Simplify the expression sqrt(32 × 22) and solve the system of equations x + y = 0, y = 2x + 9.

Question

ScanSolve AI Tutor · Accepted Answer

The image contains two distinct mathematical problems separated by a vertical line.

: Simplify the expression
The expression to simplify is $\sqrt{3^{2} \cdot 2^{2}}$ .

Evaluate the terms inside the square root.
$3^{2} = 9$ $2^{2} = 4$
Multiply the evaluated terms.
$3^{2} \cdot 2^{2} = 9 \cdot 4 = 36$
Calculate the square root.
$\sqrt{36} = 6$
The simplified expression is $\boxed{6}$ .

: Solve the system of equations
The system of equations is:
1. $x + y = 0$
2. $y = 2x + 9$
Express $y$ in terms of $x$ from the first equation.
From equation (1), subtract $x$ from both sides:
$y = -x$
Substitute this expression for $y$ into the second equation.
Substitute $y = -x$ into $y = 2x + 9$ :
$-x = 2x + 9$
Solve for $x$ .
Subtract $2x$ from both sides:
$-x - 2x = 9$ $-3x = 9$
Divide by $-3$ :
$x = \frac{9}{-3}$ $x = -3$
Substitute the value of $x$ back into $y = -x$ to find $y$ .
$y = -(-3)$ $y = 3$
The solution to the system of equations is $x = \boxed{-3}$ and $y = \boxed{3}$ .

Point	x	y
x-intercept	−4.5	0
y-intercept	0	9

Simplify the expression sqrt(32 * 22) and solve the system of equations x + y = 0, y = 2x + 9.