Simplify the expression below. Which of the following is correct? $18x^5yz\ \div\ \ 6xyz^4$

A. $3x^4z^3$

B. $3x^4yz^3$

C. $\frac{(3x)^4}{z^3}$

D. $\frac{(3x^4)}{z^3}$

Answer Explanation:

We use the properties of exponent with the same base to solve for above expression.

Multiplication of exponents with same base, we add the exponents

Division of exponents with same base, we subtract the exponents

Using these two properties, we can solve the expression:

Now we use the following properties:

y0 =1, and , thus

Therefore, the Correct Answer is D.

Q #1: The hypotenuse (side C) of a triangle is 13 inches long. Which of the following pairs of measurements could be the correct for the lengths of the other two sides of the triangle? (Note: A2 + B2= C2)

A. 5 inches, 12 inches

B. 2.5 inches, 6 inches

C. 2.5 inches, 4 inches

D. 5 inches, 8 inches

Answer Explanation

In this problem, we take the triangle as a right-angled triangle and label it as follows:

From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13. Mathematically,

But C=13 inches

If we take A=5 inches and B=12 inches, then

Next, we take A=2.5 inches, B=6 inches

Next, we take A=2.5 inches, B=4 inches

6.25+16=169

22.25≠169

Taking A=5 inches and B=8 inches

From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.
Q #2: Pat deposits $600 in a savings account at a simple interest rate 6% per year for 5 years. How much money will Pat have earned in interest at the end of 5 years?

A. $360

B. $180

C. $95

D. $36

Answer Explanation

In the simple interest, we utilize the following formula to find the simple interest after a period of time in years.

I=P*r*t

I is the interest

P=Principal or initial deposit

r=rate

t=time in years

From the given problem, P=$600, r=6%=6/100=0.06, t=5 years. Then

I=$600*0.06*5=$180

After 5 years, Pat will earn an interest of $180.
Q #3: A family is planning a driving vacation and is estimating the price of gasoline. While on the vacation, the family plans to drive 3,000 miles. The car gets about 25 miles per gallon, and the cost of gasoline is $1.66 per gallon. Which of the following is the estimate for cost of gasoline for the vacation?

A. $120.00

B. $41.50

C. $72.29

D. $199.20

Answer Explanation

We solve the problem by first finding the amount of gallons needed for the whole trip then find the cost of the gallon.

The car uses 1 gallon to cover 25 miles, which is same as:

Now, in 3000 miles, the car will use how many gallons of gasoline?

A trip of 3000 miles will need 120 gallons. And to find the cost of 120 gallons, we proceed as follows:

The family will spend $199.20 to drive for 3000 miles.