Answer:
Distance between cars rounded to the nearest foot is : 1903 ft
Step-by-step explanation:
Notice that two right triangles can be used to represent the diagram of this situation. One between the car whose angle of depression is 
, and the other with the car with angle of depression 
(see attached image)
Each triangle in the attached image is depicted with a different color. and as one can see, the distance between both cars is the addition of the side "x" in one triangle, to the side "y" in the other.
Notice as well that the information known for both right-angle triangles is one acute angle, and the side opposite to it. And what one needs to find is the side adjacent to this acute angle. Then, the function to use in both triangles, is the tangent:
a) For the [orange] triangle :
b) For the [green] triangle:
Therefore the total distance between cars is:
1081.42 ft + 821.19 ft = 1902.61 ft
which to the nearest foot can be rounded as: 1903 ft
Answer:
23
Step-by-step explanation:
This equation can be derived from the question
let a represent the initial number Gus started with
{[(a x 8) - 12] / 4 } + 7 = 50
subtract 7 from both sides of the equation
[(a x 8) - 12] / 4 } = 43
Multiply both sides of the equation by 4
(a x 8) - 12] = 172
Add 12 to both sides
8a =184
Divide both sides by 8
a = 23.
Answer:
x=14
x=−2
Step-by-step explanation:
Factoring x2-12x-28
The first term is, x2 its coefficient is 1 .
The middle term is, -12x its coefficient is -12 .
The last term, "the constant", is -28
Step-1 : Multiply the coefficient of the first term by the constant 1 • -28 = -28
Step-2 : Find two factors of -28 whose sum equals the coefficient of the middle term, which is -12 .
-28 + 1 = -27
-14 + 2 = -12 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 2
x2 - 14x + 2x - 28
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-14)
Add up the last 2 terms, pulling out common factors :
2 • (x-14)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-14)
Which is the desired factorization
I would say that (d) is the correct answer because the section between x=4 and x=6 is not linear but exponential but it is still increasing. The section between x=1 and x=3 however is linear and therefore his answer is incorrect.
