Which of the following is the length of the unknown leg of a right triangle that has one leg length of 10 feet and a hypotenuse of 24 feet? (Round to the nearest tenth.)

A. 21.8 feet

B. 25 feet

C. 13.6 feet

D. 17.7 feet

Answer Explanation:

Let the unknown length of the x. The resulting triangle is shown below.

We use the Pythagoras theorem as follows to find the unknown value of x as:

Thus, the value of unknown side of the triangle is 21.8 feet.

Therefore, the Correct Answer is A.

Q #1: A bucket containing 2 2/5 gallons of water is 4/7 full. How many gallons of water is in one fully filled bucket?

A. 4 1/5

B. 2 1/5

C. 4 4/5

D. 2 2/5

Answer Explanation

we are asked to find the number of gallons a full tank can hold. A full tank is equivalent to 1.

Convert the mixed fraction into proper fraction as follows

(2frac{2}{5}=frac{left(2ast5 ight)+2}{5}=frac{10+2}{5}=frac{12}{5})

If we let x be the number of gallons in full tank, and setting up the proportion equation with the number of gallons on the numerator and fraction of tank on denominator as follows.

(frac{x gallons}{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

Cross-multiply to find the value of x.

(frac{x }{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

(x astfrac{4}{7}full tank=frac{12}{5} gallonsast1 full tank)

(x =frac{frac{12}{5} gallonsast1 full tank}{frac{4}{7}full tank}=frac{12}{5}divfrac{4}{7} gallons=frac{12}{5}astfrac{7}{4}gallons=frac{21}{5}gallons)

Converting 21/5 to a mixed fraction is 4 1/5. Thus, when the tank is full, it holds 4 1/5 gallons of water.
Q #2: Which of the following is the value of x in the equation below

A. x= -4 or x=2

B. x= -2 or x=3

C. x =-2 or x= 4

D. x= -2 or x= 1

Answer Explanation

we find the value of x by applying the absolute conditions to the given equation.

First, add 2 to both sides of equation

The absolute conditions are:

If , a>0, then u=a or u=-a

In this case a=10, which is greater 0.

The first condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

The second condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

Then, the value of x is 3 or -2.
Q #3: As the dollar rate increases in a day, the amount of investment, stock prices, and forex exchange deposit available also decreases. Which of the following is the independent variable?

A. Amount of investment

B. Dollar rate

C. Stock prices

D. Forex exchange deposit

Answer Explanation

Based on the given scenario, the outcome of measuring the daily dollar rate is the decline in investment, stock prices, and forex exchange. The three outcomes are dependent variables while the dollar rate is the independent variable.