Simplify

Problem 2501

Condense $\log x + \log y$ to a single logarithm.

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Problem 2502

$\left(-3 x^{5} y^{\frac{1}{3}}\right)^{3}=\square x^{\square}$

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Problem 2503

Simplify $10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}$ . $18 \sqrt{6 y}$ $18 \sqrt{2 y}$ $12 \sqrt{2 y}$ $18 \sqrt{6 y^{3}}$

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Problem 2504

Simplify $5 x \sqrt{3 x}-2 x \sqrt{3 x}-x \sqrt{3 x}$ . $3 x \sqrt{6 x^{3}}$ $3 x \sqrt{3 x}$ $2 x \sqrt{9 x}$ $2 x \sqrt{3 x}$

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Problem 2505

Rewrite in simplest radical form $\frac{1}{x^{-\frac{3}{6}}}$ . Show each step of your process.

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Problem 2506

$\frac{\left(\frac{\sqrt{3}}{2}\right)^{2}+\frac{\sqrt{2}}{2}-(-\sqrt{3})^{2} \cdot\left(-\frac{1}{2}\right)^{2}+\frac{\sqrt{2}}{2} \cdot(-1)}{1 \cdot 1}$

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Problem 2507

NAME $\qquad$ DATE 4.3: Operations with Polynomials Practice dd or subtract.
1. $\left(6 a^{2}+5 a+10\right)-\left(4 a^{2}+6 a+12\right)$ $=2 a^{4}-1 a-2$
2. $(g+5)+(2 g+7)$ $=2 g^{2}+7 g+10 g+35$
3. $\left(x^{2}-3 x-3\right)+\left(2 x^{2}+7 x-2\right)$
4. $(2 x-3)-(5 x-6)$

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Problem 2508

\begin{tabular}{|l|l|} \hline Directions: Find each sum or difference. Answers must be in standard form. \\ \hline 11. $\left(x^{2}-4 x+3\right)+\left(3 x^{2}-3 x-5\right)$ & 12. $\left(8 r^{2}-12 r+4\right)-\left(3 r^{2}+5 r-1\right)$ \\ \hline 13. $\left(2 m-3+7 m^{2}\right)-\left(3-9 m^{2}-2 m\right)$ & 14. $\left(7 p^{2}+3 p\right)-\left(5 p^{2}+4\right)$ \\ \hline 15. $\left(3 a^{2}-a+3\right)+\left(4 a^{2}-5\right)$ & 16. $\left(5 w^{3}-w+2 w^{2}+4\right)+\left(3 w^{2}+1-4 w\right)$ \\ \hline 17. $\left(2 x^{2}+3 y^{2}-z^{2}\right)-\left(x^{2}-y^{2}-z^{2}\right)+\left(4 x^{2}-3 y^{2}\right)$ & \begin{tabular}{l}
18. $\left(12+8 k^{3}+3 k-4 k^{2}\right)+\left(5 k^{3}+15-k+7\right.$ \\ \end{tabular} \\ \hline 19. Find the sum of $\left(2 x^{2}-6 x-2\right)$ and $\left(x^{2}+4 x\right)$ . & \begin{tabular}{l}
20. Subtract $\left(-a^{2}-5 a b+3 b^{2}\right)$ from \\ $\left(3 a^{2}-2 a b+3 b^{2}\right)$ . \end{tabular} \\ & \end{tabular}

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Problem 2509

Pascal's Triangle to expand $\left(3+2 x^{2}\right)^{4}$ . Express your answer in simplest form.

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Problem 2510

?
Divide: $\frac{5 \sqrt{8}}{2 \sqrt{2}}$ Cannot be divided 5 $2 \sqrt{6}$

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Problem 2511

?
Subtract: $\sqrt{5}-7 \sqrt{5}$ Cannot be subtracted $-6 \sqrt{5}$ 0

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Problem 2512

Complete the square for the quadratic function $h(x) = -0.5x^2 + 2x - 3$ .

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Problem 2513

2. ( 6 points) Fill in the blank with simplified answers. If the expression is undefined, writ Assume all variables are positive real numbers, not equal to 1. (a) $\log _{8}(64)=$ $\qquad$ (b) $\log _{9}(27)=$ 1.5 $\qquad$ (c) $6^{\log _{6}(14)}=$ $\qquad$ 14 (d) $\ln \sqrt[7]{e}=$ $\qquad$ (e) $\log _{a}(1)=$ $\qquad$ (f) $\log _{c} \frac{1}{c^{3}}=$ $\qquad$
3. (12 points) Fill in the blanks. (a) If you reflect the graph of $y=5^{x}$ across the $y$ -axis, you get the graph of $\qquad$ (b) If you reflect the graph of $y=5^{x}$ across the line $y=x$ , you get the graph of (c) The domain of $y=5^{x}$ is $\qquad$ (d) The range of $y=5^{x}$ is $\qquad$ (e) The domain of $y=\log _{5}(x)$ is $\qquad$ (f) The range of $y=\log _{5}(x)$ is $\qquad$ (g) As $x \rightarrow-\infty, y=5^{x} \rightarrow$ $\qquad$ (h) As $x \rightarrow \infty, \quad y=5^{x} \rightarrow$ $\qquad$ (i) As $x \rightarrow 0^{+}, y=\log _{5}(x) \rightarrow$ $\qquad$ (j) As $x \rightarrow \infty, y=\log _{5}(x) \rightarrow$ $\qquad$ (k) As $x \rightarrow-\infty, \quad y=\left(\frac{1}{5}\right)^{x} \rightarrow$ $\qquad$ (l) As $x \rightarrow \infty, y=\left(\frac{1}{5}\right)^{x} \rightarrow$ $\qquad$

