1. Neena is listening to a song. It has a consistent beat. She counts 11 beats in 5 seconds. What is the constant of proportionality for the relationship of beats to minutes?

132

Step-by-step explanation:

132

Step-by-step explanation:

First, find how many beats are in a minute by creating a proportion:

\frac{11}{5} = \frac{x}{60}

Cross multiply and solve for x:

5x = 660

x = 132

So, there are 132 beats in one minute.

This means the constant of proportionality is 132.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)