Questions: 5. Solve the equation. -9x - 12 = 6 +12 +12 -9x = 18 x = -2 x = -2 7. The amount of water an electric dishwasher uses to wash dishes varies directly with the number of loads of dishes. The dishwasher uses 32 gallons of water to wash 4 loads of dishes. How many gallons of water will the dishwasher use to wash 10 loads of dishes? 9. Point T is translated using 7 units down and 4 units up. What is the rule that reflects the translation?

Solution Steps

To solve the equation \(-9x - 12 = 6\), we need to isolate \(x\). First, add 12 to both sides of the equation to eliminate the constant term on the left side. Then, divide both sides by -9 to solve for \(x\).

Since the amount of water used varies directly with the number of loads, we can set up a proportion. Given that 32 gallons are used for 4 loads, we can find the number of gallons used for 10 loads by solving the proportion.

To find the rule that reflects the translation of point \(T\) using 7 units down and 4 units up, we need to determine the net effect of these translations. Subtract the downward movement from the upward movement to find the overall translation.

To solve the equation

\[ -9x - 12 = 6, \]

we first add \(12\) to both sides:

\[ -9x = 18. \]

Next, we divide both sides by \(-9\):

\[ x = -2. \]

The dishwasher uses \(32\) gallons of water for \(4\) loads. To find the amount of water used per load, we calculate:

\[ \text{gallons per load} = \frac{32}{4} = 8 \text{ gallons/load}. \]

To find the water usage for \(10\) loads, we multiply:

\[ \text{gallons for 10 loads} = 8 \times 10 = 80 \text{ gallons}. \]

Point \(T\) is translated \(7\) units down and \(4\) units up. The net translation is calculated as:

\[ \text{net translation} = 4 - 7 = -3 \text{ units down}. \]

Final Answer