Math Statement

Problem 20301

Binomials and trinomials in fractions should be factored after inverting the divisor. $\begin{array}{l} \frac{x^{2}-9}{2 x^{2}-2 x} \cdot \frac{3 x}{x^{2}-x-6} \div \frac{x^{2}+3 x}{x^{2}+7 x+10}= \\ \frac{x^{2}-9}{2 x^{2}-2 x} \cdot \frac{3 x}{x^{2}-x-6} \cdot \frac{x^{2}+7 x+10}{x^{2}+3 x}= \\ \frac{(x+3)(x-3)}{\frac{2 x(x-1)}{2}} \cdot \frac{3 x}{\frac{(x+2)(x-3)}{1} \cdot \frac{(x+5)(x+2)}{x(x+3)}=} \\ \frac{3(x+5)}{2 x(x-1)}=\frac{3 x+15}{2 x^{2}-2 x} \end{array}$
Invert and change to multiplication.
Factor and cancel.
Multiply.
Work these problems.
1. $\frac{2}{3} \cdot \frac{4}{3} \div \frac{12}{9}=$
2. $\frac{4 a^{2}}{5 b} \div \frac{2 a}{b^{2}}=$
3. $\frac{a^{2}-b^{2}}{a^{2}-a b} \cdot \frac{2 a^{2}-2 a}{a-1} \div \frac{a+b}{a^{2}}=$
4. $\frac{a}{b} \div \frac{a}{b}=$
5. $\frac{a}{b^{2}} \div \frac{a^{2}}{b}=$
6. $\frac{x^{5}}{y^{2}} \div \frac{x^{6}}{y^{3}}=$

See Solution

Problem 20302

3. 7 0 \longdiv { 5 , 5 9 1 }

See Solution

Problem 20303

Convert the complex number to polar form: $4-4 i$

See Solution

Problem 20304

Convert the complex number to rectangular form: $z=7 \operatorname{cis} 120^{\circ}$

See Solution

Problem 20305

Find all $\theta$ in the interval $\left[0^{\circ}, 360^{\circ}\right)$ such that: $3 \sin ^{2} \theta+2 \sin \theta-1=0$

See Solution

Problem 20306

Use an identity to re-write the expression as a single function: $2 \sin (16 u) \cos (16 u)$

See Solution

Problem 20307

A particular circle in the standard $(x, y)$ coordinate plane has an equation of $(x-5)^{2}+y^{2}=38$ . What are the radius of the circle, in coordinate units, and the Goordinates of the center of the circle?

See Solution

Problem 20308

Use any appropriate algebraic techniques combined with trigonometric identities to simpli the expression: $\frac{1}{\cos \theta}-\cos \theta$

See Solution

Problem 20309

Use the difference formula for cosine to simplify $\cos \left(\theta-\frac{\pi}{2}\right)$ as a single function of $\theta$ :

See Solution

Problem 20310

Find the reference angle for $\theta=-455^{\circ}$ :

See Solution

Problem 20311

3. Tipo 3: Equaçöes Exponenciais com Logaritmos
Resolva: a) $3^{\log _{3}(x)}=81$ . Estratégia: Reduza a base: $3^{\log _{3}(x)}=3^{4} \Longrightarrow \log _{3}(x)=4$ . b) $5^{2 x}=25^{x+1}$ .
Estratégia: Transforme $25=5^{2}: 5^{2 x}=5_{\downarrow}^{2(x+1)}$ .

See Solution

Problem 20312

Solve the system by the substitution method. $\begin{aligned} x+y & =3 \\ y & =x^{2}-6 x+9 \end{aligned}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ 3. (Type an ordered pair. Use a comma to separate answers if needed.) B. There is no solution.

See Solution

Problem 20313

1. Simples: a) $\log _{4}(x)=2$ . b) $\log _{3}(x+2)=\log _{3}(7)$ . c) $2 \log _{2}(x)=\log _{2}(32)$ .
2. Intermediários: a) $\log _{2}(x)+\log _{2}(x+3)=4$ . b) $\log _{5}(x+4)-\log _{5}(x)=1$ .

See Solution

Problem 20314

Use transformations to graph the function. $q(x)=-(x+2)^{2}+5$

See Solution

Problem 20315

Solve \& State weather the system is inconsistent or equations are dependen $\begin{array}{c} 5 x+y=-5 \\ -15 x-3 y=a \end{array}$

See Solution

Problem 20316

8. $\frac{1}{3}=\frac{-}{9}$

See Solution

Problem 20317

10. $3 a^{2} b \div \frac{3 x}{4 x-y}$

See Solution

Problem 20318

7) $\frac{7.1 \times 10^{6}}{8.2 \times 10^{1}}$

See Solution

Problem 20319

$5 /-x=12$

See Solution

Problem 20320

Solve the formula for x . $\begin{array}{l} \frac{1}{g}+\frac{1}{n}=\frac{1}{x} \\ x=\square \end{array}$

See Solution

Problem 20321

(1 point) Solve the separable differential equation for. $\frac{d y}{d x}=\frac{1+x}{x y^{6}} ; x>0$
Use the following initial condition: $y(1)=2$ . $y^{7}=$ $\square$

