Question

1. the minimum fine for driving in excess of the speed limit is $25. an additional $6 is added to the minimum fine for each mile per hour (mph) in excess of the speed limit. rachel was issued a $103 fine for speeding in a 55 - mph speed limit zone. for driving at what speed, in mph, was rachel fined?

a. 48
b. 52
c. 62
d. 68
e. 78

1. the expression $5x^{3}×2xy×3xy^{2}$ is equivalent to:

a. $10x^{3}y^{2}$
b. $10x^{6}y^{3}$
c. $30x^{3}y^{3}$
d. $30x^{6}y^{3}$
e. $30x^{6}y^{2}$

Explanation:

Question 16

Step1: Find the amount due to excess speed

The total fine is $103$ and the minimum fine is $25$. So the amount due to excess speed is \(103 - 25=78\) dollars.

Step2: Find the number of miles over the speed limit

Since each mile over the speed limit adds $6$ dollars, the number of miles over the speed limit \(n=\frac{78}{6} = 13\) mph.

Step3: Find Rachel's speed

The speed limit is $55$ mph. So Rachel's speed \(v=55 + 13=68\) mph.

Step1: Multiply the coefficients

Multiply the coefficients \(5\times2\times3 = 30\).

Step2: Use the rule of exponents for \(x\)

For \(x\) terms: \(x^{3}\times x\times x=x^{3 + 1+1}=x^{5}\) (using \(a^{m}\times a^{n}=a^{m + n}\)).

Step3: Use the rule of exponents for \(y\)

For \(y\) terms: \(y\times y^{2}=y^{1+2}=y^{3}\) (using \(a^{m}\times a^{n}=a^{m + n}\)).

Answer:

D. 68

Question 17