Math Statement

Problem 2401

If $\mathrm{e}^{b}=a$ , which of the following must be true?
1. $b>a$
2. $\ln a=b$
3. $a+b>0$

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Problem 2402

Expand and simplify $(4 x+3)(x+6)$

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Problem 2403

Trovare il centro e il raggio della circonferenza data da $x^{2}+y^{2}+4 x-6 y+9=$ 0 .

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Problem 2404

(2) Show that the lines $5 x+2 y=8$ and $y-x=4$
Are neither parallel nor perpendicular.

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Problem 2405

Charlotte-Mecklenburg Schools post-Activity: How many solutions do these equations have? that involve imaginary numbers?
1. $x^{2}+14 x+44=0$
2. $x^{2}+14 x+49=0$
3. $x^{2}+14 x+54=0$

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Problem 2406

Divide. $\left(-10 x^{4}+18 x^{2}+8 x-3\right) \div\left(-5 x^{2}-1\right)$
Write your answer in the following form: quotient $+\frac{\text { pemainder }}{-5 x^{2}-1}$ . $\frac{-10 x^{4}+18 x^{2}+8 x-3}{-5 x^{2}-1}=\square+\frac{\square}{-5 x^{2}-1}$

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Problem 2407

$8 v=42+v$
Simplify your answer as much as possible. $v=$ $\square$
Start over

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Problem 2408

$\log (x+5) + \log (x-5) = 4 \log^2 + 2 \log^3$

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Problem 2409

$\frac{-7 \pm \sqrt{7)^{2}-4(-2)(-3)}}{2(-2)}$

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Problem 2410

Factor as the product of two binomials. $x^{2}+11 x+18=$

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Problem 2411

$x^{2}+4 x+4=49$

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Problem 2412

ctivity 1: Finding Complex Solutions Ive these equations by completing the square. $x^{2}-8 x+13=0$
2. $x^{2}-8 x+19=0$

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Problem 2413

b) $\frac{\sqrt{2}+\sqrt{5}}{\sqrt{6}-\sqrt{10}}$

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Problem 2414

Determine $\tan 2 x$ for $\csc x=4$ , where $x$ is in Quad I.

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Problem 2415

15. Convert to exponential form: $\log _{3} x=10$ $3^{x}=10$ $10^{x}=3$ $3^{10}=x$ $x^{10}=3$ Clear All

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Problem 2416

Solve the following system of equations. $\left\{\begin{array}{l} x^{2}+y^{2}=13 \\ y-2 x=4 \end{array}\right.$

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Problem 2417

3 In Exercises 25-38, solve each equation by the method of your choice. Support your solution by a second method.
31. $\frac{e^{x}+e^{-x}}{2}=4$
32. $2 e^{2 x}+5 e^{x}-3=0$
33. $\frac{500}{1+25 e^{0.3 x}}=200$
34. $\frac{400}{1+95 e^{-0.6 x}}=150$
35. $\frac{1}{2} \ln (x+3)-\ln x=0$
36. $\log x-\frac{1}{2} \log (x+4)=1$

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Problem 2418

Compute $(-27)^{\frac{2}{3}}-(-32)^{\frac{-3}{5}}$

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Problem 2419

Solve the equation. Give a general formula for all the solutions. $2 \cos x-1=0$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\mathrm{x}=$ $\square$ (Simplify your answer. Type your answer(s) as an expression, using $n$ as the variable, in the form $a+b n$ where $0 \leq a<2 \pi$ . Type any angle measures in radians, using $\pi$ as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution.

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Problem 2420

2) $2 \sin ^{2} x=\sin x$

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Problem 2421

AD1 \& AD2: Product and Quotient Rules Differentiate the following functions. Show the $[\cdot]^{\prime}$ step in your work.
1. $f(x)=\left(x^{4}+5 x-1\right) \cdot(3 x+2)$
2. $g(x)=\frac{2 x^{4}+7 x}{5 x+1}$

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Problem 2422

$\begin{array}{c}z^{2}+2 z+2=0 \\ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \\ a=\frac{2 x^{2}+b x+c=0}{2} \quad c=2 \\ -b=-2 \quad 4 a c= \\ b^{2}=\quad 2 a=\end{array}$

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Problem 2423

oint-Slope Form of a Linear Equation 1 of 10 D. Figueroa Current Skill \$ SHOW ANSWER
Write an equation for the line, in point-slope form, that passes through the following point and has the following slope:
Slope: $\frac{-3}{2}$ Point: $(3,5)$ $\square$ $\frac{y}{x}$ $x^{2}$ f(x) $\sqrt[n]{x}$ $x_{n}$ $\checkmark$ $\pi$ skill code: 302031

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Problem 2424

and more apples than oranges were purchased, how many pieces of each kind were bought? (39) Let $m, n \in \mathbf{Z}$ prove that $2 m+3 n$ is divisible by 17 if and only if $9 m+5 n$ is divisible by 17 .