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Problem 2514

27. $\frac{3}{4(x+1)}+\frac{x}{x+1}$
High School of American Studies atgebraic Fractions Unit 4; Alge
28. $\frac{2 x}{x-1}+\frac{3}{2(x-1)}$
29. $\frac{4 n-3}{15}-\frac{3(n-2)}{10}$
Write each expression as a fraction in simplest form.
9. $6+\frac{1}{x}$
10. $2+\frac{5}{a}$
11. $3-\frac{2}{x}$
12. $5-\frac{3}{n}$
Write each expression as a fraction in simplest form.
17. $2+\frac{x}{y}$
18. $3-\frac{2}{x+1}$
19. $7+\frac{y}{y-2}$
Write each expression as a fraction in simplest form. $\begin{array}{ll}\text { 29. } \frac{x}{x-1}+\frac{x-1}{x}-2 & \text { 30. } x+\frac{2 x+1}{x-2}\end{array}$
31. $\frac{3}{x+1}+\frac{x}{x+1}-1$

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Problem 2515

Express as a sum of logarithms. $\log _{7}(10 \cdot 15)$

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Problem 2516

5. Schreibe als Bruch. Kürze so weit wie möglich. a) $6 \%$ b) $25 \%$ c) $30 \%$ d) $75 \%$ e) $24 \%$ f) $70 \%$ g) $15 \%$ ${ }^{+}$ h) $36 \%$ +i) $18 \%$ +j) $44 \%$ ${ }^{+} \mathbf{k )} 45 \%$

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Problem 2517

3) semplifica l'espressione usando le proprietà degli angoli associati (indica l'angolo a e gli altri 2 angoli sulla circonferenza goniometrica) $3 \sin (2 \pi-\alpha)-\frac{\cos \alpha}{\sin \left(\frac{3}{2} \pi+\alpha\right)}$

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Problem 2518

You spin the spinner once.
What is $\mathrm{P}(4$ or odd $)$ ? Simplify your answer and write it as a fraction or whole number. $\square$

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Problem 2519

59. $6 d+4(3 d+5)$
62. $a+\frac{a}{5}+\frac{2}{5} a$
65. $7(2 x+y)+6(x+5 y)$

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Problem 2520

21 Multiple Choice 3 points Simplify, add, subtract, multiply or divide the rational expressions. Pay attention to signs so that you will know what operation should be performed. Don't forget to simplify at the end. $\frac{3 x^{2}-2 x-5}{x-2} \cdot \frac{x+10}{x+1} \cdot \frac{x-2}{x^{2}+x-90}$ $\frac{3 x-5}{x-9}$ $\frac{(3 x-5)(x+10)}{(x+9)(x-10)}$ $\frac{3 x+5}{x+9}$ $\frac{(3 x+5)(x-1)}{x+1}$

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Problem 2521

(3) $\ln \left(x^{t}\right)=t \cdot \ln (x)$
8. Vereinfachen Sie folgende Terme: a) $\ln \left(e^{2}\right)$ c) $\ln (\sqrt{e})$ e) $\ln \left(\frac{e^{2}}{k}\right)$ g) $e^{\ln (3)}$ b) $\ln \left(\frac{1}{\mathrm{e}^{2}}\right)$ d) $\ln (\sqrt[3]{e})$ f) $\ln \left(2 \cdot e^{3}\right)$ h) $e^{-\ln (2)}$

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Problem 2522

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

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Problem 2523

1. Simplify the expressions (a) $\frac{\sin 2 A}{\cos A}$ , (b) $2 \tan A \cos ^{2} A$ ,
2. If $\cos A=-\frac{2}{3}$ find $\cos 2 A$ .
3. Angle $B$ is acute and $\tan B=\frac{4}{3}$ . Find (a) $\sin B$ (b) $\cos B$ (c) $\sin 2 B$
4. If $\sin C=1 / \sqrt{5}$ find $\sin 2 C, \cos 2 C$ and $\tan 2 C$ if (a) $C$ is acute, (b) $C$ is obtuse.

