Math Statement

Problem 23601

Solve the equation $|3 k-2|=2|k+2|$ .

See Solution

Problem 23602

Find the measure of $\angle 2$ if $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ .

See Solution

Problem 23603

Simplify the expression: $\frac{1}{\cos \theta}-\cos \theta$ .

See Solution

Problem 23604

Add and simplify: $\frac{\sin \theta}{\cos \theta}+\frac{1}{\sin \theta}$ .

See Solution

Problem 23605

Multiply and simplify: $(\sin \theta+5)(\sin \theta+6)$

See Solution

Problem 23606

Multiply and simplify: $(1-\sin \theta)(1+\sin \theta)$ .

See Solution

Problem 23607

Multiply and simplify: $(4 \cos \theta + 5)(7 \cos \theta - 2)$ .

See Solution

Problem 23608

Multiply and simplify: $(2-\tan \theta)(2+\tan \theta)$ .

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Problem 23609

Prove that $\cos \theta \tan \theta = \sin \theta$ is an identity by simplifying the left side.

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Problem 23610

Simplify the expression $(\sin \theta - \cos \theta)^{2}$ .

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Problem 23611

Prove the identity $\sin \theta \sec \theta \cot \theta = 1$ by simplifying the left side using $\sin \theta$ and $\cos \theta$ .

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Problem 23612

Prove that $\frac{\csc \theta}{\cot \theta}=\sec \theta$ by simplifying the left side to match the right side.

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Problem 23613

Simplify $\sqrt{x^{2}-16}$ after substituting $x = 4 \sec(\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

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Problem 23614

Simplify the expression: $\frac{\sec \theta \cot \theta}{\csc \theta}$ . Show that it equals 1.

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Problem 23615

Prove the identity: $(1-\cos \theta)(1+\cos \theta)=\sin ^{2} \theta$ by simplifying the left side.

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Problem 23616

Prove the identity: $\csc \theta - \sin \theta = \frac{\cos^{2} \theta}{\sin \theta}$ . Simplify the left side.

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Problem 23617

Prove the identity: $\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}=1$ by simplifying the left side.

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Problem 23618

Simplify the expression $\sin \theta+\frac{1}{\cos \theta}$ .

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Problem 23619

Simplify $\sqrt{9-x^{2}}$ by substituting $x=3 \sin (\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

See Solution

Problem 23620

Find the value of $f(1)$ for the function $f(x)=9.1 x^{2}+0.5 x$ . Provide your answer as a decimal or whole number.

See Solution

Problem 23621

Create a truth table for the expression $\sim(q \leftrightarrow \sim p)$ .

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Problem 23622

Determine if the statement $(p \wedge q) \wedge(\sim p \vee \sim q)$ is a tautology, self-contradiction, or neither using a truth table.

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Problem 23623

Show that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ and solve $\log _{3} x+\log _{9} x=4$ .

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Problem 23624

Calculate the significant figures for the result of $4.5 \times 10^{14} / 8.3 \times 10^{8}.$

See Solution

Problem 23625

Convert $4.5 \mathrm{~m}^{3}$ to $\mathrm{L}$ .

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Problem 23626

Calculate $6.2 \times 10^{-13} \times 5.68 \times 10^{8}$ and report the answer with the correct significant figures.

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Problem 23627

Prove that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ .

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Problem 23628

Find the tangent line equation to the curve $y=-x^{2}+5x-4$ at $x=1$ .

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Problem 23629

Prove that $\frac{\sin \frac{\theta}{2}-\sqrt{1+\sin \theta}}{\cos \frac{\theta}{2}-\sqrt{1+\sin \theta}}=\cot \frac{\theta}{2}$ .

See Solution

Problem 23630

Find the values of the following Fibonacci numbers: $F_{22}, F_{46}, F_{20}, F_{12}, F_{18}, F_{6}, F_{28}, F_{19}, F_{25}, F_{10}$ .

See Solution

Problem 23631

Find the reflection of the line $x=4$ across the $y$ -axis.