See Solution

Problem 20322

Solve the equations
1. $\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0$
2. $2 \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=0$
3. $\frac{d^{2} y}{d x^{2}}-4 y=0$
4. $\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}-2 y=0$
5. $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+y=0$
6. $\frac{d^{2} y}{d x^{2}}-5 \frac{d y}{d x}+6 y=0$
7. $\frac{d^{2} y}{d x^{2}}+y=0$
8. $3 \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}-y=0$
9. $4 \frac{d^{2} y}{d x^{2}}+4 \frac{d y}{d x}+y=0$
10. $\frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}-10 y=0$
11. $\frac{d^{2} y}{d x^{2}}-9 y=0$
12. $\frac{d^{2} y}{d x^{2}}+9 y=0$
13. $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+y=0$
14. $\frac{d^{2} y}{d x^{2}}-10 \frac{d y}{d x}+25 y=0$
15. $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+4 y=0$
16. $3 \frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}+y=0$
17. $\frac{d^{2} y}{d x^{2}}-2 a \frac{d y}{d x}+y=0$
18. $\frac{d^{2} y}{d x^{2}}-6 \frac{d y}{d x}+13 y=0$

See Solution

Problem 20323

System C
Line 1: $y=-x+1$
Line 2: $y=-\frac{1}{2} x+\frac{1}{2}$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution

See Solution

Problem 20324

Solve this equation to find the value of d. $58=36+d$

See Solution

Problem 20325

Factor completely: $11 v^{12}-3 v^{6} k^{4}-8 k^{8}$
Answer Attempt 3 out of 4 $\square$ Submit Answer

See Solution

Problem 20326

Cell B21 What is the solution to this equation? $-4(2 m-7)=3(52-4 m)$

See Solution

Problem 20327

For 1-12, create the slope intercept form $(y=m x+b)$ based on the given information. 1) Slope $=1, b=-5$ 2) Slope $=-\frac{1}{2}, y$ -intercept $=3$

See Solution

Problem 20328

Solve the following system by substitution. $\begin{array}{l} 2 x-y=-7 \\ 4 y-x=7 \end{array}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) A. There is one solution. The solution set is $\square$ \}. (Type an ordered pair.) B. There are infinitely many solutions. The solution set is $\{(\square, y)\}$ , where $y$ is any real number. C. The solution set is $\varnothing$ .

See Solution

Problem 20329

Let $S=\left\{E_{1}, E_{2}, E_{3}, E_{4}\right\}$ be the sample space of an experiment. Event $A=\left\{E_{1}, E_{2}\right\}$ . Event $B=\left\{E_{3}\right\}$ . Event $C=\left\{E_{2}, E_{3}\right\}$ . The probabilities of the sample points are assigned as follows: \begin{tabular}{cc} \hline Sample point & Probability \\ \hline $E_{1}$ & 0.1374 \\ $E_{2}$ & 0.1301 \\ $E_{3}$ & 0.1854 \\ $E_{4}$ & 0.5471 \\ \hline \end{tabular}
Then, the events $A$ and $B$ are independent.
Select one: a. False b. True

See Solution

Problem 20330

1) Solve a) $(x+1)(x+2)=0$

See Solution

Problem 20331

Step 3 We now use the substitution $u=x^{7}+7 x$ and $d u=\left(7 x^{6}+7\right) d x$ to convert the entire integral into one involving only $u$ . $\begin{aligned} \int \frac{7 x^{6}+7}{\left(x^{7}+7 x\right)^{2}} d x & =\int\left(\frac{1}{\left(x^{7}+7 x\right)^{2}}\right)\left(\left(7 x^{6}+7\right) d x\right) \\ & =\int(\square) d u \end{aligned}$ Submit Skip_(you cannot come back)

See Solution

Problem 20332

Question Watch Video
Factor completely: $9 r^{6}+14 r^{3} t^{2}-39 t^{4}$
Answer Attempt 1 out of 4

See Solution

Problem 20333

Next, we integrate the resulting integral with respect to $u$ using the Power Rule. (Use $C$ for the constant of integration.) $\begin{aligned} \int \frac{1}{u^{2}} d u & =\int u^{-2} d u \\ & =\square \end{aligned}$
Finally, replace $u$ by $g(x)=x^{7}+7 x$ to obtain the solution as a function of $x$ . (Use $C$ for the constant of integration.) $\square$

