Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward your grade.

the number of minutes required for rylie to bake a cake varies inversely with the temperature of the oven.
yesterday, rylie baked a cake for 75 minutes at 400°. how long should he expect to have to bake the cake if he
increases the oven temperature to 415°? round your answer to the nearest minute. (1 point)

○ 60 minutes

○ 80 minutes

○ 78 minutes

○ 72 minutes

Explanation:

Step1: Define inverse variation

If two quantities \( m \) (minutes) and \( t \) (temperature) vary inversely, the relationship is \( m = \frac{k}{t} \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that when \( m = 75 \) and \( t = 400 \), substitute into the formula: \( 75=\frac{k}{400} \). Solve for \( k \) by multiplying both sides by 400: \( k = 75\times400=30000 \).

Step3: Find new time at \( t = 415 \)

Now, use \( k = 30000 \) and \( t = 415 \) in \( m=\frac{k}{t} \). So \( m=\frac{30000}{415}\approx72.29 \). Round to the nearest minute, we get \( m\approx72 \).

Answer:

72 minutes