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Problem 23632

Find the limit as $x$ approaches 4 for the expression $x^{3}+x$ .

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Problem 23633

Identify equivalent equations for $p-q=-93$ . Which of these are equivalent?
1. $\frac{p-q}{3}=-31$
2. $\frac{p-q}{3}=-32$
3. $\frac{p-q}{-3}=29$
4. $\frac{p-q}{-3}=31$

See Solution

Problem 23634

Identify equivalent equations to $15=t-u$ from the options: $20=t-u+5$ , $17=2+t-u$ , $18=t-u+3$ , $19=t-u+4$ .

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Problem 23635

Identify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

See Solution

Problem 23636

Find all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

See Solution

Problem 23637

Find all equations equivalent to: $-62 = r + s$ . Consider the following options.

See Solution

Problem 23638

Select equations equivalent to $15 = r + s$ using properties of equality: $20 = r + s + 5$ , $19 = 4 + r + s$ , $18 = 3 + r + s$ , $17 = r + s + 2$ .

See Solution

Problem 23639

Find pairs of factors for 50 and complete the equations: 50 = 2 \cdot 15, 50 = __.

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Problem 23640

Find the prime factorization of 10 and list the factors in ascending order (e.g., $2 \times 5$ ).

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Problem 23641

Find all factor pairs for 16 and complete the equations:
$16=1 \cdot 16 \\ 16=2 \cdot 8 \\ 16=$

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Problem 23642

Solve the equation $\log _{2} x - \log _{2} 7 = \log _{2}(x - 1)$ .

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Problem 23643

Solve the system of equations using an inverse matrix and show the inverse matrix $A^{-1}$ used.
$2x - 3y = -8$ $-4x + y = -2$

See Solution

Problem 23644

Find two equations that equal 48 using multiplication, similar to: $48 = 1 \cdot 48$ , $48 = 2 \cdot 24$ .

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Problem 23645

Find the vertices and foci of the hyperbola $\frac{y^{2}}{49}-\frac{x^{2}}{36}=1$ . Enter as $(0, \pm a)$ and $(0, \pm c)$ .

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Problem 23646

Solve the inequality: $\log _{\frac{3}{5}}(2-x)+\log _{\frac{3}{5}}(x+2)>\log _{\frac{3}{5}} 3 x$ .

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Problem 23647

Graph the hyperbola from the equation $25 x^{2}-36 y^{2}-900=0$ using its transverse axis, vertices, and co-vertices.

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Problem 23648

Solve the inequality: $(\log_{2} x)^{2} - \log_{2} x < 0$ .

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Problem 23649

Evaluate these limits: 1. $\lim_{x \to 4}(x^3 + x)$ 2. $\lim_{x \to 4}(x^2 + 1)$ 3. $\lim_{x \to 2} \frac{x^2 - x - 2}{x^2 - 2x}$ 4. $\lim_{x \to 1} \frac{x^2 - 2x + 1}{x^3 - x}$ 5. $\lim_{x \to \infty} \frac{\sqrt{x^2 + 1}}{x^2}$ 6. $\lim_{x \to 4}(x^2 + 3x - 5)$ 7. $\lim_{y \to \infty}(y^3 - 2y + 7)$ 8. $\lim_{t \to 0} \frac{2t^2 + 1}{t^3 + 3t - 4}$ 9. $\lim_{x \to 1} \frac{(s + 1)^2}{2x^2 + 3}$ 10. $\lim_{w \to 2} \frac{3w^2 - 4w + 2}{w^3 - 5}$ 11. $\lim_{w \to -1} \frac{3w^2 - 2w + 7}{w^2 + 1}$ 12. $\lim_{x \to 2} \frac{\sqrt{x - 2}}{\sqrt{x^2 - 4}}$ 13. $\lim_{x \to 2} \frac{(1 - x^2)^{1}}{(1 - x^2)^2}$ 14. $\lim_{x \to 3} \frac{x - 3}{\sqrt{x^2 - 9}}$ 15. $\lim_{x \to \infty} \frac{4}{2x^2 - 3}$ 16. $\lim_{x \to \infty} \frac{2x^2}{3x^2 + 5}$ 17. $\lim_{x \to \infty} \frac{x^2}{3x^2 - 4x + 1}$ 18. $\lim_{x \to \infty} 2^{\frac{3}{x}}$ 19. $\lim_{x \to 0^+} 2^{\frac{1}{x}}$ 20. $\lim_{x \to 0^+} \frac{1}{1 + 2^{\frac{1}{x}}}$

