Complete the table, find the value of expressions, simplify expressions, and solve equations.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

1. Complete the table below.
The table is already completed in the image.

$x$	$x^2$	$\sqrt{x}$	$\frac{1}{x}$
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 answer is $\boxed{\text{34}}$ .

b) $\sqrt{49}$
Find the square root of 49.
$\sqrt{49} = 7$
The answer is $\boxed{\text{7}}$ .

3. Simplify the following expressions.

a) $(2x + 3) + (x - 5)$
Remove the parentheses.
$2x + 3 + x - 5$
Combine like terms.
$(2x + x) + (3 - 5) = 3x - 2$
The answer is $\boxed{3x - 2}$ .

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

c) $2(x + 4) - 3(x - 2)$
Distribute the numbers outside the parentheses.
$2 \times x + 2 \times 4 - 3 \times x - 3 \times (-2)$ $2x + 8 - 3x + 6$
Combine like terms.
$(2x - 3x) + (8 + 6) = -x + 14$
The answer is $\boxed{-x + 14}$ .

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 answer is $\boxed{x = 6}$ .

b) $3(x - 2) = 15$
Divide both sides 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 answer is $\boxed{x = 7}$ .

Step-by-step solution