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Problem 2524

Simplify the radical expression. $\sqrt[5]{-x^{5}}$
Write your answer in the form $\mathrm{A}, \sqrt[5]{\mathrm{B}}$ , or $\mathrm{A} \sqrt[5]{\mathrm{B}}$ , where A and B are constants or expressions in x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A . $\square$ ㅁ | $\square$ $\sqrt[9]{ }$ ( $\square$ Submit

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Problem 2525

4) $-5\left[\begin{array}{cc}-3 & 0 \\ 0 & 5\end{array}\right]$

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Problem 2526

Simplify the expression to a + bi form: $-2 i^{74}+11 i^{36}+5 i^{79}-6 i^{18}$

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Problem 2527

mplify the expression to a + bi form: $2 i^{5}-3 i^{7}+i^{76}+5 i^{17}$
Answer

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Problem 2528

EXERCICE 2A. 13 - NANCY-METZ 2002 Calculer et donner A sous forme d'une fraction irréductible. $A=\frac{7}{5}+\frac{3}{5} \times \frac{11}{6}$

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Problem 2529

Test tremujori i parë Grupi A
1. Paraqite shprehjen si një thyesë të vetme në formë sa më të thjeshtë $\frac{x+1}{3}-\frac{x+2}{4}$ (2 pikë)

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Problem 2530

3. Question from 1.2: Exponents and Radicals
Simplify the expression. Assume that $x, y$ , and $z$ denote any positive real numbers. (a) $\sqrt[8]{x^{8} y^{4} z^{4}}$ $\square$ (b) $\sqrt[3]{\sqrt{729 x^{6}}}$ $\square$

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Problem 2531

4. Question from 1.2: Exponents and Radicals
Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. (a) $x^{9 / 5} x^{11 / 5}$ $\square$ (b) $y^{7 / 6} y^{11 / 6}$ $\square$
5. Question from 1.3: Algebraic Expressions
Perform the indicated operations and simplify. $(\sqrt{a}-b)(\sqrt{a}+b)$ $\square$

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Problem 2532

Watch Video
Question Express the following fraction in simplest form, only using positive exponents. $\frac{\left(3 k^{4}\right)^{5}}{-15 k^{10}}$

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Problem 2533

Exercice 4 Simplifier l'expression $\frac{2 \cosh ^{2}(x)-\sinh (2 x)}{x-\ln (\cosh x)-\ln 2}$ et donner ses limites en $-\infty$ et $+\infty$ .

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Problem 2534

Évalue les expressions suivantes. Montre ton travail. (3 points) $\frac{16!}{4!12!} \frac{16!}{48}=$ b. $6 \times 4 \times 5!24 \cdot 5!=$ c. $3\left(\frac{2 \times 12!}{4!4!}\right)$ $\frac{24!}{20!}$ e. $\frac{6 \times 7!}{5!}$ f. $3!+4!+1!+2$ !

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Problem 2535

Factor the binomial completely. $z^{4}-1$
Part: $0 / 4$ $\square$
Part 1 of 4
The GCF is 1 . $z^{4}-1$ is a difference of squares. Write in the form $a^{2}-b^{2}$ , where $a=z^{2}$ and $b=$ $\square$ .

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Problem 2536

$\begin{aligned} 4 p^{5}(v-4)(9 v-1) & =4 p^{5}\left(9 v^{2}-v-36 v+4\right) \\ & =4 p^{5}\left(9 v^{2}-\square v+4\right)\end{aligned}$

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Problem 2537

Factor the higher degree polynomial. $x^{4}-2 x^{2}-15$
Part: $0 / 3$
Part 1 of 3
To produce the product $x^{4}$ , we must use $x^{2}$ and $\square$ .

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Problem 2538

b. $2,109 \div 23$ $\approx$ $\qquad$ $\div$ $\qquad$ $=$

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Problem 2539

Simplify. Write your answers without exponents. $\begin{array}{l} \left(\frac{1}{25}\right)^{-\frac{3}{2}}= \\ 8^{-\frac{4}{3}}=\square \end{array}$ $\square$

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Problem 2540

3. $-3 \times 11$

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Problem 2541

$\sqrt{4 x^{8}}$

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Problem 2542

Simplify completely $\frac{x^{2}-10 x-24}{x^{2}-3 x-108}$ and find the restrictions on the variable. $\frac{x+2}{x+9}, x \neq-2, x \neq-9$ $\frac{x+2}{x+9}, x \neq-9, x \neq 12$ $\frac{x-2}{x-9}, x \neq-2, x \neq-9$ $\frac{x-2}{x-9}, x \neq-9, x \neq 12$

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Problem 2543

$42 \times 3-\left(2^{4}-1\right) \div 5$

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Problem 2544

the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponer buld be positive. $\log (z)+\log (11)$

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Problem 2545

Correct
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponents should be positive. $\ln (x)-\ln (3 z)$

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Problem 2546

$\{3 x-[y+3 x-(2 y+x)]-2\}-7=$

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Problem 2547

Multiply. $\begin{array}{l} \sqrt{3}(3-7 \sqrt{3}) \\ \sqrt{3}(3-7 \sqrt{3})= \end{array}$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