See Solution

Problem 23650

Risolvi la disequazione: $472\left(\log _{2} x\right)^{2}-\log _{2} x<0$ .

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Problem 23651

Find the asymptotes of the hyperbola: $\frac{(y+1)^{2}}{9}-\frac{(x-2)^{2}}{64}=1$ .

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Problem 23652

Solve the inequality: $\log ^{2} x - 7 \log x + 12 < 0$ .

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Problem 23653

Find the average rate of change of $y=2 \times 3^{x}$ from $x=0$ to $x=4$ . Options: A 40.5 B 162 C 158 D 40 E 4

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Problem 23654

Find $\frac{d y}{d x}$ for $y=\frac{2 x^{4}+9 x^{2}}{4 x}$ . Choices include options A to E.

See Solution

Problem 23655

Find $\frac{d y}{d x}$ for $y=\frac{2 x^{4}+9 x^{2}}{4 x}$ . Options: A, B, C, D, E.

See Solution

Problem 23656

Find $\frac{d y}{d x}$ for $y=\frac{2 x^{4}+9 x^{2}}{4 x}$ . Choices are A, B, C, D, E.

See Solution

Problem 23657

Which expression is NOT equal to $(3 x-12)(x+4)$ ? $3\left(x^{2}-8 x+16\right)$ , $3\left(x^{2}-16\right)$ , $3 x^{2}-48$ , $3 x(x+4)-12(x+4)$

See Solution

Problem 23658

Find the volume of a cylinder with $r=2b$ and $h=5b+3$ using $V=\pi r^{2} h$ in terms of $b$ .

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Problem 23659

Find the values of $y$ and the gradient at $x=-1$ for the function $y=-4x^3-x^2+3x+1$ .

See Solution

Problem 23660

Solve for $x$ in the equation: $12 x - 30 = -6$ .

See Solution

Problem 23661

Solve for $x$ : $3 x + 1 = 10$

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Problem 23662

Solve for $t$ in the equation: $8 - 3t = 2$ .

See Solution

Problem 23663

Solve for $y$ in the equation: $15 - 3y = 15$ .

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Problem 23664

Solve for $a$ in the equation $6 a + 5 = 9$ .

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Problem 23665

Find the derivative of $f(x)=\frac{3x+5}{4-x}$ .

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Problem 23666

Solve for c in the equation: $8 \cdot 4 - 2 = 3c$ .

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Problem 23667

Calculate $(54 \div 9) \times 3$ .

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Problem 23668

Solve for $c$ in the equation: $4 - 2 = 3c$ .

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Problem 23669

Solve the equation: $-8 x + 3 = -29$ .

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Problem 23670

Show that the curve $y=2 x^{2}-3 x+1$ and the line $y=k x+k^{2}$ intersect for any constant $k$ .

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Problem 23671

Calculate $(14-7) \times(40-32)$ .

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Problem 23672

Calculate $\frac{1}{2} \times(12+8)$ .

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Problem 23673

Solve the inequality: $6 \leq n + 3 \frac{1}{4}$ .

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Problem 23674

Solve the equation: $\frac{y-7}{2 y}=\frac{5}{y}$ .

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Problem 23675

Find the derivative of $f(x)=(2x-x^{3})\sqrt{2-x^{2}}$ .

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Problem 23676

Solve the equation: $\frac{x^{3}-2 x^{2}}{x^{3}}=-2 x^{2}$ .

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Problem 23677

Calculate $82 \times (-13)$ .

