The distance from their house the Bensons' after 412 hours will be 18, 640 miles
<h3>What is a function?</h3>
A function is an expression or rule that explains the relationship between a dependent and independent variable.
Given the function;
d= 45 t + 100
Where;
- d is the total distance
- t is the time taken
If t = 412 hours
Substitute into the formula
d = 45 ( 412) + 100
d = 18540 + 100
d = 18, 640 miles
Thus, the distance from their house the Bensons' after 412 hours will be 18, 640 miles
Learn more about functions here:
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Answer:
a = 
b = 12
c = 
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths
.
A 30-60-90 right triangle has side lengths
.
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length
. Therefore,
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to
. This means
was multiplied by
. This means that side c is
.
A different size but not does not change shape.
Take DEBC a parralelogram
Parralel sides are DE and BC
THEREFORE,
1/2*(a+b)*h
1/2*(6+15)*h
1/2*(21)*h=0
10.5*h=0
h=-10.5