Answer:
➩ 
Step-by-step explanation:
➨ We can also solve by completing both squares, however. Since we can pull out the square root.
➩ Define of Absolute Value/Square Root
➩ 
Thus, our new equation is ➩ 
To solve an absolute-value equation, let there be two conditions.
➨ Where x ≥ 0
Move x to another side
➨ Where x < 0
Let's plug in each coordinate and see what we get:
(2, 0, 0)
-> 2A + 0 + 0 = D
-> 2A = D
-> A = D/2
(0, 6, 0)
-> 0 + 6B + 0 = D
-> 6B = D
-> B = D/6
(0, 0, 5)
-> 0 + 0 + 5C = D
-> 5C = D
-> C = D/5
plugging this back into the equation:
(D/2)x + (D/6)y + (D/5)z = D [then divide through by D]
(1/2)x + (1/6)y + (1/5)z = 1
and since we have to have integer coefficients,
multiply through by 30
so we get
15x + 5y + 6z = 30
Second question
<span>Take a look at the bottom-left point in the picture.
If you move three points in the y-direction, you'll reach to the point A.
If you instead move up 4 points (or in the z-direction), you reach D.
And finally, if you walk back to point F from point E, you'll have moved back 4 points in the x direction. </span>
<span>This gives us our measurements, or dimensions: 3 x 4 x 4.
If this were a rectangular prism, the dimensions would just be each of them multiplied.
But since it's triangular, you need to divide it by two. That gives you a total volume of
(3x4x4)/2 = 24.</span>
Answer:
C.
x y
2 -24
5 -15
Step-by-step explanation:
We need to find the slope for each table
A.
x y
2 16
5 10
m = (y2-y1)/(x2-x1) = (10-16)/(5-2) = -6/3 = -2
B.
x y
2 14
6 12
m = (y2-y1)/(x2-x1) = (12-14)/(6-2) = -2/4 = -1/2
C.
x y
2 -24
5 -15
m = (y2-y1)/(x2-x1) = (-15--24)/(5-2) = (-15+24)/3 = 3
D.
x y
2 -12
6 -16
m = (y2-y1)/(x2-x1) = (-12--16)/(6-2) = (-12+16)/4 = 1
E.
x y
2 -19
6 -17
m = (y2-y1)/(x2-x1) = (-17--19)/(6-2) = (-17+19)/4 = 1
The greatest unit rate is the largest slope
8π²
2πr² is the equation to find the base, but the answer doesn't ask for the exact awsner, rather the expanded version. 4 is the radius, radius x 2 is 8.
8π²
