Find the equation of a line given that you know points it passes through
Answer:
B
Step-by-step explanation:
Givens
a^2 + b^2 = c^2
a = 4x
b = x + 2
c = 3x + 4
Solution
(4x)^2 + (x + 2)^2 = (3x + 4)^3 Remove all the brackets.
16x^2 + x^2 + 4x + 4 = 9x^2 + 24x + 16 Collect like terms on the left
17x^2 + 4x + 4 = 9x^2 + 24x + 16 Subtract the terms on the right
8x^2 - 20x - 12 = 0
This factors into
(4x - 12)(2x + 1)
There are 2 answers
4x - 12 = 0
4x = 12
x = 12/4
x = 3
or
2x + 1 = 0
2x = - 1
x = - 1/2
You have to look at x = -1/2 carefully. The problem is that 4x = 4*(-1/2) = - 2 which is not possible in Euclidean Geometry.
So the only answer is x = 3
The easiest way to find slope is to do rise/run. In this case, you rise from point (0,-3), and 'run' to point (-2,-2). The slope would be -1/2 because you are 'running' to the left, which is negative.
Volume of a cylinder is given by πr^2h
Volume of the cylindrical water cooler is π x (12/2)^2 x 15 = 3.14 x 36 x 15 = 1,695.6 in^3
Volume of water in the cylindrical cooler is 1,695.6 / 2 = 847.8 in^2
Number of drinking cups that can be filled from the cooler is 847.8/20.14 = 42 cups.