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Problem 2548

[文], Simplify the expression: $d-9 d+-2 d+-2 d$ $\square$ Submit

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Problem 2549

Multiply and simplify to lowest terms. $\frac{z^{2}-1}{z^{2}-36} \cdot \frac{z-6}{z+1}$

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Problem 2550

Add and simplify to lowest terms. $\frac{y+2}{y-6}+\frac{8 y-56}{y-6}$

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Problem 2551

Evaluate without a calculator: (7 marks) a) $\log _{2} \frac{1}{4}$ b) $\log \frac{1}{3}+(\log 27-\log 9)$ c) $\log 1200-\log 3-\log 4$

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Problem 2552

Write the expression as a single logarithm. $4 \log _{b}(9 y+1)+\frac{1}{2} \log _{b}(y+4)$ ${ }^{\log }(\square)$

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Problem 2553

Points: 00
Rationalize the denominator. Assume that all expressions under radicals represent $\sqrt{\frac{7 x}{45}}$ $\sqrt{\frac{7 x}{45}}=$ $\square$

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Problem 2554

Subtract. Write your answer in simp $5 \sqrt{75}-7 \sqrt{3}$

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Problem 2555

Simplify. Rationalize the denominator. $\frac{9}{5-\sqrt{2}}$

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Problem 2556

Use the distributive property to remove the parentheses. $6(5+u)$

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Problem 2557

Simplify. Rationalize the denominator. $\frac{-2}{4+\sqrt{15}}$

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Problem 2558

Simplify $(0.4)^{3}$ . Choose the correct answer: 0.64, 1.2, 12, or 0.064.

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Problem 2559

Simplify the expression by combining like terms: $2(3x + 2) + (2y + 1)$ .

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Problem 2560

Simplify the expression $-5x - 1 - 6x - 5 - 6x$ .

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Problem 2561

Simplify the expression: $\frac{5^{2}-4}{5+2}$ (1 point)

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Problem 2562

Simplify the expression: $3\left(x^{2}+5 x+5\right)-\left(x^{2}+3 x+1\right)$ .

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Problem 2563

Simplify the expression: $2(2a - 5) - (a - 3)$ . What is the result?

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Problem 2564

Simplify the expression: $(2 x^{2}-4 x+1)+(5 x+x^{2}-1)$ .

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Problem 2565

Find the equation of the line at the point $(x=-4, y=4)$ and simplify: $-5x - 2y + 9$ .

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Problem 2566

Multiply and simplify: $\frac{1}{4} \cdot \frac{3}{4} \cdot \frac{2}{3}$ . What is the answer?

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Problem 2567

Divide and simplify: $\frac{5}{8} \div \frac{1}{7} =$

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Problem 2568

Divide and simplify: $8 \div 3 \frac{6}{7}$ . Provide your answer as a whole number, proper fraction, or mixed number.

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Problem 2569

Find the expression equivalent to $4(4 a+6)$ . Options: $16 a+24$ , $4(6 a+4)$ , $24 a+16$ , $16 a+6$ .

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Problem 2570

Multiply and simplify: $1 \frac{1}{3} \cdot 9 \frac{5}{6}$

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Problem 2571

Choose expressions equivalent to $(-3y - 2) - (-4y + 6)$ . Options: $-2 + 4y - 6 - 3y$ , $-8y + 1$ , $-7y$ , $y - 8$ .

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Problem 2572

Find expressions equivalent to $(9 j-7)+(-5 j+5)$ . Options: $4 j-2$ , $(-5 j+5)+(9 j+-7)$ , $-2 j+4$ , $9 j+5-7+-5 j$ .

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Problem 2573

Brandi swam 6 butterfly laps and 8 freestyle laps. Find the ratio of freestyle laps to total laps. Simplify your answer. $6+8=14$ A. $6: 14$ B. $8: 6$ C. $8: 14$ D. $14: 8$

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Problem 2574

Add $\frac{8}{9}+\frac{4}{9}$ and simplify as a mixed number. Options: $1 \frac{3}{9}$ , $\frac{2}{3}$ , $\frac{12}{9}$ , $1 \frac{1}{3}$ .

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Problem 2575

Find the least common denominator and express these fractions: $\frac{3}{4}$ , $\frac{5}{6}$ , $\frac{9}{12}$ , $\frac{10}{12}$ , $\frac{3}{12}$ , $\frac{5}{12}$ , $\frac{18}{24}$ , $\frac{29}{24}$ .

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Problem 2576

Add and simplify: $2 \frac{8}{9}+3 \frac{5}{6}$ . What is the mixed number result?

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Problem 2577

A 4-ounce Greek yogurt has 160 calories. What is the calorie rate per ounce?

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Problem 2578

Calculate $\frac{3}{2}\left[\left(58-10^{2}\right) \div(\sqrt{16}+3)\right]$ .

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Problem 2579

Calculate $\frac{(\sqrt{225}-11) \cdot 12}{-12-(8-6^{2})}-|-3|$ .

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Problem 2580

Combine and simplify: $\frac{5 a-x}{6 a}-\frac{8 a+7 x}{2 a}+2$ into a single fraction.