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Problem 2425

Question Watch Video Show Examples
Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x$ . $\log 3 x^{5}$
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 2426

Problem 1. (6 points) Compute the following limits: (a) (2 points) $\lim _{n \rightarrow \infty} \frac{4 n^{7}+4 n^{4}+3}{4+3 n^{4}+4 n^{7}}$ (b) (2 points) $\lim _{n \rightarrow \infty}\left(\frac{4 n+3}{4 n-3}\right)^{4 n+12}$ (c) (2 points) $\lim _{n \rightarrow \infty} \sqrt[n]{7^{n}+4 \cos (n)}$

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Problem 2427

3. $f(x)=9 x+8 \quad g(x)=9+3 x$ Find $h(x)=f(x)+g(x)$ .

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Problem 2428

2. $f(x)=10 x+2 \quad g(x)=-6 x-8$ Find $h(x)=f(x)+g(x)$ .

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Problem 2429

$-5 \cdot x \cdot y+e^{x+y}=4$ a. Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ in terms of $x$ and $y$ . $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $a^{b}$ $\sin (a)$ $\frac{\partial}{\partial x} f$ : $\infty$ $\alpha$ $\Omega$ $\frac{5 y-e^{x+y}}{e^{x+y}-5 x}$ b. Find the value of $\frac{d y}{d x}$ at the point $P(\sqrt{5},-\sqrt{5})$ . $\left.\frac{\mathrm{d} y}{\mathrm{~d} x}\right|_{(\sqrt{5},-\sqrt{5})}=$

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Problem 2430

4. For each equation, identify the slope and $y$ -intercept of its graph. a) $y=4 x-7$ b) $y=x+12$ c) $y=-\frac{4}{9} x+7$ d) $y=11 x-\frac{3}{8}$

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Problem 2431

Simplify the following expression. $\left(2 x^{2}-x+3\right)(2 x+5)$

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Problem 2432

Solve for $w$ . $-2(-2 w+5)-6 w=4(w-3)-8$
Simplify your answer as much as possible.

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Problem 2433

Condense the logarithm $8 \log b+y \log k$

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Problem 2434

For the given cost function $C(x)=48400+200 x+x^{2}$ , which gives the total cost (\ $) for$ x $items. Find the average cost function:$ \bar{C}(x)=\square $Find the production level that will minimize the average cost:$ x=\square$ items
Find the minimal average cost: $\square$ Question Help: $\square$ Video Submit Question

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Problem 2435

$4(x-6)^{2}=36$

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Problem 2436

Find the solution of the system of equations. $\begin{array}{c} 15 x-10 y=-30 \\ 5 x-9 y=7 \end{array}$

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Problem 2437

Solve for $x$ . $-3 \log _{3}(-2 x)=-9$

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Problem 2438

Solve for the exact value of $x$ . $\log _{7}(2 x)-2 \log _{7}(8)=1$

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Problem 2439

3/10
Write $y=x^{2}-18 x+52$ in vertex form. $y=(x-9)^{2}+52$ $y=(x-9)^{2}-29$ $y=(x-9)^{2}+113$ $y=(x+9)^{2}-29$

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Problem 2440

Solve for the exact value of $x$ . $\log _{6}(3 x)+2 \log _{6}(3)=4$

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Problem 2441

5/10
What is the vertex of $y=2(x-3)^{2}+$ 6 $(-3,6)$ $(-3,-6)$ $(3,6)$ $(3,-6)$

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Problem 2442

olve for the exact value of $x$ . $5 \ln (5 x+9)-4=11$

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Problem 2443

Write the logarithmic equation as an exponential equation. $\log 1=0$
The equivalent exponential equation is $\square$ . (Use integers or fractions for any numbers in the equation.)

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Problem 2444

Write the expression with positive exponents only. Then simplify, if possible. $8^{-2}$

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Problem 2445

Solve the following log equation: $\ln (2 x-5)=\ln (x+3)$
Type your answer in the form $x=$ $\qquad$ -

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Problem 2446

$\log _{4} 256+\log _{x}\left(\frac{1}{16}\right)=2$

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Problem 2447

7/10
What is the vertex of the parabola: $y=2(x-3)^{2}+4$ $(3,-4)$ $(-3,4)$ $(-3,-4)$ $(3,4)$

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Problem 2448

Find the exact value of $\sin \frac{7 \pi}{4}$ $\sin \frac{7 \pi}{4}=$

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Problem 2449

a. Find $z_{t t}$ for $z_{t t}=\quad z(x, y, t)=\cos (\sqrt{4+49 t}) \cdot \sin (2 x) \cdot \sin (7 y)$ $a^{b}$ $\sin (a) \quad \frac{\partial}{\partial x} f$ : $\infty$ $\alpha$ $\Omega$ ? b. Does $u=\sin (\sqrt{53} \cdot t) \cdot \sin (2 x) \cdot \sin (7 y)$ satisfy the membrane equation $u_{t t}=u_{x x}+u_{y y} ?$ Yes No

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Problem 2450

8/10
Convert the equation $y=5 x^{2}-40 x+$ 67 into vertex form. $y=5(x-13)^{2}+4$ $y=-5(x+4)^{2}+13$ $y=5(x+4)^{2}-13$ $y=5(x-4)^{2}-13$

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Problem 2451

Use the power rule to expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions. $\log _{5} t^{2}$ $\log _{5} t^{2}=$ $\square$ (Type an exact answer in simplified form.)