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Problem 23678

Solve for $x$ : $-x^{2}+10 x=3 x+6$

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Problem 23679

Balance the equation $\mathrm{Ga}_{2} \mathrm{O}_{3}(s)+6 \mathrm{HCl}(aq) \rightarrow 2 \mathrm{GaCl}_{3}(aq)+3 \mathrm{H}_{2} \mathrm{O}(l)$ and perform stoichiometry calculations.

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Problem 23680

Evaluate $h + 9g$ for $g=4$ and $h=6$ .

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Problem 23681

Find values for the function $f(x)=6$ : (a) $f(9)$ , (b) $f(-9)$ , (c) $f(3.3)$ , (d) $f(-3.6)$ .

See Solution

Problem 23682

Find the value of $f(p)$ for the function $f(x)=\sqrt{-8-x}$ .

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Problem 23683

Find $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ for the piecewise function: $f(x) = \{-2x + 16 \text{ if } x \leq -4; 3 \text{ if } -4 < x < 3; x + 8 \text{ if } x \geq 3\}$ .

See Solution

Problem 23684

Evaluate $f(x)=x^{2}-4$ for (a) $f(3 p)$ , (b) $f(-3 q)$ , and (c) $f(x+5)$ .

See Solution

Problem 23685

Find the derivative of $f(x)=\frac{2-5 x}{\cos 10 x}$ .

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Problem 23686

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=9x+1$ and $h \neq 0$ . Simplify your answer.

See Solution

Problem 23687

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+4$ where $h \neq 0$ . Simplify your answer.

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Problem 23688

Calculate the state's income tax function $h(x)$ for the following incomes: (a) $h(1260)$ , (b) $h(7160)$ , (c) $h(49070)$ .

See Solution

Problem 23689

Calculate the income tax $h(x)$ for the following incomes: (a) $1260$ , (b) $7160$ , (c) $49070$ . Round to the nearest cent.

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Problem 23690

Solve: $(-4) \times\left(\frac{7}{5}\right) \times\left(-\frac{3}{4}\right) \div\left(\frac{7}{15}\right)$

See Solution

Problem 23691

Evaluate the expression when $c=6$ and $d=26$ : $d-\frac{30}{0}$ .

See Solution

Problem 23692

Evaluate $d - \frac{30}{c}$ for $c=6$ and $d=26$ .

See Solution

Problem 23693

Verify if $\frac{2^{1}}{4}$ equals $\frac{7}{4}$ .

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Problem 23694

Estimate the mean age of females at first child birth using $f(x)=22 x^{0.045}$ for the years 2010, 2013, and 2019.

See Solution

Problem 23695

Solve for $n$ in the equation $\frac{2}{m}+\frac{3}{n}=2$ .

See Solution

Problem 23696

Find $y$ for $y=\frac{1}{x}$ when $x$ is -4, -3, -2, -1, 0, 1, 2.

See Solution

Problem 23697

Find the values of $y$ for $y=\frac{1}{x}$ when $x = -4, -3, -2, -1, 0, 1, 2, 3, 4$ .

See Solution

Problem 23698

Solve for $m$ in the equation: $251 = m - 8(5m - 7)$ .

See Solution

Problem 23699

Convert $8.44 \times 10^{-3} \mathrm{~m}$ to millimeters (mm).

See Solution

Problem 23700

Calculate the value of $-8 + 10$ .

See Solution

1 ...234 235 236 237 238 239 240 ...270

Math Statement

Problem 23601

Solve the equation ∣3k−2∣=2∣k+2∣|3 k-2|=2|k+2|∣3k−2∣=2∣k+2∣.

Problem 23602

Find the measure of ∠2\angle 2∠2 if m∠1=(2x+29)∘\mathrm{m} \angle 1=(2 x+29)^{\circ}m∠1=(2x+29)∘ and m∠2=(3x−17)∘\mathrm{m} \angle 2=(3 x-17)^{\circ}m∠2=(3x−17)∘.

Problem 23603

Simplify the expression: 1cos⁡θ−cos⁡θ\frac{1}{\cos \theta}-\cos \thetacosθ1​−cosθ.

