Browse Simplify problems Studdy Solved!

Problem 401

White an equivalent expressic $-4 \mid 2(y-2) i$

See Solution

Problem 402

8. Complete:
Radical Form: $\sqrt[5]{\frac{a^{3} \cdot b^{7}}{a^{2} \cdot b^{-3}}}$
Exponential Form:
9. Complete:
Radical Form: Exponential Form: $\sqrt{ } \sqrt{ }\left(2^{\frac{1}{2}} \cdot 3^{\frac{5}{2}}\right)^{\frac{1}{3}}$
Create two different explicit equations that describe the table. Use a differ

See Solution

Problem 403

Simplify. $\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}$

See Solution

Problem 404

$3(2 x+4)+2(x-3)$

See Solution

Problem 405

$5(m-4)-3(m+1)$

See Solution

Problem 406

d $2(x+5)-(3 x-2)$

See Solution

Problem 407

Aufgabe 12: Potenzgesetze und n-te Wurzel Formuliere die Wurzeln als Potenzen und vereinfache soweit wie möglich. a) $\sqrt{x}$ d) $\sqrt[7]{a^{3}}$ g) $\sqrt[3]{x} \cdot \sqrt{x}$ j) $\sqrt[7]{5^{5}}: \sqrt[3]{5^{2}}$ m) $\sqrt{\sqrt[4]{\mathrm{x}}}$ p) $\sqrt{\sqrt[3]{16} \cdot \sqrt[9]{64}}$ b) $\sqrt[4]{\mathrm{k}}$ e) $\frac{1}{\sqrt[3]{\mathrm{x}}}$ h) $\sqrt[3]{x^{4}} \cdot \sqrt[4]{x^{5}}$ k) $\sqrt[5]{y^{3}}: \sqrt[4]{y^{5}}$ n) $\sqrt[5]{\sqrt[4]{y}}$ q) $\sqrt{a+2 \sqrt{a x}+x}$ c) $\sqrt[5]{x^{4}}$ f) $\frac{1}{\sqrt[5]{x^{2}}}$ i) $\sqrt{a}: \sqrt[3]{a}$ 1) $\sqrt[9]{m} \cdot \sqrt[9]{n}$ 0) $\sqrt{\sqrt{625}}$ r) $\sqrt[3 n]{(a-4 b)^{-3} \cdot(a-4 \sqrt{a b}+4 b)^{3}}$

See Solution

Problem 408

$\frac{6 t}{3}$

See Solution

Problem 409

$\log _{9}\left(3 x^{2}\right)+\log _{9}\left(4 x^{6}\right)$

See Solution

Problem 410

Select the correct answer.
Which expression is equivalent to $21 \sqrt[3]{15}-9 \sqrt[3]{15}$ ? A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$

See Solution

Problem 411

Simplify. $4{ }^{\log _{4}(2 x+8)}$

See Solution

Problem 412

To solve $49^{3 x}=343^{2 x+1}$ , write each side of the equation in terms of base $\square$ DONE

See Solution

Problem 413

$-3 v<18$
Simplify your answer as much as

See Solution

Problem 414

$-3 \sqrt{100 a b^{6}}$

See Solution

Problem 415

3. $-5 \sqrt{144}$

See Solution

Problem 416

2. A bike shop is offering a $20 \%$ discount on all items. a) What is the discount on a $€ 500$ bike? b) How much do I need to pay to buy the bike? Simplifying
3. Chocolate makes $40 \%$ of the total weight of cookies. A packet of cookies weighs 120 g . What is the weight of chocolate in 5 packets?
4. A gardening company says that from a packet 70 seeds, 50 seeds will grow. What percentage of the seeds that will grow?
5. Miguel needs 25 g of protein in a day. A sushi plate has $60 \%$ of the protein he needs. How many grams of protein are there in the plate?

See Solution

Problem 417

16) Factor completely: $x^{3}+6 x^{2}-3 x-18$

See Solution

Problem 418

Write each equation in standard form. State $\mathrm{A}, \mathrm{B}$ and C . 16.) $5 y-\frac{4}{3} x+6=-\frac{3}{5}(x-1)$ 17.) $3 x+\frac{2}{5} y=4+\frac{7}{3} x$ 18.) $2\left(x-\frac{5}{6}\right)=3\left(y+\frac{2}{5}\right)$

See Solution

Problem 419

15) $x^{4}-81$

See Solution

Problem 420

15) $x^{4}-81$

See Solution

Problem 421

Factor completely (mixed factoring). CHECK FOR GCF’S FIRST!!! Make sure your final answer is fully factored. If the problem is not factorable, then say so.
$x^{2} + 36$

See Solution

Problem 422

$\left(9^{5} \cdot 9^{2}\right)^{4}$

See Solution

Problem 423

b) Simplify $3(x+5)-x+3$ $2 x+18$ Answ

See Solution

Problem 424

Factor by grouping. $\begin{array}{l} x^{3}+9 x^{2}-6 x-54 \\ x^{3}+9 x^{2}-6 x-54= \end{array}$

See Solution

Problem 425

Divide $\frac{1}{20} \div 5$
Enter your answer in the box as a fraction in simplest form. $\square$

