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lesya [120]
3 years ago
14

The hypotenuse of a right triangle is 10 ft long. the shorter leg is 2ft shorter than the longer leg. find the side lengths of t

he triangle
Mathematics
1 answer:
Gwar [14]3 years ago
5 0
Since we have two possible pieces of information and 2 items to solve for, we know this is a system of equations.
Our first piece of information is that our shorter leg (s) is 2 feet shorter than our longer leg (l). This can be written as s=l-2.
Our second piece of information is that using the Pythagorean theorem that our shorter leg squared plus our longer leg squared is equal to our hypotenuse squared. This can be represented by s^2+l^2=10^2. Now we can solve.
We have already isolated for s in our first equation, so we can substitute l-2 in.
(l-2)^2+l^2=10^2
l-2+l=10
2l-2=10
2l=12
l=6
Now we can substitute in for s in our simpler equation
s=6-2
s=4
We now know that using our knowledge of systems of equations, the side lengths of this right angle triangle are 6 and 4.
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the numbers of girls in the choir is 4 times the number of boys in the choir .the total number of students is 60..how many girls
Inessa05 [86]
First, make up some variables to represent the number of Girls and Boys in the choir.  

B = number of boys
G = number of girls

You know that there are 4 times as many girls in the choir as boys.  Therefore, the equation you can write is:
\frac{B}{G} =  \frac{1}{4}

If you cross-multiply, then you get the simplified equation:
G = 4B

Intuitively this makes sense since if you multiplied the number of boys in the class by 4, that would be equal to the number of girls you have.

Now, we know that the total class size is 60. So girls plus boys equals 60:
G+B = 60

To solve the equation, replace the G in this equation with the replacement you found before, 4B.
G + B = 60 -->
4B + B = 60 -->
5B = 60 -->
B = 12

However, you are trying to find the number of girls, so plug the answer back into your equation.
G + B = 60 -->
G + 12 = 60 -->
G + 12 -12 = 60 - 12 -->
G = 48

The number of girls you have is 48.

6 0
3 years ago
So would the answer be 5 eighths?
adelina 88 [10]
No, the answer is 3/8 because if 3/4 of the cars are Sudan's, and half of that three quarters are white, you need to divide three quarters into two to get the answer. I did this question by using the equivalent fraction 6/8 and dividing both numbers into two.
3 0
2 years ago
What is the midpoint between 3.99 and 4
asambeis [7]

Answer:  

3.995

Step-by-step explanation:

A midpoint is defined as a point that is exactly in the middle between two other points. The midpoint between two numbers is the number exactly in the middle of the two numbers. Calculating the midpoint is the same thing as calculating the average of two numbers. Therefore, you can calculate the midpoint between any two numbers by adding them together and dividing by two.

6 0
2 years ago
The necklace charm shown has two parts, each shaped like a trapezoid with identical dimensions.
Daniel [21]
What is the size of trapezoid?
3 0
3 years ago
Which of the following numbers is a factor of 78?
Aloiza [94]

Step-by-step explanation:

78 = 2 * 39 = 2 * 3 * 13.

Since 6 = 2 * 3 and its factors can be found in 78,

Hence the answer is 6. (C)

4 0
3 years ago
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