See Solution

Problem 20334

12. The graph of $\mathbf{y}=3-|\mathbf{x}-2|$ can be obtained from $\quad \mathbf{y}=|\mathbf{x}|$ by a) Shifting $\mathbf{y}=|\mathbf{x}|$ 2units up and 3 units right. b) Shifting $\mathbf{y}=|\mathbf{x}| 2$ units right, reflecting it about the $x$ -axis, and shifting down 3 units. c) Shifting $\mathbf{y}=|\mathbf{x}| 2$ units left, reflecting it about the $x$ -axis, and shifting up 3 units. d) Shifting $\mathbf{y}=|\mathbf{x}|$ 2units right, reflecting it about the $x$ -axis, and shifting up 3 units
13. The graph of $\mathbf{y}=5-(\mathbf{x}-3)^{3}$ can be obtained from $y=x^{3}$ by a) Shifting $y=x^{3} 3$ units right, reflecting it about the $y$ -axis, and shifting up 5 units. 44 b) Shifting $y=x^{3} 3$ units left, reflecting it about the $x$ -axis, and shifting up 5 units. c) Shifting $y=x^{3} 3$ units up and 5 units right. d) Shifting $y=x^{3} 3$ units right, reflecting it about the $x$ -axis, and shifting up 5 units.
Exercise 3. Answer the following
1. If the graph of $\mathbf{f}(\mathbf{x})=\mathbf{x}^{2}$ is shifted 4 units right, reflected about the $x$ -axis and shifted 10 units up, then the graph of $f(x)$ becomes:
2. If the graph of $\mathbf{f}(\mathbf{x})=\mathbf{x}^{3}$ is shifted 2 units right, reflected about the $x$ -axis and shifted 1 units down, then the graph of $f(x)$ becomes:
Exercise 4. Use the graph of $f(x)=x^{3}$ to sketch the following graphs a) $f(x+2)$ b) $f(x)+2$ c) $f(x-1)+2$

See Solution

Problem 20335

wo augmented matrices for two linear systems in the variables $x, y$ , and $z$ are given The augmented matrices are in reduced row-echelon form.
For each system, choose the best description of its solution. If applicable, give the solution. (a) $\left[\begin{array}{ccc:c} 1 & 0 & -2 & 1 \\ 0 & 1 & 0 & 4 \\ 0 & 0 & 0 & -7 \end{array}\right]$ The system has no solution. The system has a unique solution. $\square$ $\square$ $\square$ $(x, y, z)=(\square, \square, \square)$ The system has infinitely many solutions. $\begin{array}{l} (x, y, z)=(x, \square, \square) \\ (x, y, z)=(\square, y, \square) \\ (x, y, z)=(\square, \square, z) \end{array}$

See Solution

Problem 20336

$13 \frac{3}{1}=$

See Solution

Problem 20337

Solve for $x$ . $\log _{2}(5 x-7)=1$

See Solution

Problem 20338

Find the derivative of the function. $q=\sqrt{17 r-r^{5}}$

See Solution

Problem 20339

Solve the following equation. $\sqrt{x-3}+5=x$
The solution set is $\square$ B. (Use a comma to separate answers as needed.)

See Solution

Problem 20340

$\left(\frac{3 m^{2} n^{7}}{m}\right)^{5}$

See Solution

Problem 20341

Multiply. $(u+1)(u-3)$

See Solution

Problem 20342

$\left|\frac{b}{12}\right|=10$

See Solution

Problem 20343

17/46 $\left(5^{3} x^{2} y^{4}\right)^{0}$ 0
1 5 5xy

See Solution

Problem 20344

Solve for $x$ . $\ln x=\ln (x-8)-\ln 2$

See Solution

Problem 20345

19/46
According to the product rule, when we multiply powers with the same base, we keep the base and $\qquad$ the exponents.

See Solution

Problem 20346

A logarithmic function has the form of $h(x)=5 \cdot \log _{b} x+d$ , where $b$ is the base and $d$ is a constant. The function contains the input-output pairs of $(10,12)$ and $(100,17)$ . 1) Write two equations that could be used to find the values of $a$ and $b$ . 2) Show that $b=10$ and $d=7$ are solutions.

See Solution

Problem 20347

$-31=-39-\frac{y}{8}$

See Solution

Problem 20348

$-7 x-9=-2 x+31$

See Solution

Problem 20349

A variable $x$ is normally distributed with mean 24 and standard deviation 9. Round your answers to the nearest hundredth as needed. a) Determine the $z$ -score for $x=29$ . $z=0.56 \quad>0^{\infty}$ b) Determine the $z$ -score for $x=23$ . $z=$ c) What value of $x$ has a $z$ -score of 0.67 ? $x=\square$
Enter an integer or decimal number [more.. d) What value of $x$ has a $z$ -score of 0 ? $x=24 \quad$ e) What value of $x$ has a $z$ -score of 0 ? $x=24 \quad 0^{\circ}$

See Solution

Problem 20350

$735 \times 53=$

See Solution

Problem 20351

3. In the equation $y=4 x$ , what is the constant of proportionality? a. $x$ b. $y$ c. 4 d. 0

See Solution

Problem 20352

Factor. $x^{2}-14 x y+24 y^{2}$

See Solution

Problem 20353

Subtract. $(-8 j-6)-(-9 j+6)$

See Solution

Problem 20354

$\int \frac{2 x^{2}+7 x+1}{x^{2}+3 x} d x$

See Solution

Problem 20355

Find the inverse of the function $f(x) = 3x + 3$ .

