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