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Problem 2452

Use the quotient rule to expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions. $\log _{8}\left(\frac{3}{a}\right)$ $\log _{8}\left(\frac{3}{a}\right)=$ $\square$ (Type an exact answer in simplified form.)

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Problem 2453

Use the change of base formula to compute $\log _{3} 5$ . Round your answer to the nearest thousandth.

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Problem 2454

$\left(k^{3}-10 k^{2}+14 k+15\right) \div(k-8)$

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Problem 2455

Find the vertex of the following functions: $y=(x+4)^{2}+9$ ( $\square$ $\square$ )

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Problem 2456

$\left(r^{3}-6 r^{2}+11 r-10\right) \div(r-1)$

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Problem 2457

Solve for $x$ . $3+\frac{10}{x}=\frac{1}{2}$
Simplify your answer as much as possible. $x=$

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Problem 2458

$5=\frac{2}{7 b}+7$
Simplify your answer as much as possible. $b=$

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Problem 2459

4) Soit $f$ une fonction définie sur $\mathbb{R}$ par: $\boldsymbol{f}(\boldsymbol{x})=\dot{x}^{3}+\dot{x}+1$ a) Montrer que l'équation $\boldsymbol{f}(\boldsymbol{x})=\mathbf{0}$ admet une solution unique $\alpha$ dans $\mathbb{R}$ et que $-1<\alpha<0$ b) Trouver un encadrement de $\alpha$ d'amplitude 0,25. (1pt) c) Déduire le signe de $f$ sur $\mathbb{R}$ (1pt) d) Montrer que $\alpha=-\sqrt[3]{\alpha+1}$ (0,5pt) 5) Soit $f$ la fonction continue sur $[a ; b]$ tel que $f(a)<0$
Montrer $\exists c \in] a ; b[;(b-c) f(c)=a-c$ (1pt)

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Problem 2460

Use algebraic procedures to find the exact $\begin{array}{l} \ln \left(x^{2}-4\right)=\ln (x+16) \\ x=\square \end{array}$

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Problem 2461

Use algebraic procedures to find the exact so $\begin{array}{l} \log _{3} x+\log _{3}(x+6)=3 \\ x=\square \end{array}$

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Problem 2462

18. The approximate value of $x$ in the equation $17^{x-1}=12^{x+3}$ is A. 10.6 B. 12.6 C. 29.5 D. 31.5

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Problem 2463

Solve the logarithmic equation. $\begin{array}{l} \log _{6} x=4 \\ x=\square \end{array}$ $\square$ (Simpary your answer. Type an exact answer, using $e$ as needed.)

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Problem 2464

19. $\frac{\log (r)}{t}+\frac{\log (d)}{t}$ is equal to A. $\log (r d)^{t}$ B. $\log (\sqrt[4]{r d})$ C. $\log (\sqrt[4]{r+d})$ D. $\log (r+d)^{t}$

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Problem 2465

$\sqrt{2 x+5}-\frac{3}{\sqrt{2 x+5}}=-2$

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Problem 2466

6. Find the exact absolute maximum and minimum of $h(x)=x e^{-x^{2}}$ on the interval $[-1,1]$ .
7. Let $f(x)=\ln \left(2 x^{3}-3 x^{2}\right)$ . Find all values of $x$ for which $f^{\prime}(x)$ is 0 or undefined. Determine

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Problem 2467

20. The $x$ -intercept of the graph of $y=\log _{b} x$ , where $b>0$ and $b \neq 1$ , is A. 0 B. 1 C. undefined D. dependent on the value of $b$

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Problem 2468

ercices et Résolution de problèmes : Trouve la valeur de : $25\left(-\log _{5} \sqrt{2}\right)$

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Problem 2469

Suppose that $w=x^{2} \cdot \exp (2 y) \cdot \cos (6 z)$ with $\begin{array}{c} x=\sin \left(t+\frac{\pi}{2}\right) \\ y=\ln (t+7) \\ z=t \end{array}$ a. Find $\frac{\mathrm{d} w}{\mathrm{~d} t}$ in terms of $t$ . $\frac{\mathrm{d} w}{\mathrm{~d} t}=$ $a^{b}$ $\sin (a) \quad \frac{\partial}{\partial x} f$ : $\infty$ $\alpha$ $\Omega$