See Solution

Problem 20356

Use a change of variables or the table to evaluate the following indefinite integral. $\int \frac{e^{3 x}}{e^{3 x}+8} d x$

See Solution

Problem 20357

Solve for $x: 6^{2 x+5}=1296$ $x=$
Question Help: Message instructor

See Solution

Problem 20358

3. $\begin{array}{l} x+5 y=2 \\ x=-4 y+5 \end{array}$

See Solution

Problem 20359

6) $\left(7 \times 5+6^{2}\right)+2$ 7) $\left(86-6^{2}\right)+(-1+3)$ 8) $(35-5)+2+2^{2}$ 9) $(2+2)^{2}+(10+5)$ 10) $\left(61-5^{2}\right) \div(8+4)$

See Solution

Problem 20360

Rewrite the following equation in slope-intercept form. $-3 y-11=11 x$
Write your answer using integers, proper fractions, and improper fractions in simplest form.

See Solution

Problem 20361

26. $-0.04 w+\frac{a}{1.4}-b^{2}$ when $a=0.56, b=-1.2$ , and
28. $\frac{a}{z}$ when $a=\frac{14}{9}$ and $z=28$
30. $\frac{a+b}{a}$ when $a=\frac{1}{6}$ and $b=\frac{3}{4}$

See Solution

Problem 20362

1) Simplify using laws of logarithms and then evaluate. a) $\log 9+\log 6$ b) $\log 48-\log 6$ c) $\log _{3} 7+\log _{3} 3$

See Solution

Problem 20363

7) Given that $\sin \frac{\pi}{6}=\frac{1}{2}$ , use an equivalent trigonometric expression to show that $\cos \frac{2 \pi}{3}=-\frac{1}{2}$

See Solution

Problem 20364

1. $f(x)=x$ , translation 4 units to the left

See Solution

Problem 20365

The equation below describes a proportional relationship between $x$ and $y$ . What is the constant of proportionality $y=\frac{2}{7} x$
The constant of proportionality is $\square$

See Solution

Problem 20366

9) Given that $\cos \frac{3 \pi}{11} \sim 0.6549$ , use equivalent trigonometric expressions to evaluate the following, to four decimal places. a) $\sin \frac{5 \pi}{22}$ b) $\sin \frac{17 \pi}{22}$

See Solution

Problem 20367

2. Solve by factoring. Confirm your results by graphing. a) $x^{2}+7 x-30=0$ c) $x^{2}-x-6=0$ b) $x^{2}+8 x+15=0$ d) $x^{2}-5 x+6=0$

See Solution

Problem 20368

3. Factor the following perfect square trinomials. a) $x^{2}+6 x+9$ c) $9 x^{2}+6 x+1$ b) $x^{2}-8 x+16$ d) $4 x^{2}-12 x+9$

See Solution

Problem 20369

PRACTICE
4. Simplify. a) $\left(2 x+5-6 x^{2}\right)+\left(5 x-9 x^{2}+3\right)$ b) $\left(4 x^{2}-3 x+7\right)-\left(2 x^{2}-3 x+1\right)$ c) $(3 x+5)(4 x-7)$ d) $(2 x-1)(2 x+1)$

See Solution

Problem 20370

Find the derivative of $y$ with respect to $x$ . $y=\tan ^{-1} \sqrt{5 x}$

See Solution

Problem 20371

5. Factor. a) $x^{2}+3 x-40$ c) $81 x^{2}-49$ b) $6 x^{2}+5 x-6$ d) $9 x^{2}+6 x+1$

See Solution

Problem 20372

6. What term will make each expression a perfect trinomial square? a) $x^{2}+6 x+$ c) $4 x^{2}+\square+49$ b) $x^{2}+\square+25$ d) $9 x^{2}-24 x+$

See Solution

Problem 20373

Write in factored form. a) $f(x)=x^{2}-7 x-18$ c) $h(x)=4 x^{2}-25$ b) $g(x)=-2 x^{2}+17 x-8$ d) $y=6 x^{2}+13 x-5$

See Solution

Problem 20374

$\begin{array}{l}f(x)=\frac{x+7}{x-8} \\ f(3)=\end{array}$

See Solution

Problem 20375

8. Determine the vertex of each quadratic function, and state the domain and range of each. a) $y=x^{2}+6 x+5$ c) $g(x)=-6 x^{2}-7 x+3$ b) $f(x)=2 x^{2}-5 x-12$ d) $h(x)=-3 x^{2}+9 x+30$

See Solution

Problem 20376

17) $9.3 \times 10^{-8}-8.3 \times 10^{-5}$ 19) $\left(2.3 \times 10^{2}\right)\left(5 \times 10^{1}\right)$ 21) $\left(2.1 \times 10^{-4}\right)\left(3.05 \times 10^{1}\right)$ 23) $\frac{6.3 \times 10^{-5}}{7 \times 10^{4}}$ 25) $\frac{8.88 \times 10^{-1}}{2 \times 10^{6}}$

See Solution

Problem 20377

possible
Use the echelon method to solve the system of two equations in two unknowns. Check your answers. $\begin{array}{l} 3 x-2 y=-3 \\ 5 x-y=2 \end{array}$
Select the correct choice below and fill in any answer boxes within your choice. A. The solution of the system is $\square$ . (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution is $\square$ ,y), where $y$ is any real number. C. There is no solution.