See Solution

Problem 426

2. Rewrite $g(x)=\frac{-5 x^{3}-18}{x^{3}+4}$ in the form $g(x)=q(x)+\frac{r}{b(x)}$ .

See Solution

Problem 427

PRACTICE PROBLEMS ON NET IONICEQUATIONS Show the complete ionic and net innic formis of the following equations. If all species are spectator ions, plesase
1. AsNOa(aq) $\mathrm{AgCI}(\mathrm{aq})-\mathrm{AgCl}(\mathrm{s})+\mathrm{KNO}$ (aq)
3. strontium bromide (aq) + potassium sultate(ag) $\rightarrow$ stronilum sulfate(s) potassium bromide (aq)
4. manganese(I)chloride(ac) + nmmonium carbonate(aq) $\rightarrow$ manganese(I)carbomate(s) + ammonium ehloride(an
5. chromium(II)nitrate(aq) + iron(II)sulfate(aq) ; chromium(III)sulfate(ag) tiromilinnitmatedag)
Please complete the following remetions, ama show the complete ionic and net ionic forms of the equarion: c. $\left.\mathrm{KalOO}_{3}(\mathrm{aq})+\mathrm{AlNO}_{3}\right)_{3}(\mathrm{aq}) \rightarrow$ 45

See Solution

Problem 428

1. Simplify the complex rational expression: $\frac{\frac{1}{x-1}-\frac{1}{x}}{\frac{1}{x^{2}-x}}$ A. 1 B. $\frac{2}{x-1}$ C. $\frac{x}{x-1}$ D. $x-x^{2}$ E. None of the above

See Solution

Problem 429

Simplify $\frac{12}{16}$ to lowest terms and find an equivalent fraction that has a denominator of 32. $\frac{3}{4}, \frac{24}{32}$ $\frac{3}{4}, \frac{12}{32}$ $\frac{2}{6}, \frac{24}{32}$ $\frac{6}{8}, \frac{285}{32}$

See Solution

Problem 430

Rewrite the equations from logarithmic to exponential and vice versa. a. $10^{x}=2500$ is equivalent to $\log _{10}(A)=B$ $A=$ $\qquad$ and $B=$ $\qquad$ b. $\ln 3=x$ is equivalent to $e^{A}=B$ . $A=$ $\qquad$ and $B=$ $\qquad$ valuate the following expressions, with exact answers in simplest form. $\begin{array}{l} \ln \left(e^{-8}\right)= \\ e^{\ln 3}= \end{array}$ lify and solve the following equation. $\ln (3 t+1)-7=15$

See Solution

Problem 431

4. $11 \frac{c}{-5}-8$

See Solution

Problem 432

Expand and simplify $(x+3)(x-5)$

See Solution

Problem 433

Aufgabe 8 : Potenzen mit gleichen Exponenten Vereinfache soweit wie möglich a) $4^{4} 3^{4} \cdot 0,25^{4}$ c) $(x+y)^{8} \cdot(x-y)^{8}$ e) $\frac{24^{3}}{8^{3}}$ g) $\frac{0,4^{2}}{0,5^{2}}$ i) $\frac{27 a^{3}}{8 b^{3}}$ k) $\frac{\left(16 x^{4}-25 y^{2}\right)^{n}}{\left(4 x^{2}-\frac{5}{y}\right)^{n}}$ b) $5^{x} \cdot 4^{x}$ d) $(-x)^{5} \cdot(-y)^{5} \cdot z^{5}$ f) $\frac{2,6^{4}}{1,3^{4}}$ h) $\frac{(12 x)^{m}}{(3 x)^{m}}$ j) $\frac{(2 a+3 b)^{-5}}{\left(4 a^{2} 9 b^{2}\right)^{-5}}$ 1) $\frac{\left(16 r^{4}-24 r^{2} s^{3} 9 s^{6}\right)^{4}}{\left(16 r^{4}-9 s^{6}\right)^{4}}$

See Solution

Problem 434

$\frac{8-3 i}{4+3 i}$

See Solution

Problem 435

Simplify the function before differentiating. $f(x)=\frac{1}{\sqrt{e^{10 x}}}$ $f(x)=$ $\square$ (Simplify your answer.)

See Solution

Problem 436

The graph of two functions, f and g , is illustrated below. Use the graph to answer parts (a) through ( f ). (a) $(\mathrm{f}+\mathrm{g})(3)=$ $\square$ (Simplify your answer.)

See Solution

Problem 437

1 2 3 4 5 6 7 8 9 Io
Which expression is equivalent to $7(x y)$ ? $7 x+y$ $7 x-y$ $x(7 y)$ $\frac{x y}{7}$

See Solution

Problem 438

You roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a number greater than $2 ?$ Simplify your answer and write it as a fraction or whole number. $\square$ Submit

See Solution

Problem 439

Question Show Examples
Find the slope of a line perpendicular to the line whose equation is $3 x+y=8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

See Solution

Problem 440

Question Show Examples
Find the slope of a line perpendicular to the line whose equation is $x-2 y=-8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

See Solution

Problem 441

$\left(x^{3}+3 x^{2}-5 x\right)-\left(x^{3}-2 x^{2}+x\right)$

See Solution

Problem 442

Simplify each expression.
1. $9 y+4.1-6 y$
2. $-3 x+5+7 x$
3. $8 x+13-3 x+9 \frac{1}{2}$
4. $y^{2}+3 y^{2}$
5. $4 x+15-3 x+10$
6. $-10 x+2 x+8 x$

See Solution

Problem 443

a) Fully factorise $3 y^{2}+11 y+10$ b) Use your answer to part a) to solve $3 y^{2}+11 y+10=0$