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Problem 2470

3. Consider the following quadratic function. $g(x)=-2 x^{2}-8 x-6$ (a) Write the equation in the form $g(x)=a(x-h)^{2}+k$ . Then give the vertex of its graph. (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the vertex, and two points to the right of the vertex. 1

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Problem 2471

15. Solve the equation beliow for a $w=7 a+4 b$ A. $a=\frac{w-7 b}{4}$ B. $a=\frac{w}{7}-4 b$ C. $a=\frac{w-4 b}{7}$ D. $a=\frac{w}{7}-28 b$

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Problem 2472

La función $g$ se define como sigue en el dominio dado. $g(x)=3 x+1, \quad \text { dominio }=\{-2,-1,0,1\}$
Escribir el rango de $g$ utilizando notación de conjuntos. Luego trazar el gráfico de $g$ . rango = $\square$

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Problem 2473

Use Taylor's formula for $f(x, y)$ at $(0,0)$ to find the quadratic approximations of $f$ near the origin when $f(x, y) \approx \quad f(x, y)=\frac{5}{7-x-2 y+7 x y} .$

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Problem 2474

Question Watch Video
Evaluate the expression shown below and write your answer as a mixed number in simplest form. $6 \frac{1}{2} \times \frac{9}{10}$

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Problem 2475

Question Show Exam
Find the distance between the two points in simplest radical form. $(8,6) \text { and }(3,-6)$

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Problem 2476

Question Find the distance between the two points in simplest radical form. $(-8,-3) \text { and }(-1,4)$
Answer Attempt 1 out of 2

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Problem 2477

11 A B C D $\mathbf{E}$
Select correct applications of the very famous identity. A) the quantity $\sin ^{4}(\theta)+\cos ^{4}(\theta)$ can always be exchanged for " 1 " $\sin ^{2}(\theta)+\cos ^{2}(\theta)=1$ B) the quantity " $\cos ^{2}(\theta)$ " can always be exchanged for $1-\sin ^{2}(\theta)$ C) "1" can always be exchanged for the quantity $\sin ^{2}(\theta)+\cos ^{2}(\theta)$ D) the quantity $\sin ^{2}(\theta)+\cos ^{2}(\theta)$ can always be exchanged for " 1 " E) the quantity $" \sin ^{2}(\theta)$ " can always be exchanged for $1-\cos ^{2}(\theta)$

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Problem 2478

9. Determine $g(x+a)-g(x)$ for the following function. $g(x)=2 x+1$
Answer: $\quad g(x+a)-g(x)=$

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Problem 2479

Question 5 Use algebra to find the inverse of the function $f(x)=-2 x^{9}+1$ The inverse function is $f^{-1}(x)=$ $\square$

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Problem 2480

Suppose $y$ is a function of $x$ , i.e. $y=y(x)$ , and $-12 \cdot x \cdot y+4 \cdot e^{x+y}=-16$ a. Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ in terms of $x$ and $y$ . $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

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Problem 2481

O Polynomial and Rational Functions Using the rational zeros theorem to find all zeros of a polynomial: Compl...
The function below has at least one rational zero. Use this fact to find all zeros of the function. $g(x)=5 x^{3}+6 x^{2}+16 x+3$
If there is more than one zero, separate them with commas. Write exact values, not decimal approximations. $\square$ Explanation Check @ 2024 McGraw Hill LLC. All Rights Reserved. Terms

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Problem 2482

Given: $\mathrm{Q}=\sqrt{\frac{3}{x-2}}-\frac{x}{5}$ 1.3.1 For which value(s) of $x$ will $Q$ be a real number? 1.3.2 Show that Q is a rational number if $x=5$ $x=-3 \pm 2 \sqrt{2}$ are the roots of a quadratic function, $f(x)$ of which the $y$ intercept is 4 Determine $f(x)$ .

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Problem 2483

Suppose $x+\frac{1}{x}=1$ compute the value of $x^{2133}+x^{-2133}$ A) $\frac{-1}{2133}$ B) $\frac{1}{2133}$ C) $x$ D) $\frac{1}{x^{-2133}}$ E) 1 F) $\frac{1}{x}$ G) 2 H) 3 I) $\frac{1}{x^{2133}}$

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Problem 2484

For $f(x)=\frac{-5 x-5}{x^{2}-x-6}$ and $g(x)=\frac{x+1}{3-x}$ , find the following. (a) $R(x)=f(x)+g(x)$ $R(x)=$ (b) $R(x)=f(x)-g(x)$ $R(x)=$

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Problem 2485

ections: Simplify each problem. SHUw AL $-3(3-2 x)+2(5 x-4)$

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Problem 2486

following are equal to 9 ? Select all that apply. Multi-select Actid to $\begin{array}{l} 3^{2} \\ (-3)^{2} \\ -(-3)^{2} \\ -3^{2} \end{array}$ $\sim$ Multi-Select