Problem 23604

Add and simplify: sin⁡θcos⁡θ+1sin⁡θ\frac{\sin \theta}{\cos \theta}+\frac{1}{\sin \theta}cosθsinθ​+sinθ1​.

Problem 23605

Multiply and simplify: (sin⁡θ+5)(sin⁡θ+6)(\sin \theta+5)(\sin \theta+6)(sinθ+5)(sinθ+6)

Problem 23606

Multiply and simplify: (1−sin⁡θ)(1+sin⁡θ)(1-\sin \theta)(1+\sin \theta)(1−sinθ)(1+sinθ).

Problem 23607

Multiply and simplify: (4cos⁡θ+5)(7cos⁡θ−2)(4 \cos \theta + 5)(7 \cos \theta - 2)(4cosθ+5)(7cosθ−2).

Problem 23608

Multiply and simplify: (2−tan⁡θ)(2+tan⁡θ)(2-\tan \theta)(2+\tan \theta)(2−tanθ)(2+tanθ).

Problem 23609

Prove that cos⁡θtan⁡θ=sin⁡θ\cos \theta \tan \theta = \sin \thetacosθtanθ=sinθ is an identity by simplifying the left side.

Problem 23610

Simplify the expression (sin⁡θ−cos⁡θ)2(\sin \theta - \cos \theta)^{2}(sinθ−cosθ)2.

Problem 23611

Prove the identity sin⁡θsec⁡θcot⁡θ=1\sin \theta \sec \theta \cot \theta = 1sinθsecθcotθ=1 by simplifying the left side using sin⁡θ\sin \thetasinθ and cos⁡θ\cos \thetacosθ.

Problem 23612

Prove that csc⁡θcot⁡θ=sec⁡θ\frac{\csc \theta}{\cot \theta}=\sec \thetacotθcscθ​=secθ by simplifying the left side to match the right side.

Problem 23613

Simplify x2−16\sqrt{x^{2}-16}x2−16​ after substituting x=4sec⁡(θ)x = 4 \sec(\theta)x=4sec(θ), where 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}0∘<θ<90∘.

Problem 23614

Simplify the expression: sec⁡θcot⁡θcsc⁡θ\frac{\sec \theta \cot \theta}{\csc \theta}cscθsecθcotθ​. Show that it equals 1.

Problem 23615

Prove the identity: (1−cos⁡θ)(1+cos⁡θ)=sin⁡2θ(1-\cos \theta)(1+\cos \theta)=\sin ^{2} \theta(1−cosθ)(1+cosθ)=sin2θ by simplifying the left side.

Problem 23616

Prove the identity: csc⁡θ−sin⁡θ=cos⁡2θsin⁡θ\csc \theta - \sin \theta = \frac{\cos^{2} \theta}{\sin \theta}cscθ−sinθ=sinθcos2θ​. Simplify the left side.

Problem 23617

Prove the identity: cos⁡θsec⁡θ+sin⁡θcsc⁡θ=1\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}=1secθcosθ​+cscθsinθ​=1 by simplifying the left side.

Problem 23618

Simplify the expression sin⁡θ+1cos⁡θ\sin \theta+\frac{1}{\cos \theta}sinθ+cosθ1​.

Problem 23619

Simplify 9−x2\sqrt{9-x^{2}}9−x2​ by substituting x=3sin⁡(θ)x=3 \sin (\theta)x=3sin(θ), where 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}0∘<θ<90∘.

Problem 23620

Find the value of f(1)f(1)f(1) for the function f(x)=9.1x2+0.5xf(x)=9.1 x^{2}+0.5 xf(x)=9.1x2+0.5x. Provide your answer as a decimal or whole number.

Problem 23621

Create a truth table for the expression ∼(q↔∼p)\sim(q \leftrightarrow \sim p)∼(q↔∼p).

Problem 23622

Determine if the statement (p∧q)∧(∼p∨∼q)(p \wedge q) \wedge(\sim p \vee \sim q)(p∧q)∧(∼p∨∼q) is a tautology, self-contradiction, or neither using a truth table.