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Problem 2581

Calculate the expression: $\frac{56 \div(7-9)^{3}-25}{23-5 \cdot 4}$ .

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Problem 2582

Simplify the expression $a^{2}+2(b-6)-17$ .

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Problem 2583

If you sleep 6 hours daily for a year (365 days), how many days is that as a mixed number? Simplify your answer.

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Problem 2584

Simplify the expression: $4y - y(3 - 7y) + 5 + 2(8 - y)$ . What should you do first?

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Problem 2585

Condense and simplify: $2(\log 18 - \log 3) + \frac{1}{2} \log \frac{1}{16} = \log [?]$

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Problem 2586

Add and simplify the mixed number if needed: $\frac{3}{8} + \frac{2}{3}$ .

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Problem 2587

Add and simplify: $3 \frac{7}{8} + 2 \frac{1}{5}$ . Write your answer as a mixed number.

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Problem 2588

Add and simplify the mixed numbers: $3 \frac{7}{8} + 2 \frac{1}{5}$ . What is the answer as a mixed number?

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Problem 2589

Find the revenue and profit functions for Gymnast Clothing, where cost is $C(x)=3,250+8x+0.1x^2$ and price is \$130 per pair.

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Problem 2590

Find the weekly profit function $P(x)$ for T-shirts with demand $q=-50x+7200$ and cost $C(x)=-1800x+340200$ . Also, find the break-even price.

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Problem 2591

Divide and simplify: $20 \div 1 \frac{25}{31}$ . Provide a whole number, proper fraction, or mixed number.

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Problem 2592

Gymnast Clothing's cost for $x$ pairs of cleats is $C(x)=3,250+8x+0.1x^{2}$ . Selling price is \$130 per pair. Find revenue and profit functions. How many pairs for profit?

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Problem 2593

Simplify the fraction 12/16 to its lowest terms.

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Problem 2594

The cost of laser eye surgery in Country B is $\$ 1500$ for each eye.

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Problem 2595

Simplify the fraction to its lowest terms: $\frac{21}{28}$ .

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Problem 2596

Divide and simplify to the lowest terms, expressing as a whole or mixed number if possible: $\frac{3}{5} \div \frac{1}{2}$

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Problem 2597

Multiply and simplify: $\frac{1}{4} \cdot \frac{3}{4} \cdot \frac{2}{3}$ .

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Problem 2598

Multiply and simplify: $6 \frac{1}{4} \cdot 7 \frac{5}{6}$

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Problem 2599

Divide and simplify to lowest terms or as a whole/mixed number: $\frac{21}{2} \div \frac{7}{16}$

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Problem 2600

Find the expression for $f(x+3)$ if $f(x) = 3x - 5$ .

See Solution

1 ...23 24 25 26 27 28 29 ...56

Simplify

Problem 2501

Condense log⁡x+log⁡y\log x + \log ylogx+logy to a single logarithm.

Problem 2502

(−3x5y13)3=□x□\left(-3 x^{5} y^{\frac{1}{3}}\right)^{3}=\square x^{\square}(−3x5y31​)3=□x□

Problem 2503

Simplify 102y+52y+32y10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}102y​+52y​+32y​. 186y18 \sqrt{6 y}186y​ 182y18 \sqrt{2 y}182y​ 122y12 \sqrt{2 y}122y​ 186y318 \sqrt{6 y^{3}}186y3​

Problem 2504

Simplify 5x3x−2x3x−x3x5 x \sqrt{3 x}-2 x \sqrt{3 x}-x \sqrt{3 x}5x3x​−2x3x​−x3x​. 3x6x33 x \sqrt{6 x^{3}}3x6x3​ 3x3x3 x \sqrt{3 x}3x3x​ 2x9x2 x \sqrt{9 x}2x9x​ 2x3x2 x \sqrt{3 x}2x3x​

Problem 2505

Rewrite in simplest radical form 1x−36\frac{1}{x^{-\frac{3}{6}}}x−63​1​. Show each step of your process.

Problem 2506

(32)2+22−(−3)2⋅(−12)2+22⋅(−1)1⋅1\frac{\left(\frac{\sqrt{3}}{2}\right)^{2}+\frac{\sqrt{2}}{2}-(-\sqrt{3})^{2} \cdot\left(-\frac{1}{2}\right)^{2}+\frac{\sqrt{2}}{2} \cdot(-1)}{1 \cdot 1}1⋅1(23​​)2+22​​−(−3​)2⋅(−21​)2+22​​⋅(−1)​

Problem 2507

Problem 2508

Problem 2509

Pascal's Triangle to expand (3+2x2)4\left(3+2 x^{2}\right)^{4}(3+2x2)4. Express your answer in simplest form.

Problem 2510

?Divide: 5822\frac{5 \sqrt{8}}{2 \sqrt{2}}22​58​​ Cannot be divided 5 262 \sqrt{6}26​

Problem 2511

?Subtract: 5−75\sqrt{5}-7 \sqrt{5}5​−75​ Cannot be subtracted −65-6 \sqrt{5}−65​ 0

Problem 2512

Complete the square for the quadratic function h(x)=−0.5x2+2x−3 h(x) = -0.5x^2 + 2x - 3 h(x)=−0.5x2+2x−3.