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Problem 2487

BXERCTCR 63 La figure en-dessous est la représentation de la restriction d'une fonction $f$ sur $[-2 ; 2]$ . ésou 1) Montrer que pour tout $x \in[-2 ; 2]$ : $f(x)=|x+1|+|x-1|$ 2) On suppose que la fonction $f$ est périodiqued période 4 et on considère l'intervalle : $I_{k}=[4 k ; 4(k+1)[\text { où } k \in \mathbb{Z}$

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Problem 2488

Next question Get a similar ques given $f(x)=\frac{13 x-6}{-4 x-9}$ , find $f^{-1}(x)$

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Problem 2489

The function $g$ is defined by the following rule. $g(x)=-3 x+5$
Complete the function table. \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline-4 & $\square$ \\ \hline-3 & $\square$ \\ \hline 0 & $\square$ \\ \hline 2 & $\square$ \\ \hline 3 & $\square$ \\ \hline \end{tabular}

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Problem 2490

3.) $-4(x+2)-\frac{1}{2}(2 x-6)$

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Problem 2491

The function $h$ is defined by the following $h(x)=-4 x-4$
Complete the function table. \begin{tabular}{|c|c|} \hline $x$ & $h(x)$ \\ \hline-3 & $\square$ \\ \hline 0 & $\square$ \\ \hline 3 & $\square$ \\ \hline 4 & $\square$ \\ \hline 5 & $\square$ \\ \hline \end{tabular}

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Problem 2492

4.) $4 x+10(2 x)-8 x$

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Problem 2493

Consider the following function. $u(x)=(x+6)^{3}$
Step 2 of 2: Determine the domain and range of the original function. Express your answer in interval notation.
Answer 2 Points

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Problem 2494

Divide: $4,081 \div 17=$ $\square$ R $\square$ Submit

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Problem 2495

Divide: $16,500 \div 330=$ $\square$ R $\square$ Submit

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Problem 2496

Consider the following functions. $f(1)=3 \text { and } g(1)=-15$
Step 1 of 4: Find $(f+g)(1)$ .
AnswerHow to enter your answer (opens in new window) 2 Points $(f+g)(1)=$ $\square$

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Problem 2497

Divide: $41,885 \div 274=$ $\square$ R $\square$
Submit

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Problem 2498

5.) $-6 x-10(x-4)$

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Problem 2499

Divide: $39,973 \div 17=$ $\square$ R $\square$ Submit

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Problem 2500

Divide: $7,761 \div 37=$ $\square$ R $\square$ Submit

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1 ...22 23 24 25 26 27 28 ...269

Math Statement

Problem 2401

If eb=a\mathrm{e}^{b}=aeb=a, which of the following must be true?1. b>ab>ab>a2. ln⁡a=b\ln a=blna=b3. a+b>0a+b>0a+b>0

Problem 2402

Expand and simplify (4x+3)(x+6)(4 x+3)(x+6)(4x+3)(x+6)

Problem 2403

Trovare il centro e il raggio della circonferenza data da x2+y2+4x−6y+9=x^{2}+y^{2}+4 x-6 y+9=x2+y2+4x−6y+9= 0 .

Problem 2404

(2) Show that the lines 5x+2y=85 x+2 y=85x+2y=8 and y−x=4y-x=4y−x=4Are neither parallel nor perpendicular.

Problem 2405

Charlotte-Mecklenburg Schools post-Activity: How many solutions do these equations have? that involve imaginary numbers?1. x2+14x+44=0x^{2}+14 x+44=0x2+14x+44=02. x2+14x+49=0x^{2}+14 x+49=0x2+14x+49=03. x2+14x+54=0x^{2}+14 x+54=0x2+14x+54=0

Problem 2406

Problem 2407

8v=42+v8 v=42+v8v=42+vSimplify your answer as much as possible. v=v=v= □\square□Start over

Problem 2408

log⁡(x+5)+log⁡(x−5)=4log⁡2+2log⁡3\log (x+5) + \log (x-5) = 4 \log^2 + 2 \log^3log(x+5)+log(x−5)=4log2+2log3

Problem 2409

−7±7)2−4(−2)(−3)2(−2)\frac{-7 \pm \sqrt{7)^{2}-4(-2)(-3)}}{2(-2)}2(−2)−7±7)2−4(−2)(−3)​​

Problem 2410

Factor as the product of two binomials. x2+11x+18=x^{2}+11 x+18=x2+11x+18=

Problem 2411

x2+4x+4=49x^{2}+4 x+4=49x2+4x+4=49

Problem 2412

ctivity 1: Finding Complex Solutions Ive these equations by completing the square. x2−8x+13=0x^{2}-8 x+13=0x2−8x+13=02. x2−8x+19=0x^{2}-8 x+19=0x2−8x+19=0

Problem 2413

b) 2+56−10\frac{\sqrt{2}+\sqrt{5}}{\sqrt{6}-\sqrt{10}}6​−10​2​+5​​

Problem 2414

Determine tan⁡2x\tan 2 xtan2x for csc⁡x=4\csc x=4cscx=4, where xxx is in Quad I.

