Answer:
<u>The correct answer is Hypotenuse = 3.61 units (Rounding to two decimal places)</u>
Step-by-step explanation:
We can use the Pythagoras theorem formula for solving this questions. It can be expressed symbolically as follows:
Hypotenuse² = First leg² + Second leg²
"The amount of units comprising the hypotenuse squared is equal to the addition of the measure of both legs squared."
Hypotenuse² = First leg² + Second leg²
Hypotenuse = √(First leg² + Second leg²
)
Replacing with the real values:
Hypotenuse = √(3² + 2²
)
Hypotenuse = √(9 + 4
)
Hypotenuse = √13
Hypotenuse = 3.60555
<u>Hypotenuse = 3.61 units (Rounding to two decimal places)</u>
Answer: For the sum of 130
First: $90
Second: $40
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=130 since their sum is 130.
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=130, rearrange to b=130-a and substitute into 15a+5b=1550.
15a + 5 (130-a)=1550
15a+650-5a=1550
10a+650-650=1550-650
10a=900
a=$90 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
90+b=130
90-90+b=130-90
b= $40 was charged by the second mechanic
You have to derive for a multiplication in both terms:
=e^x+xe^x-(e^x-1 + (x-2)e^x-1) now apply distributive property in the last term:
=e^x+xe^x+e^x-1-xe^x-1 now replace each x by 0 (x=0)
=1 + 0 + e^-1 + 0 = 1+ e^-1 = 1.3679