Problem 2513

Problem 2514

Problem 2515

Express as a sum of logarithms. log⁡7(10⋅15)\log _{7}(10 \cdot 15)log7​(10⋅15)

Problem 2516

5. Schreibe als Bruch. Kürze so weit wie möglich. a) 6%6 \%6% b) 25%25 \%25% c) 30%30 \%30% d) 75%75 \%75% e) 24%24 \%24% f) 70%70 \%70% g) 15%15 \%15% +{ }^{+}+h) 36%36 \%36% +i) 18%18 \%18% +j) 44%44 \%44% +k)45%{ }^{+} \mathbf{k )} 45 \%+k)45%

Problem 2517

Problem 2518

You spin the spinner once.What is P(4\mathrm{P}(4P(4 or odd ))) ? Simplify your answer and write it as a fraction or whole number. □\square□

Problem 2519

59. 6d+4(3d+5)6 d+4(3 d+5)6d+4(3d+5)62. a+a5+25aa+\frac{a}{5}+\frac{2}{5} aa+5a​+52​a65. 7(2x+y)+6(x+5y)7(2 x+y)+6(x+5 y)7(2x+y)+6(x+5y)

Problem 2520

Problem 2521

Problem 2522

2(−22−1)−3=2\left(-2^{2}-1\right)-3=2(−22−1)−3=

Problem 2523

Problem 2524

Problem 2525

4) −5[−3005]-5\left[\begin{array}{cc}-3 & 0 \\ 0 & 5\end{array}\right]−5[−30​05​]

Problem 2526

Simplify the expression to a + bi form: −2i74+11i36+5i79−6i18-2 i^{74}+11 i^{36}+5 i^{79}-6 i^{18}−2i74+11i36+5i79−6i18

Problem 2527

mplify the expression to a + bi form: 2i5−3i7+i76+5i172 i^{5}-3 i^{7}+i^{76}+5 i^{17}2i5−3i7+i76+5i17Answer

Problem 2528

EXERCICE 2A. 13 - NANCY-METZ 2002 Calculer et donner A sous forme d'une fraction irréductible. A=75+35×116A=\frac{7}{5}+\frac{3}{5} \times \frac{11}{6}A=57​+53​×611​

Problem 2529

Test tremujori i parë Grupi A1. Paraqite shprehjen si një thyesë të vetme në formë sa më të thjeshtë x+13−x+24\frac{x+1}{3}-\frac{x+2}{4}3x+1​−4x+2​ (2 pikë)

Problem 2530

3. Question from 1.2: Exponents and RadicalsSimplify the expression. Assume that x,yx, yx,y, and zzz denote any positive real numbers. (a) x8y4z48\sqrt[8]{x^{8} y^{4} z^{4}}8x8y4z4​ □\square□ (b) 729x63\sqrt[3]{\sqrt{729 x^{6}}}3729x6​​ □\square□

Problem 2531

Problem 2532

Watch VideoQuestion Express the following fraction in simplest form, only using positive exponents. (3k4)5−15k10\frac{\left(3 k^{4}\right)^{5}}{-15 k^{10}}−15k10(3k4)5​

Problem 2533

Exercice 4 Simplifier l'expression 2cosh⁡2(x)−sinh⁡(2x)x−ln⁡(cosh⁡x)−ln⁡2\frac{2 \cosh ^{2}(x)-\sinh (2 x)}{x-\ln (\cosh x)-\ln 2}x−ln(coshx)−ln22cosh2(x)−sinh(2x)​ et donner ses limites en −∞-\infty−∞ et +∞+\infty+∞.

Problem 2534

Problem 2535

Factor the binomial completely. z4−1z^{4}-1z4−1Part: 0/40 / 40/4 □\square□Part 1 of 4The GCF is 1 . z4−1z^{4}-1z4−1 is a difference of squares. Write in the form a2−b2a^{2}-b^{2}a2−b2, where a=z2a=z^{2}a=z2 and b=b=b= □\square□ .

Problem 2536

4p5(v−4)(9v−1)=4p5(9v2−v−36v+4)=4p5(9v2−□v+4)\begin{aligned} 4 p^{5}(v-4)(9 v-1) & =4 p^{5}\left(9 v^{2}-v-36 v+4\right) \\ & =4 p^{5}\left(9 v^{2}-\square v+4\right)\end{aligned}4p5(v−4)(9v−1)​=4p5(9v2−v−36v+4)=4p5(9v2−□v+4)​

Problem 2537

Factor the higher degree polynomial. x4−2x2−15x^{4}-2 x^{2}-15x4−2x2−15Part: 0/30 / 30/3Part 1 of 3To produce the product x4x^{4}x4, we must use x2x^{2}x2 and □\square□ .