Problem 2415

15. Convert to exponential form: log⁡3x=10\log _{3} x=10log3​x=10 3x=103^{x}=103x=10 10x=310^{x}=310x=3 310=x3^{10}=x310=x x10=3x^{10}=3x10=3 Clear All

Problem 2416

Solve the following system of equations. {x2+y2=13y−2x=4\left\{\begin{array}{l} x^{2}+y^{2}=13 \\ y-2 x=4 \end{array}\right.{x2+y2=13y−2x=4​

Problem 2417

Problem 2418

Compute (−27)23−(−32)−35(-27)^{\frac{2}{3}}-(-32)^{\frac{-3}{5}}(−27)32​−(−32)5−3​

Problem 2419

Problem 2420

2) 2sin⁡2x=sin⁡x2 \sin ^{2} x=\sin x2sin2x=sinx

Problem 2421

AD1 \& AD2: Product and Quotient Rules Differentiate the following functions. Show the [⋅]′[\cdot]^{\prime}[⋅]′ step in your work.1. f(x)=(x4+5x−1)⋅(3x+2)f(x)=\left(x^{4}+5 x-1\right) \cdot(3 x+2)f(x)=(x4+5x−1)⋅(3x+2)2. g(x)=2x4+7x5x+1g(x)=\frac{2 x^{4}+7 x}{5 x+1}g(x)=5x+12x4+7x​

Problem 2422

Problem 2423

Problem 2424

and more apples than oranges were purchased, how many pieces of each kind were bought? (39) Let m,n∈Zm, n \in \mathbf{Z}m,n∈Z prove that 2m+3n2 m+3 n2m+3n is divisible by 17 if and only if 9m+5n9 m+5 n9m+5n is divisible by 17 .

Problem 2425

Question Watch Video Show ExamplesExpand the logarithm fully using the properties of logs. Express the final answer in terms of log⁡x\log xlogx. log⁡3x5\log 3 x^{5}log3x5Answer Attempt 1 out of 2 □\square□ Submit Answer

Problem 2426

Problem 2427

3. f(x)=9x+8g(x)=9+3xf(x)=9 x+8 \quad g(x)=9+3 xf(x)=9x+8g(x)=9+3x Find h(x)=f(x)+g(x)h(x)=f(x)+g(x)h(x)=f(x)+g(x).

Problem 2428

2. f(x)=10x+2g(x)=−6x−8f(x)=10 x+2 \quad g(x)=-6 x-8f(x)=10x+2g(x)=−6x−8 Find h(x)=f(x)+g(x)h(x)=f(x)+g(x)h(x)=f(x)+g(x).

Problem 2429

Problem 2430

4. For each equation, identify the slope and yyy-intercept of its graph. a) y=4x−7y=4 x-7y=4x−7 b) y=x+12y=x+12y=x+12 c) y=−49x+7y=-\frac{4}{9} x+7y=−94​x+7 d) y=11x−38y=11 x-\frac{3}{8}y=11x−83​

Problem 2431

Simplify the following expression. (2x2−x+3)(2x+5)\left(2 x^{2}-x+3\right)(2 x+5)(2x2−x+3)(2x+5)

Problem 2432

Solve for www. −2(−2w+5)−6w=4(w−3)−8-2(-2 w+5)-6 w=4(w-3)-8−2(−2w+5)−6w=4(w−3)−8Simplify your answer as much as possible.

Problem 2433

Condense the logarithm 8log⁡b+ylog⁡k8 \log b+y \log k8logb+ylogk

Problem 2434

Problem 2435

4(x−6)2=364(x-6)^{2}=364(x−6)2=36

Problem 2436

Find the solution of the system of equations. 15x−10y=−305x−9y=7\begin{array}{c} 15 x-10 y=-30 \\ 5 x-9 y=7 \end{array}15x−10y=−305x−9y=7​

Problem 2437

Solve for xxx. −3log⁡3(−2x)=−9-3 \log _{3}(-2 x)=-9−3log3​(−2x)=−9

Problem 2438

Solve for the exact value of xxx. log⁡7(2x)−2log⁡7(8)=1\log _{7}(2 x)-2 \log _{7}(8)=1log7​(2x)−2log7​(8)=1

Problem 2439

3/10Write y=x2−18x+52y=x^{2}-18 x+52y=x2−18x+52 in vertex form. y=(x−9)2+52y=(x-9)^{2}+52y=(x−9)2+52 y=(x−9)2−29y=(x-9)^{2}-29y=(x−9)2−29 y=(x−9)2+113y=(x-9)^{2}+113y=(x−9)2+113 y=(x+9)2−29y=(x+9)^{2}-29y=(x+9)2−29