See Solution

Problem 444

You pick a card at random, put it back, and then pick another card at random.
What is the probability of picking an even number and then picking a factor of 10 ? Simplify your answer and write it as a fraction or whole number. $\square$ Submit Next up

See Solution

Problem 445

write $z=\ln ((8+10 j)(7-9 j))$ in the form $z=x+y j$ $z=\square+\square \text { (to 2decimal places) }$

See Solution

Problem 446

姣, All factors in your answer should have integer coefficients. $512 w^{3}+27 x^{3}=$ $\square$

See Solution

Problem 447

㪱, Factor the polynomial. 㸚 Ald factors in your answer should have integer coefficients. $135 p^{3}+5000 q^{3}=$ $\square$ Submit

See Solution

Problem 448

Simplify completely: $\frac{2+\frac{10}{m}}{1-\frac{25}{m^{2}}}$
Enter the numerator and denominator separately in the boxes below. If the denominator is 1 , enter the number 1. Do not leave either box blank. Make sure that the coefficient on the variable is positive. Answer: $\square$ $\square$ Numerator preview:

See Solution

Problem 449

1. Rewrite as the first rational expression [A] by the reciprocal of the second.
2. $[B]$ the numerators and denominators.
3. Multiply the numerators.
4. Multiply the denominators.
5. Simplify.
Choose the words for $[A]$ and $[B]$ that correctly complete the steps. [A] : multiplied $[B]$ : Factor [A] : multiply [B] : Look at [A] : divided [B] : Factor [A] : divided [B] : Look at

See Solution

Problem 450

40) $(7 i)(-5 i)(-2-8 i)$

See Solution

Problem 451

32) $(2-4 i)(-2-4 i)$

See Solution

Problem 452

26) $(7+5 i)(8+i)$

See Solution

Problem 453

rm the indicated opera $(-4+\sqrt{-9})^{2}$

See Solution

Problem 454

b. $\left(3 x^{2}+2 x-7\right)-\left(7 x^{2}+x-1\right)=$ $\square$ (Simplify your answer. Do not factor.)

See Solution

Problem 455

11. $\qquad$ $(a+3 b)(a+3 b)=$
12. $\qquad$ $(3 x y+6)(3 x y-6)=$
13. $\qquad$ $(m-2)(m-2)=$
14. $\qquad$ $(3 t-2)(3 t-2)=$
15. $\qquad$ $(x-5)(x+5)=$
16. $\qquad$ $\left(8 r^{2} s^{2}-4\right)\left(8 r^{2} s^{2}-4\right)=$
17. $\qquad$ $(a+b)^{2}=$
18. $\qquad$ $(a+b)(a-b)=$
19. $\qquad$ $(2 a b-c)^{2}=$
20. $\qquad$ $(2 a b+c)(2 a b-c)=$

See Solution

Problem 456

Question Watch Video Show Examples
Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $8 x \sqrt{175 x^{5} y^{3}}$

See Solution

Problem 457

d. $\left(-3 x^{4}+6 x^{3}-11 x^{2}+5\right)-\left(5 x^{4}+2 x^{3}-x\right)=$ (Simplify your answer. Do not factor.)

See Solution

Problem 458

Simplify. Assume that all variables represent positive numbers. $\frac{\sqrt{\frac{z^{2}}{36 x^{2}}}}{\frac{|z|}{6|x|}}$
Suggested tutorial: Learn It: Simplify a radical expression.

See Solution

Problem 459

Practice
1. Express the following powers in exponent form a. $\sqrt[7]{3}$ b. $\sqrt[5]{-5}$ d. $\sqrt{\frac{5}{9}}$ c. $\frac{2}{\sqrt[4]{2}}$ e. $\sqrt[3]{y^{2}}$

See Solution

Problem 460

sider the following quadratic function. $g(x)=-3 x^{2}+24 x-41$ (a) Write the equation in the form $g(x)=a(x-h)^{2}+k$ . Then give the vertex of its graph.
Writing in the form specified: $g(x)=$ $\square$ II
Vertex: $\square$ $\square$ D)

See Solution

Problem 461

Write the complete factored form of $f(x)$ . $\begin{array}{l} f(x)=-4 x^{3}+9 x^{2}+30 x-8 ; \text { zeros: }-2, \frac{1}{4}, 4 \\ f(x)=\square \end{array}$ $\square$ (Type your answer in factored form. Use integers or fractions fo

See Solution

Problem 462

Simplify. The variable represents a positive number. $\frac{2 \sqrt[3]{648 a^{5}}-2 \sqrt[3]{-375 a^{5}}}{2 \sqrt[3]{648 a^{5}}-2 \sqrt[3]{-375 a^{5}}}$

See Solution

Problem 463

Perform the indicated operation. $\frac{6-5 i}{6+i}$

See Solution

Problem 464

Ally factors in your answer should have integer coefficients. $125 w^{4}-216 w x^{3}=$ $\square$ Submit

