Questions: The equation M(x, y)=63+0.6 x-0.4 y gives the mileage (in mpg) of a new car a of tire pressure x (in psi) and speed y (in mph). Find M(35,41) (include the appro and explain what it means. M(35,41)= (Type an integer or a decimal.) Explain what the answer in the previous step means. Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals.) 1. A. Increasing the speed by one mph and maintaining a tire pressure of increase mileage by psi B. Increasing the tire pressure by one psi and maintaining a speed of increase mileage by mpg mph will C. Increasing the tire pressure by one psi and maintaining a speed of decrease mileage by mpg psi will D. Increasing the speed by one mph and maintaining a tire pressure of increase mileage by psi will E. Mileage is mmpl at a tire pressure of psi and a speed of mph

The equation M(x, y)=63+0.6 x-0.4 y gives the mileage (in mpg) of a new car a of tire pressure x (in psi) and speed y (in mph). Find M(35,41) (include the appro and explain what it means.
M(35,41)=
(Type an integer or a decimal.)
Explain what the answer in the previous step means. Select the correct choice below and fill in the answer boxes within your choice.
(Type integers or decimals.) 1.
A. Increasing the speed by one mph and maintaining a tire pressure of increase mileage by psi
B. Increasing the tire pressure by one psi and maintaining a speed of increase mileage by mpg mph will
C. Increasing the tire pressure by one psi and maintaining a speed of decrease mileage by mpg
psi will
D. Increasing the speed by one mph and maintaining a tire pressure of increase mileage by psi will
E. Mileage is mmpl at a tire pressure of psi and a speed of mph

Transcript text: The equation $M(x, y)=63+0.6 x-0.4 y$ gives the mileage (in mpg) of a new car a of tire pressure $x$ (in psi) and speed $y$ (in mph). Find $M(35,41)$ (include the appro and explain what it means. $M(35,41)=$ $\square$ $\square$ (Type an integer or a decimal.) Explain what the answer in the previous step means. Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals.) 1. A. Increasing the speed by one mph and maintaining a tire pressure of increase mileage by mpg $\qquad$ psi B. Increasing the tire pressure by one psi and maintaining a speed of increase mileage by $\qquad$ mpg $\qquad$ mph will C. Increasing the tire pressure by one psi and maintaining a speed of decrease mileage by mpg psi will D. Increasing the speed by one mph and maintaining a tire pressure of increase mileage by $\qquad$ psi will E. Mileage is mmpl at a tire pressure of psi and a speed of mph

Solution

Solution Steps

To solve the given problem, we need to evaluate the function $ M(x, y) = 63 + 0.6x - 0.4y $ at the given values $ x = 35 $ and $ y = 41 $. This will give us the mileage of the car at the specified tire pressure and speed. After calculating the mileage, we will interpret the result based on the given choices.

Solution Approach

Substitute $ x = 35 $ and $ y = 41 $ into the equation $ M(x, y) = 63 + 0.6x - 0.4y $.
Calculate the value of $ M(35, 41) $.
Interpret the result based on the given choices.

Step 1: Substitute the Given Values into the Equation

We are given the equation for mileage: \[ M(x, y) = 63 + 0.6x - 0.4y \] We need to find $ M(35, 41) $. Substitute $ x = 35 $ and $ y = 41 $ into the equation: \[ M(35, 41) = 63 + 0.6(35) - 0.4(41) \]

Step 2: Perform the Calculations

Calculate the values step-by-step: \[ 0.6 \times 35 = 21 \] \[ 0.4 \times 41 = 16.4 \] Now substitute these values back into the equation: \[ M(35, 41) = 63 + 21 - 16.4 \] \[ M(35, 41) = 67.6 \]

Step 3: Interpret the Result

The calculated mileage is $ 67.6 $ mpg. This means that at a tire pressure of $ 35 $ psi and a speed of $ 41 $ mph, the car's mileage is $ 67.6 $ mpg.

Step 4: Choose the Correct Interpretation

Based on the function $ M(x, y) = 63 + 0.6x - 0.4y $:

Increasing the tire pressure $ x $ by $ 1 $ psi increases the mileage by $ 0.6 $ mpg.
Increasing the speed $ y $ by $ 1 $ mph decreases the mileage by $ 0.4 $ mpg.

The correct interpretation is: C. Increasing the tire pressure by one psi and maintaining a speed of $ y $ decreases mileage by $ 0.4 $ mpg.