Problem 2440

Solve for the exact value of xxx. log⁡6(3x)+2log⁡6(3)=4\log _{6}(3 x)+2 \log _{6}(3)=4log6​(3x)+2log6​(3)=4

Problem 2441

5/10What is the vertex of y=2(x−3)2+y=2(x-3)^{2}+y=2(x−3)2+ 6 (−3,6)(-3,6)(−3,6) (−3,−6)(-3,-6)(−3,−6) (3,6)(3,6)(3,6) (3,−6)(3,-6)(3,−6)

Problem 2442

olve for the exact value of xxx. 5ln⁡(5x+9)−4=115 \ln (5 x+9)-4=115ln(5x+9)−4=11

Problem 2443

Write the logarithmic equation as an exponential equation. log⁡1=0\log 1=0log1=0The equivalent exponential equation is □\square□ . (Use integers or fractions for any numbers in the equation.)

Problem 2444

If $\mathrm{e}^{b}=a$ , which of the following must be true?
1. $b>a$
2. $\ln a=b$
3. $a+b>0$

Expand and simplify $(4 x+3)(x+6)$

Trovare il centro e il raggio della circonferenza data da $x^{2}+y^{2}+4 x-6 y+9=$ 0 .

(2) Show that the lines $5 x+2 y=8$ and $y-x=4$
Are neither parallel nor perpendicular.

Charlotte-Mecklenburg Schools post-Activity: How many solutions do these equations have? that involve imaginary numbers?
1. $x^{2}+14 x+44=0$
2. $x^{2}+14 x+49=0$
3. $x^{2}+14 x+54=0$

$8 v=42+v$
Simplify your answer as much as possible. $v=$ $\square$
Start over

$\log (x+5) + \log (x-5) = 4 \log^2 + 2 \log^3$

$\frac{-7 \pm \sqrt{7)^{2}-4(-2)(-3)}}{2(-2)}$

Factor as the product of two binomials. $x^{2}+11 x+18=$

$x^{2}+4 x+4=49$

ctivity 1: Finding Complex Solutions Ive these equations by completing the square. $x^{2}-8 x+13=0$
2. $x^{2}-8 x+19=0$

b) $\frac{\sqrt{2}+\sqrt{5}}{\sqrt{6}-\sqrt{10}}$

Determine $\tan 2 x$ for $\csc x=4$ , where $x$ is in Quad I.

15. Convert to exponential form: $\log _{3} x=10$ $3^{x}=10$ $10^{x}=3$ $3^{10}=x$ $x^{10}=3$ Clear All

Solve the following system of equations. $\left\{\begin{array}{l} x^{2}+y^{2}=13 \\ y-2 x=4 \end{array}\right.$

Compute $(-27)^{\frac{2}{3}}-(-32)^{\frac{-3}{5}}$

2) $2 \sin ^{2} x=\sin x$

AD1 \& AD2: Product and Quotient Rules Differentiate the following functions. Show the $[\cdot]^{\prime}$ step in your work.
1. $f(x)=\left(x^{4}+5 x-1\right) \cdot(3 x+2)$
2. $g(x)=\frac{2 x^{4}+7 x}{5 x+1}$

and more apples than oranges were purchased, how many pieces of each kind were bought? (39) Let $m, n \in \mathbf{Z}$ prove that $2 m+3 n$ is divisible by 17 if and only if $9 m+5 n$ is divisible by 17 .

Question Watch Video Show Examples
Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x$ . $\log 3 x^{5}$
Answer Attempt 1 out of 2 $\square$ Submit Answer

3. $f(x)=9 x+8 \quad g(x)=9+3 x$ Find $h(x)=f(x)+g(x)$ .

2. $f(x)=10 x+2 \quad g(x)=-6 x-8$ Find $h(x)=f(x)+g(x)$ .

4. For each equation, identify the slope and $y$ -intercept of its graph. a) $y=4 x-7$ b) $y=x+12$ c) $y=-\frac{4}{9} x+7$ d) $y=11 x-\frac{3}{8}$

Simplify the following expression. $\left(2 x^{2}-x+3\right)(2 x+5)$

Solve for $w$ . $-2(-2 w+5)-6 w=4(w-3)-8$
Simplify your answer as much as possible.

