Answer:
24
Step-by-step explanation:
To calculate the output substitute x = - 3 into f(x), that is
f(- 3) = (- 3)² - 4(- 3) + 3 = 9 + 12 + 3 = 24 ← output
Answer:
the guy wire is 7.211 ft long
Step-by-step explanation:
Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.
Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:
![Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft](https://tex.z-dn.net/?f=Hypotenuse%3D%5Csqrt%7Bside1%5E2%20%2Bside2%5E2%7D%20%5C%5CHypotenuse%3D%20%5Csqrt%7B6%5E2%2B4%5E2%7D%5C%5CHypotenuse%3D%5Csqrt%7B36%2B16%7D%20%5C%5CHypotenuse%3D%5Csqrt%7B52%7D%20%5C%5CHypotenuse%3D7.2111%5C%2C%20ft)
Answer:
m∠ABD = 126°
Step-by-step explanation:
if both angles make a linear pair then their sum equals to 180°
you can solve for x
m∠ABD + m∠CBD = 180
6x-12 + x+31= 180
7x + 19 = 180
7x = 161
x=23; now solve for
m∠ABD = 6x - 12 = 6(23) - 12 = 126°