Answer:
r = 20
Step-by-step explanation:
-4 = r/20 - 5
-4 + 5 = r/20 - 5 + 5
1 = r/20
1 * 20 = r/20 * 20
r = 20
Integers are closed under subtraction.
1. If the line that we are searching for is perpendicular to the line y = -4x, this means that the gradient of our line and the gradient of the perpendicular line will multiply to give -1. Thus if we call the gradient of our line m, then:
m*(-4) = -1
-4m = -1
m = 1/4
2. Since we know that m = 1/4 and we have a point (2,6) on our line, we can use the formula y - y1 = m(x - x1) to find the equation of our line, where (x1, y1) is the coordinates of a point on the line. Thus:
y - y1 = m(x - x1)
y - 6 = (1/4)(x - 2)
y - 6 = (1/4)x - 2/4 (Expand (1/4)(x - 2))
y = (1/4)x - 1/2 + 6 (Simplify 2/4 and add 6 to each side)
y = (1/4)x + 11/2 (Evaluate -1/2 + 6)
Slope-intercept form is given by y = mx + c. As our equation is already in this form, there is nothing more to do. Thus, the answer is y = (1/4)x + 11/2
Answer:
- difference: -4 cubic inches
- % change: -10%
Step-by-step explanation:
The difference between the new volume and the original volume is ...
(new volume) - (original volume) = (36 in³) - (40 in³) = -4 in²
__
The percentage change is figured with respect to the original volume:
% change = (difference)/(original volume) × 100% = (-4 in³)/(40 in³) × 100%
= -1/10 × 100% = -10%