Condense the logarithm $8 \log b+y \log k$

$4(x-6)^{2}=36$

Find the solution of the system of equations. $\begin{array}{c} 15 x-10 y=-30 \\ 5 x-9 y=7 \end{array}$

Solve for $x$ . $-3 \log _{3}(-2 x)=-9$

Solve for the exact value of $x$ . $\log _{7}(2 x)-2 \log _{7}(8)=1$

3/10
Write $y=x^{2}-18 x+52$ in vertex form. $y=(x-9)^{2}+52$ $y=(x-9)^{2}-29$ $y=(x-9)^{2}+113$ $y=(x+9)^{2}-29$

Solve for the exact value of $x$ . $\log _{6}(3 x)+2 \log _{6}(3)=4$

5/10
What is the vertex of $y=2(x-3)^{2}+$ 6 $(-3,6)$ $(-3,-6)$ $(3,6)$ $(3,-6)$

olve for the exact value of $x$ . $5 \ln (5 x+9)-4=11$

Write the logarithmic equation as an exponential equation. $\log 1=0$
The equivalent exponential equation is $\square$ . (Use integers or fractions for any numbers in the equation.)

Write the expression with positive exponents only. Then simplify, if possible. $8^{-2}$

Solve the following log equation: $\ln (2 x-5)=\ln (x+3)$
Type your answer in the form $x=$ $\qquad$ -

$\log _{4} 256+\log _{x}\left(\frac{1}{16}\right)=2$

7/10
What is the vertex of the parabola: $y=2(x-3)^{2}+4$ $(3,-4)$ $(-3,4)$ $(-3,-4)$ $(3,4)$

Find the exact value of $\sin \frac{7 \pi}{4}$ $\sin \frac{7 \pi}{4}=$

8/10
Convert the equation $y=5 x^{2}-40 x+$ 67 into vertex form. $y=5(x-13)^{2}+4$ $y=-5(x+4)^{2}+13$ $y=5(x+4)^{2}-13$ $y=5(x-4)^{2}-13$

Use the power rule to expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions. $\log _{5} t^{2}$ $\log _{5} t^{2}=$ $\square$ (Type an exact answer in simplified form.)

Use the quotient rule to expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions. $\log _{8}\left(\frac{3}{a}\right)$ $\log _{8}\left(\frac{3}{a}\right)=$ $\square$ (Type an exact answer in simplified form.)

Use the change of base formula to compute $\log _{3} 5$ . Round your answer to the nearest thousandth.

$\left(k^{3}-10 k^{2}+14 k+15\right) \div(k-8)$

Find the vertex of the following functions: $y=(x+4)^{2}+9$ ( $\square$ $\square$ )

$\left(r^{3}-6 r^{2}+11 r-10\right) \div(r-1)$

Solve for $x$ . $3+\frac{10}{x}=\frac{1}{2}$
Simplify your answer as much as possible. $x=$

$5=\frac{2}{7 b}+7$
Simplify your answer as much as possible. $b=$

Use algebraic procedures to find the exact $\begin{array}{l} \ln \left(x^{2}-4\right)=\ln (x+16) \\ x=\square \end{array}$

Use algebraic procedures to find the exact so $\begin{array}{l} \log _{3} x+\log _{3}(x+6)=3 \\ x=\square \end{array}$

18. The approximate value of $x$ in the equation $17^{x-1}=12^{x+3}$ is A. 10.6 B. 12.6 C. 29.5 D. 31.5

Solve the logarithmic equation. $\begin{array}{l} \log _{6} x=4 \\ x=\square \end{array}$ $\square$ (Simpary your answer. Type an exact answer, using $e$ as needed.)

19. $\frac{\log (r)}{t}+\frac{\log (d)}{t}$ is equal to A. $\log (r d)^{t}$ B. $\log (\sqrt[4]{r d})$ C. $\log (\sqrt[4]{r+d})$ D. $\log (r+d)^{t}$

$\sqrt{2 x+5}-\frac{3}{\sqrt{2 x+5}}=-2$

20. The $x$ -intercept of the graph of $y=\log _{b} x$ , where $b>0$ and $b \neq 1$ , is A. 0 B. 1 C. undefined D. dependent on the value of $b$

ercices et Résolution de problèmes : Trouve la valeur de : $25\left(-\log _{5} \sqrt{2}\right)$

15. Solve the equation beliow for a $w=7 a+4 b$ A. $a=\frac{w-7 b}{4}$ B. $a=\frac{w}{7}-4 b$ C. $a=\frac{w-4 b}{7}$ D. $a=\frac{w}{7}-28 b$

La función $g$ se define como sigue en el dominio dado. $g(x)=3 x+1, \quad \text { dominio }=\{-2,-1,0,1\}$
Escribir el rango de $g$ utilizando notación de conjuntos. Luego trazar el gráfico de $g$ . rango = $\square$

Use Taylor's formula for $f(x, y)$ at $(0,0)$ to find the quadratic approximations of $f$ near the origin when $f(x, y) \approx \quad f(x, y)=\frac{5}{7-x-2 y+7 x y} .$

Question Watch Video
Evaluate the expression shown below and write your answer as a mixed number in simplest form. $6 \frac{1}{2} \times \frac{9}{10}$