Problem 23623

Show that log⁡3x+log⁡9x=3lg⁡x2lg⁡3\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}log3​x+log9​x=2lg33lgx​ and solve log⁡3x+log⁡9x=4\log _{3} x+\log _{9} x=4log3​x+log9​x=4.

Problem 23624

Calculate the significant figures for the result of 4.5×1014/8.3×108.4.5 \times 10^{14} / 8.3 \times 10^{8}.4.5×1014/8.3×108.

Problem 23625

Convert 4.5 m34.5 \mathrm{~m}^{3}4.5 m3 to L\mathrm{L}L.

Problem 23626

Calculate 6.2×10−13×5.68×1086.2 \times 10^{-13} \times 5.68 \times 10^{8}6.2×10−13×5.68×108 and report the answer with the correct significant figures.

Problem 23627

Prove that log⁡3x+log⁡9x=3lg⁡x2lg⁡3\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}log3​x+log9​x=2lg33lgx​.

Problem 23628

Find the tangent line equation to the curve y=−x2+5x−4y=-x^{2}+5x-4y=−x2+5x−4 at x=1x=1x=1.

Problem 23629

Prove that sin⁡θ2−1+sin⁡θcos⁡θ2−1+sin⁡θ=cot⁡θ2\frac{\sin \frac{\theta}{2}-\sqrt{1+\sin \theta}}{\cos \frac{\theta}{2}-\sqrt{1+\sin \theta}}=\cot \frac{\theta}{2}cos2θ​−1+sinθ​sin2θ​−1+sinθ​​=cot2θ​.

Problem 23630

Find the values of the following Fibonacci numbers: F22,F46,F20,F12,F18,F6,F28,F19,F25,F10F_{22}, F_{46}, F_{20}, F_{12}, F_{18}, F_{6}, F_{28}, F_{19}, F_{25}, F_{10}F22​,F46​,F20​,F12​,F18​,F6​,F28​,F19​,F25​,F10​.

Problem 23631

Find the reflection of the line x=4x=4x=4 across the yyy-axis.

Problem 23632

Find the limit as xxx approaches 4 for the expression x3+xx^{3}+xx3+x.

Problem 23633

Identify equivalent equations for p−q=−93p-q=-93p−q=−93. Which of these are equivalent? 1. p−q3=−31\frac{p-q}{3}=-313p−q​=−31 2. p−q3=−32\frac{p-q}{3}=-323p−q​=−32 3. p−q−3=29\frac{p-q}{-3}=29−3p−q​=29 4. p−q−3=31\frac{p-q}{-3}=31−3p−q​=31

Problem 23634

Identify equivalent equations to 15=t−u15=t-u15=t−u from the options: 20=t−u+520=t-u+520=t−u+5, 17=2+t−u17=2+t-u17=2+t−u, 18=t−u+318=t-u+318=t−u+3, 19=t−u+419=t-u+419=t−u+4.

Problem 23635

Identify all equations equivalent to: −30=14y-30=14 y−30=14y. Consider properties of equality. Options: 60=−2⋅14y60=-2 \cdot 14 y60=−2⋅14y, −60=14y⋅2-60=14 y \cdot 2−60=14y⋅2, 90=14y⋅−390=14 y \cdot-390=14y⋅−3, −90=14y⋅3-90=14 y \cdot 3−90=14y⋅3.

Problem 23636

Find all equations equivalent to 12=4c12=4c12=4c using properties of equality: 2=4c−102=4c-102=4c−10, 9=4c−29=4c-29=4c−2, 10=4c−210=4c-210=4c−2, 4=4c−84=4c-84=4c−8.

Problem 23637

Find all equations equivalent to: −62=r+s-62 = r + s−62=r+s. Consider the following options.

Problem 23638

Select equations equivalent to 15=r+s15 = r + s15=r+s using properties of equality: 20=r+s+520 = r + s + 520=r+s+5, 19=4+r+s19 = 4 + r + s19=4+r+s, 18=3+r+s18 = 3 + r + s18=3+r+s, 17=r+s+217 = r + s + 217=r+s+2.