See Solution

Problem 465

$(19-7) \div 4 \cdot 11$

See Solution

Problem 466

$11^{2}-8 \cdot 7+2$

See Solution

Problem 467

$y=\ln \left(\frac{2 x}{x}\right)$

See Solution

Problem 468

Question 3 (4 points) Expand each logarithm on the left and match to its equivalent form on the right. Be sure to factor fully inside the logarithm first! $\square$ $\log \left(\frac{3 x^{3}}{y}\right)$
1. $\log (3)+\log (x)+\log (y)$ $\square$ $\log \left(\frac{3}{x^{2}-y^{2}}\right)$
2. $\log (3)+\log (x)+3 \log (y)$ $\sim \log \left(\frac{x}{3 y}\right)$
3. $\log (x)-\log (3)-\log (y)$ $\log (3 x y)$
4. $\log (3)+3 \log (x)-\log (y)$ $\square$ $\log \left[3 x y^{3}\right]$ $\square$ $\log \left(\frac{3}{(x-y)^{3}}\right)$
5. $\log (3) \log (x) \log (y)$
6. $\frac{\log (x)}{\log (3) \log (y)}$
7. $\frac{\log (3) \log (x)}{\log (y)}$ $\square$ $\log (3 x-3 y)$
8. $\log (3)-2 \log (x)-2 \log (y)$
9. $\log (3)+\log (x-y)$
10. $\log (3)-\log (x-y)-\log (x+y)$
11. $\log (3)-3 \log (x-y)$

See Solution

Problem 469

Rewrite the following in exponential form: a) $\log _{8}\left(\frac{1}{8}\right)=-1$ $\square$ b) $\log (117)=x$ $\square$ c) $\ln (x)=-1$ $\square$

See Solution

Problem 470

Factor the four-term polynomial by grouping. $\begin{array}{r} 7 q^{2}+5 p q-7 q-5 p \\ 7 q^{2}+5 p q-7 q-5 p=\square \end{array}$ $\square$ (FactoF completely.)

See Solution

Problem 471

$-4(3m + 2n) - 5m + y$

See Solution

Problem 472

\begin{tabular}{|l|l|l|l} \hline $9 \sqrt[3]{125}$ & -2 \\ \hline 45 & $9 \sqrt{5}$ & $45 \sqrt[3]{5}$ & $45 \sqrt[3]{25}$ \\ \hline \end{tabular}

See Solution

Problem 473

$\frac{9}{z-6} \div \frac{27}{2 z-12}$

See Solution

Problem 474

Factor the following polynomial. $\begin{array}{c} 12 x^{2} y-20 x^{2}-18 y+30 \\ 12 x^{2} y-20 x^{2}-18 y+30= \end{array}$ $\square$ (Factor completely.)

See Solution

Problem 475

Evaluate the expression. (Simplify your answer completely.) (a) $\log _{8}(64)$ $\square$ (b) $\log _{7}(49)$ $\square$ (c) $\log _{8}\left(8^{13}\right)$

See Solution

Problem 476

Use the Laws of Logarithms to combine the expression. $\ln (a+b)+\ln (a-b)-2 \ln (c)$

See Solution

Problem 477

$(+3)-(+3)+(-4)$

See Solution

Problem 478

Use the Laws of Logarithms to combine the expression. $2\left(\log _{5}(x)+2 \log _{5}(y)-3 \log _{5}(z)\right)$

See Solution

Problem 479

1. 5200000 тоог стандарт хэлбэрт бич. A. 5200000 B. $0.52 \cdot 10^{7}$ C. $520 \cdot 10^{4}$ D. $52 \cdot 10^{5}$

See Solution

Problem 480

Trisha made a scale drawing of a restaurant. A countertop in the restaurant, which is 5 feet long in real life, is 10 inches long in the drawing. What scale $f=$ does the drawing use?
Simplify your answer and write it as a fraction. $\square$
Submit

See Solution

Problem 481

Lisa drew a scale drawing of an apartment. The dining room, which is 3 meters wide in real life, is 5 millimeters wide in the drawing. What is the drawing's scale factor?
Simplify your answer and write it as a fraction. $\square$
Submit

See Solution

Problem 482

Problems 17 - 22, Find the exact value of the logarithm without using a calculator. If this is not possible, state the reason.
17. $\log _{5} 125-\log _{5} 5$
18. $6 \ln e^{5}+4 \ln e^{-2}$
19. $\ln \frac{1}{\sqrt{e}}$
20. $\log _{3}(-27)$
21. $\log _{2} \sqrt[1]{32}$
22. $\log _{3}\left(\frac{1}{81}\right)$
Problems 23 - 24, Solve.
23. Mrs. Adams gave her students a quiz on logarithms. Every week for three months they took another quiz to see how much they remembered. The average scores of the students can be modeled by the human memory model $S(t)=87-12 \log (t+1)$ for $0 \leq t \leq 12$ where $t$ is the time in weeks. A. Find the average score on the original quiz. $s(0)=87-12 \log (0+1)^{87}$ B. What was the average score after 1 month ( 4 weeks)? $S(4)=87-12 \log (4+1)=87-8.39=78.61$ C. Find the average score at the end of the 12 weeks. $S(12)=8-12 \log (12+1)=87-13.37=73.63$
24. The Richter scale model for measuring magnitude $R$ of an earthquake is modeled by the equation $R=\log \left(\frac{a}{r}\right)+B$ , where $a$ is the amplitude in micrometers, $T$ is the period in seconds, and $B$ represents the dampening effect (weakening) of the wave due to the distance from the epicenter of the quake. A. Find the magnitude $R$ of a quake where $a=325, T=4$ and $B=3.25$ B. Find the magnitude $R$ of a quake where $a=230, T=2$ and $B=4.5$

