Complete the table, find values for expressions involving squares and square roots, and simplify algebraic…

Question

Complete the table, find values for expressions involving squares and square roots, and simplify algebraic expressions.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems, step by step:

1. Complete the table below.

The table is already completed in the image. Here it is for reference:

$x$	$x^2$	$\sqrt{x}$	$\frac{1}{x}$
1	1	1	1
4	16	2	$\frac{1}{4}$
9	81	3	$\frac{1}{9}$
16	256	4	$\frac{1}{16}$
25	625	5	$\frac{1}{25}$

2. Find:

a) $3^2 + 5^2$

Calculate the squares.
$3^2 = 3 \times 3 = 9$ $5^2 = 5 \times 5 = 25$
Add the results.
$9 + 25 = 34$
The value is $\boxed{\textbf{34}}$ .

b) $\sqrt{49}$
Find the number that, when multiplied by itself, equals 49.
$\sqrt{49} = 7$
The value is $\boxed{\textbf{7}}$ .

3. Simplify the following expressions.

a) $(2x + 3) + (x - 5)$
Remove the parentheses.
$2x + 3 + x - 5$
Group like terms.
$(2x + x) + (3 - 5)$
Combine like terms.
$3x - 2$
The simplified expression is $\boxed{\textbf{3x - 2}}$ .

b) $(3x^2 - 2x + 1) - (x^2 + x - 4)$
Distribute the negative sign to the terms in the second parenthesis.
$3x^2 - 2x + 1 - x^2 - x + 4$
Group like terms.
$(3x^2 - x^2) + (-2x - x) + (1 + 4)$
Combine like terms.
$2x^2 - 3x + 5$
The simplified expression is \boxed{\textbf{2x^2 - 3x + 5}}.

c) $2(x + 4) - 3(x - 2)$
Distribute the numbers outside the parentheses to the terms inside.
$2 \times x + 2 \times 4 - 3 \times x - 3 \times (-2)$ $2x + 8 - 3x + 6$
Group like terms.
$(2x - 3x) + (8 + 6)$
Combine like terms.
$-x + 14$
The simplified expression is $\boxed{\textbf{-x + 14}}$ .

4. Solve the following equations.

a) $2x + 5 = 17$
Subtract 5 from both sides of the equation.
$2x + 5 - 5 = 17 - 5$ $2x = 12$
Divide both sides by 2.
$\frac{2x}{2} = \frac{12}{2}$ $x = 6$
The solution is $\boxed{\textbf{x = 6}}$ .

b) $3(x - 2) = 15$
Divide both sides of the equation by 3.
$\frac{3(x - 2)}{3} = \frac{15}{3}$ $x - 2 = 5$
Add 2 to both sides of the equation.
$x - 2 + 2 = 5 + 2$ $x = 7$
The solution is $\boxed{\textbf{x = 7}}$ .

Complete the table, find values for expressions involving squares and square roots, and simplify algebraic expressions.

Step-by-step solution

Calculate the squares.

Add the results.

Find the number that, when multiplied by itself, equals 49.

Remove the parentheses.

Group like terms.

Combine like terms.

Distribute the negative sign to the terms in the second parenthesis.

Group like terms.

Combine like terms.

Distribute the numbers outside the parentheses to the terms inside.

Group like terms.

Combine like terms.

Subtract 5 from both sides of the equation.

Divide both sides by 2.

Divide both sides of the equation by 3.

Add 2 to both sides of the equation.

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