Enter the value of x that makes the equation 5+3x-37=6x+23-8x
2 answers:
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Answer: Choice B. sqrt(2)
Draw out a right triangle in quadrant IV as you see in the attached image below. The horizontal and vertical legs are both 1 unit long. To ensure that the signs are properly set up, I am making the vertical leg BC have a label "-1" to mean this is below the x axis. Note how
tan(theta) = opposite/adjacent = BC/AB = -1/1 = -1
Use the pythagorean theorem to find that the hypotenuse AC is sqrt(2) units long
a^2 + b^2 = c^2
(1)^2 + (1)^2 = c^2
2 = c^2
c^2 = 2
c = sqrt(2)
The secant of theta is the ratio of the hypotenuse over the adjacent side, so we end up with
sec(theta) = hypotenuse/adjacent
sec(theta) = AC/AB
sec(theta) = sqrt(2)/1
sec(theta) = sqrt(2) which is why choice B is the answer
Answer:
Theresa's height is 60 inches
Step-by-step explanation:
The given parameters are;
The height of Paul = The height of Steve
Paul's height = times Theresa's height - 16 inches
Steve's height = times Theresa's height - 6 inches
Let 'T' represents Theresa's height, we have;
Paul's height = ×T - 16
Steve's height = ×T - 6
Paul's height = Steve's height
Therefore;
×T - 16 =
×T - 6
×T -
×T = 10
×T -
×T = 10
×T = 10
T = 10 × 6 = 60
Theresa's height, T = 60 inches