See Solution

Problem 483

Problems $1-6$ , Assuming $x$ and $y$ are positive, use properties of logarithms to write the expression as a sum or difference of logarithms.
1. $\log 16 x$
2. $\ln \left(\frac{3}{y}\right) \ln 3-\ln y$
3. $\ln \left(e^{3} y^{5}\right)$
4. $\log \left(1000 x^{5}\right)$
5. $\ln \sqrt{\frac{x^{3}}{y}}$
6. $\log _{2}\left(x^{3} y^{2}\right)$
Problems 7 - 12, Assuming $x, y$ , and $z$ are positive, use properties of logarithms to write the expression as a single logarithm.
7. $\log _{2} 64-\log _{2} 4$
8. $\ln (x+3)+2 \ln x$
9. $4 \ln x+7 \ln y-3 \ln z$
10. $\frac{1}{3}(\log x-2 \log y)$
11. $\frac{1}{3}[2 \log (x+1)-\log x-\log (x-3)]$
12. $3[\ln x+\ln (x-2)]-4 \ln \left(x^{2}-4\right)$
Problems 13 - 16, Use a calculator to evaluate to three decimal places.
13. $\log _{4} 18$
14. $\log _{\frac{1}{2}} 23$
15. $\log _{\pi} 57$
16. $\log _{0.8} 16$

See Solution

Problem 484

$\frac{\frac{3}{x}+\frac{5}{y^{2}}}{\frac{7}{y}-\frac{6}{x^{4}}}$

See Solution

Problem 485

7 Asegninet 41 16 instructure com/courses/38499/assignments/1025898 Epic| The Leading. Syrngted Pubics. Dastboard Hon
07 , Assignments > 7 Assignment 4.1 7 Assignment 4.1
Due Thursday by 4pm Points 10 (7)
Math Usten cet (LT) Factor out the coefficient of the va $4 x-20$
Factored expression: $\square$
Basic
7 8 9 4 5 6

See Solution

Problem 486

Simplify the expression: $\sqrt{\frac{28 a^{2} b}{c^{2}}}$

See Solution

Problem 487

Mock/Practice Thst 8 (eptional) Question 18 of 20 (1) poin) I Gueatlon Attempts 1 of 1 Time Remaining: 144 1 2 3 4 5 6 7 8 9 10 11 12
The formula $P=2 a+2 b$ represents the perimeter, $P$ , of a parallelogram given the base, $b$ , and an adjacent side, $a$ . Factor out the GCF and write an equivalent formula in factored form. $P \equiv$ $\square$ Continue Submit Assig 2024 MeGraw HIIILC. All Righte Reserved. Torms of Use Privagy Center

See Solution

Problem 488

Pre-Test Active 1 2 3 4 5
What is the simplified expression for the expression below? $-1(2 x+3)-2(x-1)$ $-4 x+1$ $-4 x-2$ $-4 x+2$ $-4 x-1$

See Solution

Problem 489

$3\left(n^{2}-3+2\right)$

See Solution

Problem 490

Add and simplify. $\begin{array}{l} (4+\sqrt{-16})+(9+\sqrt{-36}) \\ (4+\sqrt{-16})+(9+\sqrt{-36})= \end{array}$ $\square$ (Simplify your answer. Type your answer in the form a +bi .)

See Solution

Problem 491

Amira mowed 6 lawns in 9 hours. What was her rate of mowing in lawns per hour?
Resize the right columns to represent the unit rate.

See Solution

Problem 492

Watch Video
Write an equivalent expression by distributing the "-" sign outside the parentheses: $-(-4.2 r-s+3.9)$
Answer Attempt 1 out of 2 $\square$ Submit Answer

See Solution

Problem 493

Practice Use the Distributive Property to simplify each expression. PRACTICES
9. $6(a+10)$
13. $10(9-t)$
10. $8(4+x)$
11. $(5+w) 5$
See Problem 1.
17. $(3-8 c) 1.5$
14. $12(2 j-6)$
15. $16(7 b+6)$
12. $(2 t+3) 11$
19. $\frac{1}{4}(4 f-8)$
21. $(-8 z-10)(-1.5)$
18. $(5 w-15) 2.1$
16. $(1+3 d) 9$
20. $6\left(\frac{1}{3} h+1\right)$
22. $0(3.7 x-4.21)$
23. $1\left(\frac{3}{11}-\frac{7 d}{17}\right)$
24. $\frac{1}{2}\left(\frac{1}{2} y-\frac{1}{2}\right)$
Write each fraction as a sum or difference.
25. $\frac{2 x+7}{5}$
26. $\frac{17+5 n}{4}$
29. $\frac{25-8 t}{5}$
30. $\frac{18 x+51}{17}$
27. $\frac{8-9 x}{3}$
See Problem 2.
31. $\frac{22-2 n}{2}$
Simplify each expression.
33. $-(20+d)$
34. $-(-5-4 y)$
37. $-(18 a-17 b)$
38. $-(2.1 c-4 d)$
35. $-(9-7 c)$
See Problem 3.
36. $-(-x+15)$
39. $-(-m+n+1)$
40. $-(x+3 y-3)$
Use mental math to find each product.
41. $5.1 \times 8$
42. $3 \times 7.25$
45. $3.9 \times 6$
46. $5 \times 2.7$
43. $299 \times 3$ (1.) See Problem 4.
44. $4 \times 197$
47. $6.15 \times 4$
48. $6 \times 9.1$
49. You buy 50 of your favorite songs from a Web site that charges $\$ .99$ for each song. What is the cost of 50 songs? Use mental math.
50. The perimeter of a baseball diamond is about 360 ft . If you take 12 laps around the diamond, what is the total distance you run? Use mental math.
51. One hundred and five students see a play. Each ticket costs $\$ 45$ . What is the total amount the students spend for tickets? Use mental math.
52. Suppose the distance you travel to school is 5 mi . What is the total distance for 197 trips from home to school? Use mental math.
Simplify each expression by combining like terms.
53. $11 x+9 x$
54. $8 y-7 y$
See Problem 5.
56. $-n+4 n$
57. $5 w^{2}+12 w^{2}$
55. $5 t-7 t$
59. $-4 y^{2}+9 y^{2}$
60. $6 c-4+2 c-7$
58. $2 x^{2}-9 x^{2}$
62. $2 n+1-4 m-n$
63. $-7 h+3 h^{2}-4 h-3$
61. $5-3 x+y+6$
64. $10 a b+2 a b^{2}-9 a b$
Write a word phrase for each expression. Then simplify each expression.
65. $3(t-1)$
66. $4(d+7)$
67. $\frac{1}{3}(6 x-1)$

