The answer is 120 miles , because it is a proportion
We know that
The square root property<span> is one method that is used to find the solutions to a quadratic equation. This method involves taking the square roots of both sides of the equation.
</span>(x – 3)² – 32 = 17-------> (x – 3)² = 17+32-----------> (x – 3)² = 49
(x – 3)² = 7²--------> <span>will take the square root of each side
</span>so
√(x – 3)²=(+-)√7²------> <span>notice the use of the </span> sign (+-), this will give us both a positive and<span> a negative root
</span>
then
x-3=7--------> x=10
x-3=-7-------> x=-4
the answer Part a) is
x=10
x=-4
Part b) Explain why the given equation has two solutions.
the answer part b) is
Because exist<span> the possibility of two roots for every square root, one positive and one negative</span>
We can solve this by drawing a triangle with three points. The first point at Fort Collins (F), the second at Cheyenne (C) and the third at Laramie (L).
The angle at F = 46.5, the angle at L = 43.6. We know the side opposite angle L = 3.2 (side FC), now we must solve for the side opposite angle F (side LC).
We can use the law of sines to solve this where:
sinA/a = sinB/b
sin43.6/ 3.2 = sin46.5/LC
LC = 3.2 (sin46.5/sin43.6)
LC = 3.37 inches
We are told 1 in = 10.6 miles, therefore:
3.37 inches x 10.6 miles/in = 36 miles from Laramie to Cheyenne.
Answer: A) -1.026x2 + 1016.402x - 162075
Step-by-step explanation: I aced the test on e2020 ;)
+5 to both sides
9x<-27
divide both sides by 9
x<-3