Problem 23639

Find pairs of factors for 50 and complete the equations: 50 = 2 \cdot 15, 50 = __.

Problem 23640

Solve the equation $|3 k-2|=2|k+2|$ .

Find the measure of $\angle 2$ if $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ .

Simplify the expression: $\frac{1}{\cos \theta}-\cos \theta$ .

Add and simplify: $\frac{\sin \theta}{\cos \theta}+\frac{1}{\sin \theta}$ .

Multiply and simplify: $(\sin \theta+5)(\sin \theta+6)$

Multiply and simplify: $(1-\sin \theta)(1+\sin \theta)$ .

Multiply and simplify: $(4 \cos \theta + 5)(7 \cos \theta - 2)$ .

Multiply and simplify: $(2-\tan \theta)(2+\tan \theta)$ .

Prove that $\cos \theta \tan \theta = \sin \theta$ is an identity by simplifying the left side.

Simplify the expression $(\sin \theta - \cos \theta)^{2}$ .

Prove the identity $\sin \theta \sec \theta \cot \theta = 1$ by simplifying the left side using $\sin \theta$ and $\cos \theta$ .

Prove that $\frac{\csc \theta}{\cot \theta}=\sec \theta$ by simplifying the left side to match the right side.

Simplify $\sqrt{x^{2}-16}$ after substituting $x = 4 \sec(\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

Simplify the expression: $\frac{\sec \theta \cot \theta}{\csc \theta}$ . Show that it equals 1.

Prove the identity: $(1-\cos \theta)(1+\cos \theta)=\sin ^{2} \theta$ by simplifying the left side.

Prove the identity: $\csc \theta - \sin \theta = \frac{\cos^{2} \theta}{\sin \theta}$ . Simplify the left side.

Prove the identity: $\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}=1$ by simplifying the left side.

Simplify the expression $\sin \theta+\frac{1}{\cos \theta}$ .

Simplify $\sqrt{9-x^{2}}$ by substituting $x=3 \sin (\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

Find the value of $f(1)$ for the function $f(x)=9.1 x^{2}+0.5 x$ . Provide your answer as a decimal or whole number.

Create a truth table for the expression $\sim(q \leftrightarrow \sim p)$ .

Determine if the statement $(p \wedge q) \wedge(\sim p \vee \sim q)$ is a tautology, self-contradiction, or neither using a truth table.

Show that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ and solve $\log _{3} x+\log _{9} x=4$ .

Calculate the significant figures for the result of $4.5 \times 10^{14} / 8.3 \times 10^{8}.$

Convert $4.5 \mathrm{~m}^{3}$ to $\mathrm{L}$ .

Calculate $6.2 \times 10^{-13} \times 5.68 \times 10^{8}$ and report the answer with the correct significant figures.

Prove that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ .

Find the tangent line equation to the curve $y=-x^{2}+5x-4$ at $x=1$ .

Prove that $\frac{\sin \frac{\theta}{2}-\sqrt{1+\sin \theta}}{\cos \frac{\theta}{2}-\sqrt{1+\sin \theta}}=\cot \frac{\theta}{2}$ .

Find the values of the following Fibonacci numbers: $F_{22}, F_{46}, F_{20}, F_{12}, F_{18}, F_{6}, F_{28}, F_{19}, F_{25}, F_{10}$ .

Find the reflection of the line $x=4$ across the $y$ -axis.

Find the limit as $x$ approaches 4 for the expression $x^{3}+x$ .

Identify equivalent equations for $p-q=-93$ . Which of these are equivalent?
1. $\frac{p-q}{3}=-31$
2. $\frac{p-q}{3}=-32$
3. $\frac{p-q}{-3}=29$
4. $\frac{p-q}{-3}=31$

Identify equivalent equations to $15=t-u$ from the options: $20=t-u+5$ , $17=2+t-u$ , $18=t-u+3$ , $19=t-u+4$ .

Identify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

Find all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

Find all equations equivalent to: $-62 = r + s$ . Consider the following options.