Problem 2538

b. 2,109÷232,109 \div 232,109÷23 ≈\approx≈ \qquad ÷\div÷ \qquad ===

Problem 2539

Simplify. Write your answers without exponents. (125)−32=8−43=□\begin{array}{l} \left(\frac{1}{25}\right)^{-\frac{3}{2}}= \\ 8^{-\frac{4}{3}}=\square \end{array}(251​)−23​=8−34​=□​ □\square□

Problem 2540

3. −3×11-3 \times 11−3×11

Problem 2541

4x8\sqrt{4 x^{8}}4x8​

Problem 2542

Problem 2543

42×3−(24−1)÷542 \times 3-\left(2^{4}-1\right) \div 542×3−(24−1)÷5

Problem 2544

the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponer buld be positive. log⁡(z)+log⁡(11)\log (z)+\log (11)log(z)+log(11)

Problem 2545

CorrectUse the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponents should be positive. ln⁡(x)−ln⁡(3z)\ln (x)-\ln (3 z)ln(x)−ln(3z)

Problem 2546

Condense $\log x + \log y$ to a single logarithm.

$\left(-3 x^{5} y^{\frac{1}{3}}\right)^{3}=\square x^{\square}$

Simplify $10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}$ . $18 \sqrt{6 y}$ $18 \sqrt{2 y}$ $12 \sqrt{2 y}$ $18 \sqrt{6 y^{3}}$

Simplify $5 x \sqrt{3 x}-2 x \sqrt{3 x}-x \sqrt{3 x}$ . $3 x \sqrt{6 x^{3}}$ $3 x \sqrt{3 x}$ $2 x \sqrt{9 x}$ $2 x \sqrt{3 x}$

Rewrite in simplest radical form $\frac{1}{x^{-\frac{3}{6}}}$ . Show each step of your process.

$\frac{\left(\frac{\sqrt{3}}{2}\right)^{2}+\frac{\sqrt{2}}{2}-(-\sqrt{3})^{2} \cdot\left(-\frac{1}{2}\right)^{2}+\frac{\sqrt{2}}{2} \cdot(-1)}{1 \cdot 1}$

Pascal's Triangle to expand $\left(3+2 x^{2}\right)^{4}$ . Express your answer in simplest form.

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Divide: $\frac{5 \sqrt{8}}{2 \sqrt{2}}$ Cannot be divided 5 $2 \sqrt{6}$

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Subtract: $\sqrt{5}-7 \sqrt{5}$ Cannot be subtracted $-6 \sqrt{5}$ 0

Complete the square for the quadratic function $h(x) = -0.5x^2 + 2x - 3$ .

Express as a sum of logarithms. $\log _{7}(10 \cdot 15)$

5. Schreibe als Bruch. Kürze so weit wie möglich. a) $6 \%$ b) $25 \%$ c) $30 \%$ d) $75 \%$ e) $24 \%$ f) $70 \%$ g) $15 \%$ ${ }^{+}$ h) $36 \%$ +i) $18 \%$ +j) $44 \%$ ${ }^{+} \mathbf{k )} 45 \%$

You spin the spinner once.
What is $\mathrm{P}(4$ or odd $)$ ? Simplify your answer and write it as a fraction or whole number. $\square$

59. $6 d+4(3 d+5)$
62. $a+\frac{a}{5}+\frac{2}{5} a$
65. $7(2 x+y)+6(x+5 y)$

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

4) $-5\left[\begin{array}{cc}-3 & 0 \\ 0 & 5\end{array}\right]$

Simplify the expression to a + bi form: $-2 i^{74}+11 i^{36}+5 i^{79}-6 i^{18}$

mplify the expression to a + bi form: $2 i^{5}-3 i^{7}+i^{76}+5 i^{17}$
Answer

EXERCICE 2A. 13 - NANCY-METZ 2002 Calculer et donner A sous forme d'une fraction irréductible. $A=\frac{7}{5}+\frac{3}{5} \times \frac{11}{6}$

Test tremujori i parë Grupi A
1. Paraqite shprehjen si një thyesë të vetme në formë sa më të thjeshtë $\frac{x+1}{3}-\frac{x+2}{4}$ (2 pikë)

3. Question from 1.2: Exponents and Radicals
Simplify the expression. Assume that $x, y$ , and $z$ denote any positive real numbers. (a) $\sqrt[8]{x^{8} y^{4} z^{4}}$ $\square$ (b) $\sqrt[3]{\sqrt{729 x^{6}}}$ $\square$

Watch Video
Question Express the following fraction in simplest form, only using positive exponents. $\frac{\left(3 k^{4}\right)^{5}}{-15 k^{10}}$

Exercice 4 Simplifier l'expression $\frac{2 \cosh ^{2}(x)-\sinh (2 x)}{x-\ln (\cosh x)-\ln 2}$ et donner ses limites en $-\infty$ et $+\infty$ .

Factor the binomial completely. $z^{4}-1$
Part: $0 / 4$ $\square$
Part 1 of 4
The GCF is 1 . $z^{4}-1$ is a difference of squares. Write in the form $a^{2}-b^{2}$ , where $a=z^{2}$ and $b=$ $\square$ .