See Solution

Problem 494

Perform the indicated operation. $\begin{array}{l} \frac{x+7}{2 x^{2}+5 x+3}+\frac{x}{2 x^{2}+3 x+1} \\ \frac{x+7}{2 x^{2}+5 x+3}+\frac{x}{2 x^{2}+3 x+1}= \end{array}$ $\square$ (Simplify your answer. Type your answer in factored form.)

See Solution

Problem 495

Put the following equation of a line into slope-intercept form, simplifying all fractions. $4 y-4 x=-36$

See Solution

Problem 496

Put the following equation of a line into slope-intercept form, simplifying all fractions. $20 y-4 x=100$

See Solution

Problem 497

Factor the following
37. $x^{2}-37 x-120$

See Solution

Problem 498

$\left(\frac{1}{27}\right)^{\frac{2}{3}}=$

See Solution

Problem 499

$\left(64 m^{4}\right)^{\frac{3}{2}}$

See Solution

Problem 500

[-/2 Points] DETAILS MY NOTES MCKTRIG7 5.1.
Multiply the numerator and denominator of the fraction by the conjugat (a) $\frac{1-\sqrt{2}}{1+\sqrt{2}}$ $\square$ (b) $\frac{1-\sin x}{1+\sin x}$ $\square$

See Solution

Simplify

Problem 401

White an equivalent expressic −4∣2(y−2)i-4 \mid 2(y-2) i−4∣2(y−2)i

Problem 402

Problem 403

Simplify. (6−i)+(5−8i)[?]+i\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}(6−i)+(5−8i)[?]+i​

Problem 404

3(2x+4)+2(x−3)3(2 x+4)+2(x-3)3(2x+4)+2(x−3)

Problem 405

5(m−4)−3(m+1)5(m-4)-3(m+1)5(m−4)−3(m+1)

Problem 406

d 2(x+5)−(3x−2)2(x+5)-(3 x-2)2(x+5)−(3x−2)

Problem 407

Problem 408

6t3\frac{6 t}{3}36t​

Problem 409

log⁡9(3x2)+log⁡9(4x6)\log _{9}\left(3 x^{2}\right)+\log _{9}\left(4 x^{6}\right)log9​(3x2)+log9​(4x6)

Problem 410

Select the correct answer.Which expression is equivalent to 21153−915321 \sqrt[3]{15}-9 \sqrt[3]{15}21315​−9315​ ? A. 12 B. 3015330 \sqrt[3]{15}30315​ C. 125312 \sqrt[3]{5}1235​ D. 1215312 \sqrt[3]{15}12315​

Problem 411

Simplify. 4log⁡4(2x+8)4{ }^{\log _{4}(2 x+8)}4log4​(2x+8)

Problem 412

To solve 493x=3432x+149^{3 x}=343^{2 x+1}493x=3432x+1, write each side of the equation in terms of base □\square□ DONE

Problem 413

−3v<18-3 v<18−3v<18Simplify your answer as much as

Problem 414

−3100ab6-3 \sqrt{100 a b^{6}}−3100ab6​

Problem 415

3. −5144-5 \sqrt{144}−5144​

Problem 416

Problem 417

16) Factor completely: x3+6x2−3x−18x^{3}+6 x^{2}-3 x-18x3+6x2−3x−18

Problem 418

Problem 419

15) x4−81x^{4}-81x4−81

Problem 420

15) x4−81x^{4}-81x4−81

Problem 421

Factor completely (mixed factoring). CHECK FOR GCF’S FIRST!!! Make sure your final answer is fully factored. If the problem is not factorable, then say so. x2+36 x^{2} + 36 x2+36

Problem 422

(95⋅92)4\left(9^{5} \cdot 9^{2}\right)^{4}(95⋅92)4

Problem 423

b) Simplify 3(x+5)−x+33(x+5)-x+33(x+5)−x+3 2x+182 x+182x+18 Answ

Problem 424

Factor by grouping. x3+9x2−6x−54x3+9x2−6x−54=\begin{array}{l} x^{3}+9 x^{2}-6 x-54 \\ x^{3}+9 x^{2}-6 x-54= \end{array}x3+9x2−6x−54x3+9x2−6x−54=​

Problem 425

Divide 120÷5\frac{1}{20} \div 5201​÷5Enter your answer in the box as a fraction in simplest form. □\square□

Problem 426

2. Rewrite g(x)=−5x3−18x3+4g(x)=\frac{-5 x^{3}-18}{x^{3}+4}g(x)=x3+4−5x3−18​ in the form g(x)=q(x)+rb(x)g(x)=q(x)+\frac{r}{b(x)}g(x)=q(x)+b(x)r​.