See Solution

Problem 20378

$2 \text { or } 6$
Solve. Show your work on paper. Enter your answer in the box. $12 \times \frac{3}{8}=$ $\square$
3 of 6

See Solution

Problem 20379

We want to compute the limit below with the l'Hospital's Rule if it applies. $\lim _{x \rightarrow 0} \frac{1-e^{7 x}}{\sin (5 x)}$ a) What is the indeterminate type of the limit? $0 / 0$ $0^{0}$ + /00 $0^{\infty}$ b) According to l'Hospital's Rule, where $\begin{array}{l} \qquad \lim _{x \rightarrow 0} \frac{1-e^{7 x}}{\sin (5 x)}=\lim _{x \rightarrow 0} \frac{A(x)}{B(x)} \\ \text { where } \\ {[A(x), B(x)]=\square \text { 目 }} \end{array}$ $\square$ FORMATTING: Enter your answer as $[A(x), B(x)]$ , including the square brackets and with a comma (,) between the te strict scientific calculator notation: multiplication is written *; for example, you must write $2 x$ as $2^{\star} \boldsymbol{x}$ . c) Conclude that $\lim _{x \rightarrow 0} \frac{1-e^{7 x}}{\sin (5 x)}=\lim _{x \rightarrow 0} \frac{A(x)}{B(x)}=$ $\square$ FORMATTING: Give the exact answer.

See Solution

Problem 20380

Let $\mathbf{x}(t)$ be the solution of the following initial value problem. What is $\mathbf{x}(\pi / 2)$ ? $\dot{\mathbf{x}}=\left[\begin{array}{rr} 5 & -10 \\ 1 & -1 \end{array}\right] \mathbf{x}, \quad \mathbf{x}(0)=\left[\begin{array}{l} 1 \\ 1 \end{array}\right]$

See Solution

Problem 20381

Question Watch Video Show Ex
The expression $\frac{\sec ^{2} x-\tan ^{2} x}{1-\cos ^{2} x}$ is equivalent to

See Solution

Problem 20382

2. (16 points) Let $\mathbf{x}(t)$ be the solution of the following initial value problem. What is $\mathbf{x}(\pi / 2)$ ? $\dot{\mathbf{x}}=\left[\begin{array}{rr} 5 & -10 \\ 1 & -1 \end{array}\right] \mathbf{x}, \quad \mathbf{x}(0)=\left[\begin{array}{l} 1 \\ 1 \end{array}\right]$ (A) $\left[\begin{array}{l}-7 e^{\pi} \\ -2 e^{\pi}\end{array}\right]$ . B) $\left[\begin{array}{c}13 e^{\pi} \\ 4 e^{\pi}\end{array}\right]$ . C) $\left[\begin{array}{l}-13 e^{\pi} \\ -4 e^{\pi}\end{array}\right]$ . D) $\left[\begin{array}{l}7 e^{\pi} \\ 2 e^{\pi}\end{array}\right]$ . E) $\left[\begin{array}{c}3 e^{\pi} \\ e^{\pi}\end{array}\right]$ . F) $\left[\begin{array}{c}-3 e^{\pi} \\ -e^{\pi}\end{array}\right]$ .

See Solution

Problem 20383

Consider the following system of equations. $\begin{array}{l} 2 x+3 y=22 \\ 3 x+5 y=35 \end{array}$ (a) Write a matrix equation that is equivalent to the system of linear equat $\left[\begin{array}{ll} 2 & 3 \\ 3 & 5 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{l} 22 \\ 35 \end{array}\right]$ (b) Solve the system using the inverse of the coefficient matrix. $(x, y)=(\square)$ Need Help? Read It Watch it

See Solution

Problem 20384

$\int_{2}^{\infty} \frac{9}{(1-3 z)^{4}} d z$

See Solution

Problem 20385

18. $\begin{array}{l} 2 x-y=0 \\ 3 x-2 y=-3 \end{array}$

See Solution

Problem 20386

$\int 7 x e^{4 x} d x=$ $\square$ $+C$

See Solution

Problem 20387

Solve for $d$ in the proportion. $\frac{5}{9.5}=\frac{d}{7.6}$ $d=$ $\square$
Submit

See Solution

Problem 20388

$\frac{8 s^{4} t^{-2}}{2 s^{3} t^{3}} \cdot \frac{3 s^{2} t^{7}}{2 s^{-1}}$

See Solution

Problem 20389

The function $f(x)=6 x-2$ is one-to-one. (a) Find the inverse of $f$ and check the answer. (b) Find the domain and the range of $f$ and $f^{-1}$ . (c) Graph $f, f^{-1}$ , and $y=x$ on the same coordinate axes. (a) $f^{-1}(x)=$ $\square$ (Simplify your answer. Use integers or fractions for any numbers in the expression.)