$\begin{aligned} 4 p^{5}(v-4)(9 v-1) & =4 p^{5}\left(9 v^{2}-v-36 v+4\right) \\ & =4 p^{5}\left(9 v^{2}-\square v+4\right)\end{aligned}$

Factor the higher degree polynomial. $x^{4}-2 x^{2}-15$
Part: $0 / 3$
Part 1 of 3
To produce the product $x^{4}$ , we must use $x^{2}$ and $\square$ .

b. $2,109 \div 23$ $\approx$ $\qquad$ $\div$ $\qquad$ $=$

Simplify. Write your answers without exponents. $\begin{array}{l} \left(\frac{1}{25}\right)^{-\frac{3}{2}}= \\ 8^{-\frac{4}{3}}=\square \end{array}$ $\square$

3. $-3 \times 11$

$\sqrt{4 x^{8}}$

$42 \times 3-\left(2^{4}-1\right) \div 5$

the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponer buld be positive. $\log (z)+\log (11)$

Correct
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponents should be positive. $\ln (x)-\ln (3 z)$

$\{3 x-[y+3 x-(2 y+x)]-2\}-7=$

Multiply. $\begin{array}{l} \sqrt{3}(3-7 \sqrt{3}) \\ \sqrt{3}(3-7 \sqrt{3})= \end{array}$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

[文], Simplify the expression: $d-9 d+-2 d+-2 d$ $\square$ Submit

Multiply and simplify to lowest terms. $\frac{z^{2}-1}{z^{2}-36} \cdot \frac{z-6}{z+1}$

Add and simplify to lowest terms. $\frac{y+2}{y-6}+\frac{8 y-56}{y-6}$

Evaluate without a calculator: (7 marks) a) $\log _{2} \frac{1}{4}$ b) $\log \frac{1}{3}+(\log 27-\log 9)$ c) $\log 1200-\log 3-\log 4$

Write the expression as a single logarithm. $4 \log _{b}(9 y+1)+\frac{1}{2} \log _{b}(y+4)$ ${ }^{\log }(\square)$

Points: 00
Rationalize the denominator. Assume that all expressions under radicals represent $\sqrt{\frac{7 x}{45}}$ $\sqrt{\frac{7 x}{45}}=$ $\square$

Subtract. Write your answer in simp $5 \sqrt{75}-7 \sqrt{3}$

Simplify. Rationalize the denominator. $\frac{9}{5-\sqrt{2}}$

Use the distributive property to remove the parentheses. $6(5+u)$

Simplify. Rationalize the denominator. $\frac{-2}{4+\sqrt{15}}$

Simplify $(0.4)^{3}$ . Choose the correct answer: 0.64, 1.2, 12, or 0.064.

Simplify the expression by combining like terms: $2(3x + 2) + (2y + 1)$ .

Simplify the expression $-5x - 1 - 6x - 5 - 6x$ .

Simplify the expression: $\frac{5^{2}-4}{5+2}$ (1 point)

Simplify the expression: $3\left(x^{2}+5 x+5\right)-\left(x^{2}+3 x+1\right)$ .

Simplify the expression: $2(2a - 5) - (a - 3)$ . What is the result?

Simplify the expression: $(2 x^{2}-4 x+1)+(5 x+x^{2}-1)$ .

Find the equation of the line at the point $(x=-4, y=4)$ and simplify: $-5x - 2y + 9$ .

Multiply and simplify: $\frac{1}{4} \cdot \frac{3}{4} \cdot \frac{2}{3}$ . What is the answer?

Divide and simplify: $\frac{5}{8} \div \frac{1}{7} =$

Divide and simplify: $8 \div 3 \frac{6}{7}$ . Provide your answer as a whole number, proper fraction, or mixed number.

Find the expression equivalent to $4(4 a+6)$ . Options: $16 a+24$ , $4(6 a+4)$ , $24 a+16$ , $16 a+6$ .

Multiply and simplify: $1 \frac{1}{3} \cdot 9 \frac{5}{6}$

Choose expressions equivalent to $(-3y - 2) - (-4y + 6)$ . Options: $-2 + 4y - 6 - 3y$ , $-8y + 1$ , $-7y$ , $y - 8$ .

Find expressions equivalent to $(9 j-7)+(-5 j+5)$ . Options: $4 j-2$ , $(-5 j+5)+(9 j+-7)$ , $-2 j+4$ , $9 j+5-7+-5 j$ .

Brandi swam 6 butterfly laps and 8 freestyle laps. Find the ratio of freestyle laps to total laps. Simplify your answer. $6+8=14$ A. $6: 14$ B. $8: 6$ C. $8: 14$ D. $14: 8$

Add $\frac{8}{9}+\frac{4}{9}$ and simplify as a mixed number. Options: $1 \frac{3}{9}$ , $\frac{2}{3}$ , $\frac{12}{9}$ , $1 \frac{1}{3}$ .