Problem 427

Problem 428

1. Simplify the complex rational expression: 1x−1−1x1x2−x\frac{\frac{1}{x-1}-\frac{1}{x}}{\frac{1}{x^{2}-x}}x2−x1​x−11​−x1​​ A. 1 B. 2x−1\frac{2}{x-1}x−12​ C. xx−1\frac{x}{x-1}x−1x​ D. x−x2x-x^{2}x−x2 E. None of the above

Problem 429

Problem 430

Problem 431

4. 11c−5−811 \frac{c}{-5}-811−5c​−8

Problem 432

Expand and simplify (x+3)(x−5)(x+3)(x-5)(x+3)(x−5)

Problem 433

Problem 434

8−3i4+3i\frac{8-3 i}{4+3 i}4+3i8−3i​

Problem 435

Simplify the function before differentiating. f(x)=1e10xf(x)=\frac{1}{\sqrt{e^{10 x}}}f(x)=e10x​1​ f(x)=f(x)=f(x)= □\square□ (Simplify your answer.)

Problem 436

The graph of two functions, f and g , is illustrated below. Use the graph to answer parts (a) through ( f ). (a) (f+g)(3)=(\mathrm{f}+\mathrm{g})(3)=(f+g)(3)= □\square□ (Simplify your answer.)

Problem 437

1 2 3 4 5 6 7 8 9 IoWhich expression is equivalent to 7(xy)7(x y)7(xy) ? 7x+y7 x+y7x+y 7x−y7 x-y7x−y x(7y)x(7 y)x(7y) xy7\frac{x y}{7}7xy​

Problem 438

You roll a 6-sided die two times.What is the probability of rolling a 5 and then rolling a number greater than 2?2 ?2? Simplify your answer and write it as a fraction or whole number. □\square□ Submit

Problem 439

Question Show ExamplesFind the slope of a line perpendicular to the line whose equation is 3x+y=83 x+y=83x+y=8. Fully simplify your answer.Answer Attempt 1 out of 2

Problem 440

Question Show ExamplesFind the slope of a line perpendicular to the line whose equation is x−2y=−8x-2 y=-8x−2y=−8. Fully simplify your answer.Answer Attempt 1 out of 2

Problem 441

(x3+3x2−5x)−(x3−2x2+x)\left(x^{3}+3 x^{2}-5 x\right)-\left(x^{3}-2 x^{2}+x\right)(x3+3x2−5x)−(x3−2x2+x)

Problem 442

Simplify each expression.1. 9y+4.1−6y9 y+4.1-6 y9y+4.1−6y2. −3x+5+7x-3 x+5+7 x−3x+5+7x3. 8x+13−3x+9128 x+13-3 x+9 \frac{1}{2}8x+13−3x+921​4. y2+3y2y^{2}+3 y^{2}y2+3y25. 4x+15−3x+104 x+15-3 x+104x+15−3x+106. −10x+2x+8x-10 x+2 x+8 x−10x+2x+8x

Problem 443

a) Fully factorise 3y2+11y+103 y^{2}+11 y+103y2+11y+10 b) Use your answer to part a) to solve 3y2+11y+10=03 y^{2}+11 y+10=03y2+11y+10=0

Problem 444

White an equivalent expressic $-4 \mid 2(y-2) i$

Simplify. $\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}$

$3(2 x+4)+2(x-3)$

$5(m-4)-3(m+1)$

d $2(x+5)-(3 x-2)$

$\frac{6 t}{3}$

$\log _{9}\left(3 x^{2}\right)+\log _{9}\left(4 x^{6}\right)$

Select the correct answer.
Which expression is equivalent to $21 \sqrt[3]{15}-9 \sqrt[3]{15}$ ? A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$

Simplify. $4{ }^{\log _{4}(2 x+8)}$

To solve $49^{3 x}=343^{2 x+1}$ , write each side of the equation in terms of base $\square$ DONE

$-3 v<18$
Simplify your answer as much as

$-3 \sqrt{100 a b^{6}}$

3. $-5 \sqrt{144}$

16) Factor completely: $x^{3}+6 x^{2}-3 x-18$

15) $x^{4}-81$

15) $x^{4}-81$

Factor completely (mixed factoring). CHECK FOR GCF’S FIRST!!! Make sure your final answer is fully factored. If the problem is not factorable, then say so.
$x^{2} + 36$

$\left(9^{5} \cdot 9^{2}\right)^{4}$

b) Simplify $3(x+5)-x+3$ $2 x+18$ Answ

Factor by grouping. $\begin{array}{l} x^{3}+9 x^{2}-6 x-54 \\ x^{3}+9 x^{2}-6 x-54= \end{array}$

Divide $\frac{1}{20} \div 5$
Enter your answer in the box as a fraction in simplest form. $\square$

2. Rewrite $g(x)=\frac{-5 x^{3}-18}{x^{3}+4}$ in the form $g(x)=q(x)+\frac{r}{b(x)}$ .

1. Simplify the complex rational expression: $\frac{\frac{1}{x-1}-\frac{1}{x}}{\frac{1}{x^{2}-x}}$ A. 1 B. $\frac{2}{x-1}$ C. $\frac{x}{x-1}$ D. $x-x^{2}$ E. None of the above

4. $11 \frac{c}{-5}-8$

Expand and simplify $(x+3)(x-5)$

$\frac{8-3 i}{4+3 i}$

Simplify the function before differentiating. $f(x)=\frac{1}{\sqrt{e^{10 x}}}$ $f(x)=$ $\square$ (Simplify your answer.)

