ensuring the correct significant digits:
8.700 g + 1.37 g = \square g 16.600 g - 0.70 g = \square g 7.827 g - 1.2 g = \square g

Calculate: 405.36 g ÷ 0.57 mL = $\square$ g/mL; 7.808 g/mL × 0.6 mL = $\square$ g; 269.58 g ÷ 0.86 mL = $\square$ g/mL.

Calculate the following: 78.08 cm × 50 cm = $\square$ cm², 792.4 g ÷ 43.37 mL = $\square$ g/mL, 0.93 g/mL × 4.925 mL = $\square$ g.

Find the corner points of the following inequalities: $3x - 2y \leq 6$ , $x + y \geq -5$ , $y \geq 4$ .

Solve the inequality: $21 x - 18 \leq 5 x + 14$ . Subtract $5 x$ and simplify.

Solve the inequality by subtracting $5x$ from both sides: $21x - 18 \leq 5x + 14$ .

Solve the inequality: $-\frac{13}{4} < x < -\frac{5}{2}$ .

Solve the inequality: $21 x - 18 \leq 5 x + 14$ by simplifying both sides.

Simplify the expression $\left(\frac{a+1}{a-1}+\frac{a-1}{a+1}\right) \div\left(\frac{a+1}{a-1}-\frac{a-1}{a+1}\right)$ .

Identify which function is continuous for all $x$ in the interval $(-\infty, \infty)$ from the given options.

Divide and multiply these measurements, ensuring correct significant digits:
173.39 mol ÷ 0.61 L = \square mol/L 7.8084 mol/L × 2.3 L = \square mol 714.4 m ÷ 39.05 s = \square m/s

Divide or multiply these measurements, ensuring correct significant digits:
213.30 mol ÷ 85.1 L = $\square$ mol/L 7.808 mol/L × 3.1 L = $\square$ mol 248.6 mol ÷ 0.46 L = $\square$ mol/L

Factoriza $a^{4}+a^{2}-2$ .

Find the six trigonometric functions for the angle $-\frac{5 \pi}{4}$ without using a calculator.

Find the values of the six trigonometric functions for the angle $\frac{\pi}{4}$ without using a calculator.

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

Solve the equation: $\frac{x}{5}-4=\frac{x}{4}-6$ .

Solve the equation: $\frac{4}{x-4}=\frac{-4}{x+3}+\frac{12}{(x-4)(x+3)}$

Solve for $x$ in the equation $\frac{3}{x}+3=\frac{3}{5 x}+\frac{31}{10}$ .

Find the exact value of $\sin(13 \pi)$ without using a calculator.

Find the exact value of $\tan(11 \pi)$ without using a calculator.

Find the exact value of $\cos (-2 \pi)$ without using a calculator.

Find the six trigonometric functions for the angle $\frac{3 \pi}{4}$ . State "not defined" if applicable.

Find the exact value of $\cot \frac{3 \pi}{2} - \cos \frac{3 \pi}{2}$ without a calculator.

Find the equation of the line passing through the point $(-4,5)$ with a slope of $m=\frac{1}{2}$ .

Find the exact values of the six trigonometric functions for the angle $\theta$ with the point (4, -5) on its terminal side.

Convert $2x + 5y = 12$ to slope-intercept form, $y = mx + b$ .

Find the exact values of the six trigonometric functions of $t$ for the point $P=\left(\frac{2 \sqrt{2}}{3},-\frac{1}{3}\right)$ on the unit circle.

Calculate the value of $\cos 90^{\circ} + \cot 45^{\circ}$ without using a calculator.

Calculate the exact value of $\sin 46^{\circ} - \cos 44^{\circ}$ without a calculator.

Calculate the value of $\sin 90^{\circ} + \tan 45^{\circ}$ without a calculator.

Calculate the value of $2 \cos \frac{\pi}{3} - 6 \tan \frac{\pi}{6}$ without using a calculator.

Find the value of $\cot \frac{3 \pi}{2} + \cos \frac{3 \pi}{2}$ without a calculator.

Find the exact value of $\sin 29^{\circ} - \cos 61^{\circ}$ without a calculator.

Find the midpoint of the segment with endpoints $(9,5)$ and $(1,1)$ .

Find the midpoint between the points $(8,7)$ and $(2,10)$ .

Find the range of values of $p$ such that both $3x^{2}+2px+3=0$ and $x^{2}+4x-p=0$ have real roots.

Find the equations of lines through $(-2,3)$ : one parallel to $y=-2x+4$ and one perpendicular to it.

Find the distance between the points (6,9) and (-3,7) in simplest radical form: $d = \sqrt{(6 - (-3))^2 + (9 - 7)^2}$

Define the function $f$ : $f(x) = -3x + 4$ for $x < 1$ and $f(x) = 4x - 3$ for $x \geq 1$ . Find its domain, intercepts, graph, and range.

Solve the system of equations: $x - \frac{y}{7} = -1$ and $-\frac{x}{2} + \frac{y}{16} = \frac{1}{4}$ .

Find the values of $x$ and $y$ that satisfy the equation $2x + 3y = 12$ for the point $(3,1)$ .

Define the function $f(x)$ as: $f(x)=x$ if $x<0$ and $f(x)=x^{2}$ if $x \geq 0$ . Find its domain, intercepts, graph, and range.

Find the sum function $(f+g)(x)$ for $f(x)=5x+4$ if $x<2$ and $x^2+4x$ if $x \geq 2$ , and $g(x)=-3x+1$ if $x \leq 0$ and $g(x)=x-7$ if $x > 0$ .

Find the values of $m$ such that $2x - 2m + (x + m)^{2} > 0$ for all real $x$ .

Identify the types of functions $f(x)=x^{3}+x^{2}-3 x+4$ and $g(x)=2^{x}-4$ . What do they have in common?

Find the slope of the line given by the equation $2x + 3y = 12$ .

Calculate the wind chill $W$ for $t=10^{\circ}C$ and $v=1 \text{ m/s}$ using the given formula. Round to the nearest degree.

Find the prime factors of the number 105. What is its prime factorization? $105 =$

Solve $(x+1)(x-2)=3$ and express your answers in surd form.

Find the coordinates of the point $(x,y)$ that satisfies the equation $3x - 5y = 15$ at the point $(6,1)$ .

Find the prime factorization of 76 using exponents for repeated factors. $76=$

Find the roots of $2 x = -5 + 3 x^{2}$ and the values of $c$ for which $3 x^{2} + 5 x + c > 0$ .

Find the least common multiple (LCM) of 84 and 24. The LCM is $\text{lcm}(84, 24)$ .

Find the prime factorization of 44 using exponents for repeated factors. $44 =$

Determine the number of significant figures in $20.00_{3}$ .

Calculate the product of 3.15, 2.5, and 4.00 with the correct significant figures: $3.15 \times 2.5 \times 4.00 =$

Find the result of $313.0 - (1.2 \times 10^{3})$ with the correct significant figures.

Calculate $(4.123 \times 0.12) + 24.2$ and give the result with the right significant figures.

Calculate $(17.103 + 2.03) \times 1.02521$ with the correct number of significant figures.

Find the value of $k$ for the function $f(x)=\left\{\begin{array}{ll}\frac{\sqrt{x+3}-\sqrt{3 x-1}}{x-2} & x \neq 2 \\ k & x=2\end{array}\right.$ to be continuous.

Rewrite the equation $x^{2}-14 x-1$ as $(x+ a)^2 + b$ with integers $a$ and $b$ .