Answer:
First: $65
Second: $115
Step-by-step explanation:
We write equations for each part of this situation.
<u>The Total Charge</u>
Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.
<u>The Sum of the Rates</u>
Since the first's rate is a and the second is b, we can write a+b=180 since their sum is 180.
We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.
For a+b=180, rearrange to b=180-a and substitute into 15a+5b=1550.
15a + 5 (180-a)=1550
15a+900-5a=1550
10a+900-900=1550-900
10a=650
a=$65 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
65+b=180
65-65+b=180-65
b= $115 was charged by the second mechanic
Write the equation in POINT-SLOPE FORM of the line that passes throught (5,9) and has a slope of -7.
I hope this helps you
42=4n-7n-7. (-9)
42=-3n+63
-3n=-21
n=7
Answer:
![\frac{4\sqrt{3} }3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B3%7D%20%7D3%7D)
Step-by-step explanation:
Since it is an equilaterla triangle, we can see the side opposite to that of side length 4 is 60 degrees. Since the other angle is a right angle (90 degrees), we can find that the other side is 30 degrees (the degrees add up to 180). We can also see that this is a 30-60-90. We can see that the side x, through the identity (you can find 30-60-90 identity online), we see that the side x is
. However, it is also asking us to simplify this, so we multiply the top and bottom by
and get ![\frac{4}{\sqrt{3} } = \frac{4\sqrt{3} }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%5Csqrt%7B3%7D%20%7D%20%3D%20%5Cfrac%7B4%5Csqrt%7B3%7D%20%7D%7B3%7D)