The graph of two functions, f and g , is illustrated below. Use the graph to answer parts (a) through ( f ). (a) $(\mathrm{f}+\mathrm{g})(3)=$ $\square$ (Simplify your answer.)

1 2 3 4 5 6 7 8 9 Io
Which expression is equivalent to $7(x y)$ ? $7 x+y$ $7 x-y$ $x(7 y)$ $\frac{x y}{7}$

You roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a number greater than $2 ?$ Simplify your answer and write it as a fraction or whole number. $\square$ Submit

Question Show Examples
Find the slope of a line perpendicular to the line whose equation is $3 x+y=8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

Question Show Examples
Find the slope of a line perpendicular to the line whose equation is $x-2 y=-8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

$\left(x^{3}+3 x^{2}-5 x\right)-\left(x^{3}-2 x^{2}+x\right)$

Simplify each expression.
1. $9 y+4.1-6 y$
2. $-3 x+5+7 x$
3. $8 x+13-3 x+9 \frac{1}{2}$
4. $y^{2}+3 y^{2}$
5. $4 x+15-3 x+10$
6. $-10 x+2 x+8 x$

a) Fully factorise $3 y^{2}+11 y+10$ b) Use your answer to part a) to solve $3 y^{2}+11 y+10=0$

You pick a card at random, put it back, and then pick another card at random.
What is the probability of picking an even number and then picking a factor of 10 ? Simplify your answer and write it as a fraction or whole number. $\square$ Submit Next up

write $z=\ln ((8+10 j)(7-9 j))$ in the form $z=x+y j$ $z=\square+\square \text { (to 2decimal places) }$

姣, All factors in your answer should have integer coefficients. $512 w^{3}+27 x^{3}=$ $\square$

㪱, Factor the polynomial. 㸚 Ald factors in your answer should have integer coefficients. $135 p^{3}+5000 q^{3}=$ $\square$ Submit

40) $(7 i)(-5 i)(-2-8 i)$

32) $(2-4 i)(-2-4 i)$

26) $(7+5 i)(8+i)$

rm the indicated opera $(-4+\sqrt{-9})^{2}$

b. $\left(3 x^{2}+2 x-7\right)-\left(7 x^{2}+x-1\right)=$ $\square$ (Simplify your answer. Do not factor.)

Question Watch Video Show Examples
Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $8 x \sqrt{175 x^{5} y^{3}}$

d. $\left(-3 x^{4}+6 x^{3}-11 x^{2}+5\right)-\left(5 x^{4}+2 x^{3}-x\right)=$ (Simplify your answer. Do not factor.)

Simplify. Assume that all variables represent positive numbers. $\frac{\sqrt{\frac{z^{2}}{36 x^{2}}}}{\frac{|z|}{6|x|}}$
Suggested tutorial: Learn It: Simplify a radical expression.

Practice
1. Express the following powers in exponent form a. $\sqrt[7]{3}$ b. $\sqrt[5]{-5}$ d. $\sqrt{\frac{5}{9}}$ c. $\frac{2}{\sqrt[4]{2}}$ e. $\sqrt[3]{y^{2}}$

Simplify. The variable represents a positive number. $\frac{2 \sqrt[3]{648 a^{5}}-2 \sqrt[3]{-375 a^{5}}}{2 \sqrt[3]{648 a^{5}}-2 \sqrt[3]{-375 a^{5}}}$

Perform the indicated operation. $\frac{6-5 i}{6+i}$

Ally factors in your answer should have integer coefficients. $125 w^{4}-216 w x^{3}=$ $\square$ Submit

$(19-7) \div 4 \cdot 11$

$11^{2}-8 \cdot 7+2$

$y=\ln \left(\frac{2 x}{x}\right)$

Rewrite the following in exponential form: a) $\log _{8}\left(\frac{1}{8}\right)=-1$ $\square$ b) $\log (117)=x$ $\square$ c) $\ln (x)=-1$ $\square$

Factor the four-term polynomial by grouping. $\begin{array}{r} 7 q^{2}+5 p q-7 q-5 p \\ 7 q^{2}+5 p q-7 q-5 p=\square \end{array}$ $\square$ (FactoF completely.)

$-4(3m + 2n) - 5m + y$

\begin{tabular}{|l|l|l|l} \hline $9 \sqrt[3]{125}$ & -2 \\ \hline 45 & $9 \sqrt{5}$ & $45 \sqrt[3]{5}$ & $45 \sqrt[3]{25}$ \\ \hline \end{tabular}

$\frac{9}{z-6} \div \frac{27}{2 z-12}$

Factor the following polynomial. $\begin{array}{c} 12 x^{2} y-20 x^{2}-18 y+30 \\ 12 x^{2} y-20 x^{2}-18 y+30= \end{array}$ $\square$ (Factor completely.)