Select equations equivalent to $15 = r + s$ using properties of equality: $20 = r + s + 5$ , $19 = 4 + r + s$ , $18 = 3 + r + s$ , $17 = r + s + 2$ .

Find the prime factorization of 10 and list the factors in ascending order (e.g., $2 \times 5$ ).

Find all factor pairs for 16 and complete the equations:
$16=1 \cdot 16 \\ 16=2 \cdot 8 \\ 16=$

Solve the equation $\log _{2} x - \log _{2} 7 = \log _{2}(x - 1)$ .

Solve the system of equations using an inverse matrix and show the inverse matrix $A^{-1}$ used.
$2x - 3y = -8$ $-4x + y = -2$

Find two equations that equal 48 using multiplication, similar to: $48 = 1 \cdot 48$ , $48 = 2 \cdot 24$ .

Find the vertices and foci of the hyperbola $\frac{y^{2}}{49}-\frac{x^{2}}{36}=1$ . Enter as $(0, \pm a)$ and $(0, \pm c)$ .

Solve the inequality: $\log _{\frac{3}{5}}(2-x)+\log _{\frac{3}{5}}(x+2)>\log _{\frac{3}{5}} 3 x$ .

Graph the hyperbola from the equation $25 x^{2}-36 y^{2}-900=0$ using its transverse axis, vertices, and co-vertices.

Solve the inequality: $(\log_{2} x)^{2} - \log_{2} x < 0$ .

Risolvi la disequazione: $472\left(\log _{2} x\right)^{2}-\log _{2} x<0$ .

Find the asymptotes of the hyperbola: $\frac{(y+1)^{2}}{9}-\frac{(x-2)^{2}}{64}=1$ .

Solve the inequality: $\log ^{2} x - 7 \log x + 12 < 0$ .

Find the average rate of change of $y=2 \times 3^{x}$ from $x=0$ to $x=4$ . Options: A 40.5 B 162 C 158 D 40 E 4

Find $\frac{d y}{d x}$ for $y=\frac{2 x^{4}+9 x^{2}}{4 x}$ . Choices include options A to E.

Find $\frac{d y}{d x}$ for $y=\frac{2 x^{4}+9 x^{2}}{4 x}$ . Options: A, B, C, D, E.

Find $\frac{d y}{d x}$ for $y=\frac{2 x^{4}+9 x^{2}}{4 x}$ . Choices are A, B, C, D, E.

Which expression is NOT equal to $(3 x-12)(x+4)$ ? $3\left(x^{2}-8 x+16\right)$ , $3\left(x^{2}-16\right)$ , $3 x^{2}-48$ , $3 x(x+4)-12(x+4)$

Find the volume of a cylinder with $r=2b$ and $h=5b+3$ using $V=\pi r^{2} h$ in terms of $b$ .

Find the values of $y$ and the gradient at $x=-1$ for the function $y=-4x^3-x^2+3x+1$ .

Solve for $x$ in the equation: $12 x - 30 = -6$ .

Solve for $x$ : $3 x + 1 = 10$

Solve for $t$ in the equation: $8 - 3t = 2$ .

Solve for $y$ in the equation: $15 - 3y = 15$ .

Solve for $a$ in the equation $6 a + 5 = 9$ .

Find the derivative of $f(x)=\frac{3x+5}{4-x}$ .

Solve for c in the equation: $8 \cdot 4 - 2 = 3c$ .

Calculate $(54 \div 9) \times 3$ .

Solve for $c$ in the equation: $4 - 2 = 3c$ .

Solve the equation: $-8 x + 3 = -29$ .

Show that the curve $y=2 x^{2}-3 x+1$ and the line $y=k x+k^{2}$ intersect for any constant $k$ .

Calculate $(14-7) \times(40-32)$ .

Calculate $\frac{1}{2} \times(12+8)$ .

Solve the inequality: $6 \leq n + 3 \frac{1}{4}$ .

Solve the equation: $\frac{y-7}{2 y}=\frac{5}{y}$ .