See Solution

Problem 20390

For $x \in[-12,14]$ the function $f$ is defined by $f(x)=x^{7}(x+6)^{2}$
On which two intervals is the function increasing (enter intervals in ascending order)? $\square$ $\square$ an ${ }^{2}$ $\square$ to $\square$ Find the region in which the function is positive: $\square$ to $\square$ Where does the function achieve its minimum? $\square$

See Solution

Problem 20391

a. compute the area under the curve b. rotate the region about the indicated axis and compute the volume of the solid obtained in this way $5 y=3 x+2, y=0, x=0, x=2$ about the $x$ -axis

See Solution

Problem 20392

Solve for $x$ . $15^{x-4}=17^{-7 x}$
Write the exact answer using either base-10 or base-e logarithms. $x=$ $\square$ $\square \log$
In
No solution

See Solution

Problem 20393

Which expression is equivalent to $\sqrt{\frac{2 x^{5}}{18}} ?$ Assume $x \geq 0$ . $\frac{x^{2} \sqrt{x}}{3}$ $\frac{3 \sqrt{x}}{x^{2}}$ $\frac{\sqrt{x}}{3 x^{2}}$ $\frac{2 x \sqrt{x}}{3}$

See Solution

Problem 20394

Factor out the greatest common factor from the expression $8b^2 - 4b + 20$ .

See Solution

Problem 20395

Solve the inequality. $-2 n<30$ (A) $n>-15$ (B) $n<-15$ (C) $n<15$ (D) $n>15$

See Solution

Problem 20396

2 Solve the following inequality. $9 \mathrm{x}-2>43$
Here, x >

See Solution

Problem 20397

Evaluate the following expressions. (a) $\log _{2}\left(\frac{1}{32}\right)=$ $\square$ (b) $\log _{9} 1=$ $\square$ (c) $\log _{4} \sqrt{256}=$ $\square$ (d) $5^{\log _{5} 9}=$ $\square$

See Solution

Problem 20398

17 Make $f$ the subject of the formula $d=\frac{3(1-f)}{f-4}$

See Solution

Problem 20399

Solve $\frac{x}{25}-\frac{4}{5}=-\frac{4}{5}$

See Solution

Problem 20400

Solve the following inequality and plot the answer on the number line shown below. $3+2 n>9$ $\square$ $C$ REDO RESET REMOVE

See Solution

1 ...201 202 203 204 205 206 207 ...269

Math Statement

Problem 20301

Problem 20302

3. 7 0 \longdiv { 5 , 5 9 1 }

Problem 20303

Convert the complex number to polar form: 4−4i4-4 i4−4i

Problem 20304

Convert the complex number to rectangular form: z=7cis⁡120∘z=7 \operatorname{cis} 120^{\circ}z=7cis120∘

Problem 20305

Find all θ\thetaθ in the interval [0∘,360∘)\left[0^{\circ}, 360^{\circ}\right)[0∘,360∘) such that: 3sin⁡2θ+2sin⁡θ−1=03 \sin ^{2} \theta+2 \sin \theta-1=03sin2θ+2sinθ−1=0

Problem 20306

Use an identity to re-write the expression as a single function: 2sin⁡(16u)cos⁡(16u)2 \sin (16 u) \cos (16 u)2sin(16u)cos(16u)

Problem 20307

A particular circle in the standard (x,y)(x, y)(x,y) coordinate plane has an equation of (x−5)2+y2=38(x-5)^{2}+y^{2}=38(x−5)2+y2=38. What are the radius of the circle, in coordinate units, and the Goordinates of the center of the circle?

Problem 20308

Use any appropriate algebraic techniques combined with trigonometric identities to simpli the expression: 1cos⁡θ−cos⁡θ\frac{1}{\cos \theta}-\cos \thetacosθ1​−cosθ

Problem 20309

Use the difference formula for cosine to simplify cos⁡(θ−π2)\cos \left(\theta-\frac{\pi}{2}\right)cos(θ−2π​) as a single function of θ\thetaθ :

Problem 20310

Find the reference angle for θ=−455∘\theta=-455^{\circ}θ=−455∘ :

Problem 20311

Problem 20312

Problem 20313

Problem 20314

Use transformations to graph the function. q(x)=−(x+2)2+5q(x)=-(x+2)^{2}+5q(x)=−(x+2)2+5

Problem 20315

Solve \& State weather the system is inconsistent or equations are dependen 5x+y=−5−15x−3y=a\begin{array}{c} 5 x+y=-5 \\ -15 x-3 y=a \end{array}5x+y=−5−15x−3y=a​

Problem 20316

8. 13=−9\frac{1}{3}=\frac{-}{9}31​=9−​

Problem 20317

10. 3a2b÷3x4x−y3 a^{2} b \div \frac{3 x}{4 x-y}3a2b÷4x−y3x​

Problem 20318

7) 7.1×1068.2×101\frac{7.1 \times 10^{6}}{8.2 \times 10^{1}}8.2×1017.1×106​

Problem 20319

5/−x=125 /-x=125/−x=12

Problem 20320

Solve the formula for x . 1g+1n=1xx=□\begin{array}{l} \frac{1}{g}+\frac{1}{n}=\frac{1}{x} \\ x=\square \end{array}g1​+n1​=x1​x=□​

