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 14 feet? (Round to the nearest tenth.)
6 feet
15.6 feet
9.8 feet
20 feet
Correct Answer : C
The sides of a right-angled triangle are determined by the Pythagoras theorem. If we let the unknown side to x as in the figure below, then theory is applied as follows.
The value of x is found as:
The value of the unknown leg side of a triangle is about 9.8 feet.
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Related Questions
Correct Answer is C
Explanation
The SI units of measuring length is meter. However, a meter can be a large unit or small quantity depending what is being measured. Therefore, derived units of meters are used to measure the length of an object. In our case, centimeters is the appropriate unit to measure the width of the window.
Correct Answer is A
Explanation
To answer this question, we need to convert the numbers into a similar form. Converting decimal numbers into fraction is appropriate to finding the greatest number.
-0.9 becomes 9/10
-1.9 becomes 19/10
Now we find the LCM of the denominators of the four fractions. The LCM of 5, 10 and 3 is 30. Multiply each fraction with the LCM to compare the fractions.
-3/5*30=-18
-9/10*30=-27
-19/10*30=-57
-8/3*30=-24
The greatest number is -18, meaning -3/5 is the greatest number.
Correct Answer is B
Explanation
By inspection, we find the corresponding values of the given denominations in the following manner.
Correct Answer is A
Explanation
This problem asks us to compare the number of dimes to nickels.
If we let p be number of pennies in the bottle. Then,
Number of quarters in the bottle = 4p
Number of nickels in the bottle = 2p
Number of dimes in the bottle =7(2p)=14p
To find the number of dimes the child has than nickels, we use the ratio:
\(\frac{Dimes}{nickels} =\frac {14p}{2p}\ =\ 7\)
Thus, there are 7times as many dimes as nickels in the box.
Correct Answer is C
Explanation
we set the conversion equation to find the unknown unit. Arrange the equation such that the unwanted units cancel out and the wanted unit remains.
The value 365.76 cm is close to 365 cm. Therefore, 4 yards is approximately 365 cm.
Correct Answer is A
Explanation
we use the relation 1 L=1000 mL and organize our equation in such a way that L cancels as:
Thus, 0.65 L is 650 mL.
Correct Answer is D
Explanation
in this case, we express James’ uncle’s age in terms of James’ age. From the equation:
James’ age is n
James’s uncle’s age is m=3n-13
Thus, the relation that relates James’ uncle’s age in terms of James’ age is m=3n-13.
Correct Answer is C
Explanation
We are given the equation:
6x−5=10x+15
Step 1: Move all xxx-terms to one side
Subtract 6x from both sides:
−5=10x−6x+15
Step 2: Move constants to the other side
Subtract 15 from both sides:
−5−15=4x
−20=4x
Step 3: Solve for x
Divide both sides by 4:
x=−20/4 = −5
Correct Answer is D
Explanation
To simplify this expression, we follow the order of operations as follows:
First, we start with the numerator and solve it as follows
[2(6+3*9)]
We start with multiplication in inner brackets, 3 * 9 = 27. The expression becomes
[2(6+27)]
Then, we carry out the addition of 6+27=33. Then, the expression yields
[2(33)]=2*33=66
Now, we solve for denominator, which is 6/2=3.
Thus, the expression is reduced into
The expression reduces into 22.
Correct Answer is C
Explanation
We required to find the units of finding the weight of a sheet of paper. The SI unit of mass of an object is kilogram. However, kilogram is a large quantity that cannot be used to measure smaller objects.
Thus, derived units of mass are used to find the mass of other objects. In this case, the mass of a sheet paper can be recorded in grams.
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