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Q23.

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Precalculus Mathematics for Calculus

Found in: Page 252

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Properties of Real Numbers Use properties of real numbers to write the expression without parentheses.
$3 (x + y)$

The given expression can be written as $3 x + 3 y$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given expression is:

$3 (x + y)$

Step 2. Write the concept.

According to the distributive property of real numbers, if $a, b, c$ are three real numbers, then

$a (b + c) = a b + a c$

Step 3. Rewrite the expression.

Using the distributive property of real numbers, the given expression can be rewritten as:

$\begin{array}{l} 3 (x + y) = 3 (x) + 3 (y) \\ = 3 x + 3 y \end{array}$

Thus, the given expression can be written as $3 x + 3 y$ .

Most popular questions for Math Textbooks

a. Using exponential notation, we can write $\sqrt[3]{5}$ as _______.

b. Using radicals, we can write $5^{\frac{1}{2}}$ as _____.

c. Is there a difference between $\sqrt{5^{2}}$ and ${(\sqrt{5})}^{2}$ ? Explain.

Properties of Real Numbers Use properties of real numbers to write the expression without parentheses.

$\frac{4}{3} (- 6 y)$

Properties of Real Numbers Use properties of real numbers to write the expression without parentheses.

$4 (2 m)$

Yes or No? If No, give a reason.

a. Is the expression ${(x^{2})}^{3}$ equal to $x^{5}$ ?

b. Is the expression ${(2 x^{4})}^{3}$ equal to $2 x^{12}$ ?

c. Is the expression $\sqrt{4 a^{2}}$ equal to $2 a$ ?

d. Is the expression $\sqrt{a^{2} + 4}$ equal to $a + 2$ ?

A quadratic function $f$ is given.

(a) Express $f$ in standard form.

(b) Find the vertex and $x$ - and $y$ - intercepts of $f$ .

(c) Sketch a graph of $f$ .

(d) Find the domain and range of $f$ .

$f (x) = - x^{2} + 10 x$

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