Problem 20321

(1 point) Solve the separable differential equation for. dydx=1+xxy6;x>0\frac{d y}{d x}=\frac{1+x}{x y^{6}} ; x>0dxdy​=xy61+x​;x>0Use the following initial condition: y(1)=2y(1)=2y(1)=2. y7=y^{7}=y7= □\square□

Problem 20322

Problem 20323

Problem 20324

Solve this equation to find the value of d. 58=36+d58=36+d58=36+d

Problem 20325

Factor completely: 11v12−3v6k4−8k811 v^{12}-3 v^{6} k^{4}-8 k^{8}11v12−3v6k4−8k8Answer Attempt 3 out of 4 □\square□ Submit Answer

Problem 20326

Cell B21 What is the solution to this equation? −4(2m−7)=3(52−4m)-4(2 m-7)=3(52-4 m)−4(2m−7)=3(52−4m)

Problem 20327

For 1-12, create the slope intercept form (y=mx+b)(y=m x+b)(y=mx+b) based on the given information. 1) Slope =1,b=−5=1, b=-5=1,b=−5 2) Slope =−12,y=-\frac{1}{2}, y=−21​,y-intercept =3=3=3

Problem 20328

Problem 20329

Problem 20330

1) Solve a) (x+1)(x+2)=0(x+1)(x+2)=0(x+1)(x+2)=0

Problem 20331

Problem 20332

Question Watch VideoFactor completely: 9r6+14r3t2−39t49 r^{6}+14 r^{3} t^{2}-39 t^{4}9r6+14r3t2−39t4Answer Attempt 1 out of 4

Problem 20333

Problem 20334

Problem 20335

Problem 20336

1331=13 \frac{3}{1}=1313​=

Problem 20337

Solve for xxx. log⁡2(5x−7)=1\log _{2}(5 x-7)=1log2​(5x−7)=1

Problem 20338

Find the derivative of the function. q=17r−r5q=\sqrt{17 r-r^{5}}q=17r−r5​

Problem 20339

Solve the following equation. x−3+5=x\sqrt{x-3}+5=xx−3​+5=xThe solution set is □\square□ B. (Use a comma to separate answers as needed.)

Problem 20340

(3m2n7m)5\left(\frac{3 m^{2} n^{7}}{m}\right)^{5}(m3m2n7​)5

Problem 20341

Multiply. (u+1)(u−3)(u+1)(u-3)(u+1)(u−3)

Problem 20342

∣b12∣=10\left|\frac{b}{12}\right|=10∣∣​12b​∣∣​=10

Problem 20343

17/46 (53x2y4)0\left(5^{3} x^{2} y^{4}\right)^{0}(53x2y4)0 01 5 5xy

Problem 20344

Solve for xxx. ln⁡x=ln⁡(x−8)−ln⁡2\ln x=\ln (x-8)-\ln 2lnx=ln(x−8)−ln2

Problem 20345

19/46According to the product rule, when we multiply powers with the same base, we keep the base and \qquad the exponents.

Problem 20346

Convert the complex number to polar form: $4-4 i$

Convert the complex number to rectangular form: $z=7 \operatorname{cis} 120^{\circ}$

Find all $\theta$ in the interval $\left[0^{\circ}, 360^{\circ}\right)$ such that: $3 \sin ^{2} \theta+2 \sin \theta-1=0$

Use an identity to re-write the expression as a single function: $2 \sin (16 u) \cos (16 u)$

A particular circle in the standard $(x, y)$ coordinate plane has an equation of $(x-5)^{2}+y^{2}=38$ . What are the radius of the circle, in coordinate units, and the Goordinates of the center of the circle?

Use any appropriate algebraic techniques combined with trigonometric identities to simpli the expression: $\frac{1}{\cos \theta}-\cos \theta$

Use the difference formula for cosine to simplify $\cos \left(\theta-\frac{\pi}{2}\right)$ as a single function of $\theta$ :

Find the reference angle for $\theta=-455^{\circ}$ :

Use transformations to graph the function. $q(x)=-(x+2)^{2}+5$

Solve \& State weather the system is inconsistent or equations are dependen $\begin{array}{c} 5 x+y=-5 \\ -15 x-3 y=a \end{array}$

8. $\frac{1}{3}=\frac{-}{9}$

10. $3 a^{2} b \div \frac{3 x}{4 x-y}$

7) $\frac{7.1 \times 10^{6}}{8.2 \times 10^{1}}$

$5 /-x=12$

Solve the formula for x . $\begin{array}{l} \frac{1}{g}+\frac{1}{n}=\frac{1}{x} \\ x=\square \end{array}$

(1 point) Solve the separable differential equation for. $\frac{d y}{d x}=\frac{1+x}{x y^{6}} ; x>0$
Use the following initial condition: $y(1)=2$ . $y^{7}=$ $\square$

Solve this equation to find the value of d. $58=36+d$

Factor completely: $11 v^{12}-3 v^{6} k^{4}-8 k^{8}$
Answer Attempt 3 out of 4 $\square$ Submit Answer

Cell B21 What is the solution to this equation? $-4(2 m-7)=3(52-4 m)$

For 1-12, create the slope intercept form $(y=m x+b)$ based on the given information. 1) Slope $=1, b=-5$ 2) Slope $=-\frac{1}{2}, y$ -intercept $=3$

1) Solve a) $(x+1)(x+2)=0$

Question Watch Video
Factor completely: $9 r^{6}+14 r^{3} t^{2}-39 t^{4}$
Answer Attempt 1 out of 4

$13 \frac{3}{1}=$

Solve for $x$ . $\log _{2}(5 x-7)=1$

Find the derivative of the function. $q=\sqrt{17 r-r^{5}}$

Solve the following equation. $\sqrt{x-3}+5=x$
The solution set is $\square$ B. (Use a comma to separate answers as needed.)

$\left(\frac{3 m^{2} n^{7}}{m}\right)^{5}$

Multiply. $(u+1)(u-3)$

$\left|\frac{b}{12}\right|=10$

17/46 $\left(5^{3} x^{2} y^{4}\right)^{0}$ 0
1 5 5xy

Solve for $x$ . $\ln x=\ln (x-8)-\ln 2$

19/46
According to the product rule, when we multiply powers with the same base, we keep the base and $\qquad$ the exponents.

$-31=-39-\frac{y}{8}$

$-7 x-9=-2 x+31$

$735 \times 53=$

3. In the equation $y=4 x$ , what is the constant of proportionality? a. $x$ b. $y$ c. 4 d. 0

Factor. $x^{2}-14 x y+24 y^{2}$

Subtract. $(-8 j-6)-(-9 j+6)$

$\int \frac{2 x^{2}+7 x+1}{x^{2}+3 x} d x$

Find the inverse of the function $f(x) = 3x + 3$ .

Use a change of variables or the table to evaluate the following indefinite integral. $\int \frac{e^{3 x}}{e^{3 x}+8} d x$

Solve for $x: 6^{2 x+5}=1296$ $x=$
Question Help: Message instructor

3. $\begin{array}{l} x+5 y=2 \\ x=-4 y+5 \end{array}$

6) $\left(7 \times 5+6^{2}\right)+2$ 7) $\left(86-6^{2}\right)+(-1+3)$ 8) $(35-5)+2+2^{2}$ 9) $(2+2)^{2}+(10+5)$ 10) $\left(61-5^{2}\right) \div(8+4)$

Rewrite the following equation in slope-intercept form. $-3 y-11=11 x$
Write your answer using integers, proper fractions, and improper fractions in simplest form.

26. $-0.04 w+\frac{a}{1.4}-b^{2}$ when $a=0.56, b=-1.2$ , and
28. $\frac{a}{z}$ when $a=\frac{14}{9}$ and $z=28$
30. $\frac{a+b}{a}$ when $a=\frac{1}{6}$ and $b=\frac{3}{4}$

1) Simplify using laws of logarithms and then evaluate. a) $\log 9+\log 6$ b) $\log 48-\log 6$ c) $\log _{3} 7+\log _{3} 3$

7) Given that $\sin \frac{\pi}{6}=\frac{1}{2}$ , use an equivalent trigonometric expression to show that $\cos \frac{2 \pi}{3}=-\frac{1}{2}$

1. $f(x)=x$ , translation 4 units to the left

The equation below describes a proportional relationship between $x$ and $y$ . What is the constant of proportionality $y=\frac{2}{7} x$
The constant of proportionality is $\square$

9) Given that $\cos \frac{3 \pi}{11} \sim 0.6549$ , use equivalent trigonometric expressions to evaluate the following, to four decimal places. a) $\sin \frac{5 \pi}{22}$ b) $\sin \frac{17 \pi}{22}$

2. Solve by factoring. Confirm your results by graphing. a) $x^{2}+7 x-30=0$ c) $x^{2}-x-6=0$ b) $x^{2}+8 x+15=0$ d) $x^{2}-5 x+6=0$

3. Factor the following perfect square trinomials. a) $x^{2}+6 x+9$ c) $9 x^{2}+6 x+1$ b) $x^{2}-8 x+16$ d) $4 x^{2}-12 x+9$

Find the derivative of $y$ with respect to $x$ . $y=\tan ^{-1} \sqrt{5 x}$

5. Factor. a) $x^{2}+3 x-40$ c) $81 x^{2}-49$ b) $6 x^{2}+5 x-6$ d) $9 x^{2}+6 x+1$

6. What term will make each expression a perfect trinomial square? a) $x^{2}+6 x+$ c) $4 x^{2}+\square+49$ b) $x^{2}+\square+25$ d) $9 x^{2}-24 x+$

Write in factored form. a) $f(x)=x^{2}-7 x-18$ c) $h(x)=4 x^{2}-25$ b) $g(x)=-2 x^{2}+17 x-8$ d) $y=6 x^{2}+13 x-5$

$\begin{array}{l}f(x)=\frac{x+7}{x-8} \\ f(3)=\end{array}$