Answer:
(g - h)(-4x) = 4x - 2
Step-by-step explanation:
This problem is one dealing with "composite functions." We are given the definitions of functions g(x) and h(x) and are asked to find the difference between g and h, namely, what is left if we subtact h from g. After having done that, we replace x in this composite function with the input (-4x).
The difference (g - h)(x) is as follows: g(x) - h(x) = -x + 4x - [4x + 2].
If we simplify the algebra, we get g(x) - h(x) = -x + 4x - [4x + 2] = -x - 2.
Next, substitute -4x for x in this last result. We get (g - h)(-4x) = 4x - 2.
Please note: You might want to check out your g(x) = -x + 4x. Normally we would write this as +3x.
Answer:
x = 16
Step-by-step explanation:
6x - y = 98, find x if y = -2.
Plug in y = - 2 into the equation
6x - (-2) = 98
6x + 2 = 98
Subtract 2 from both sides
6x = 96
Divide both sides by 6
x = 16
Answer:
Step-by-step explanation:
Find the mean ( average):
105 + 104 + 110 + 112 + 114 + 106 + 108 +109 = 868
Mean = 868 / 8 = 108.5
Standard deviation:
108.5 - 105 = 3.5, 3.5^2 = 12.25
108.5 - 104 = 4, 4^2 = 16
110 - 108.5 = 1.5, 1.5^2 = 2.25
112 - 108.5 = 3.5, 3.5^2 = 12.25
114 - 108.5 = 5.5, 5.5^2 = 30.25
108.5 - 106 = 2.5, 2.5^2 = 6.25
108.5 - 108 = 0.5, 0.5^2 = 0.25
109 - 108.5 = 0.5, 0.5^2 = 0.25
12.25 + 16 +2.25 + 12.25 + 30.25 +6.25+0.25+0.25 = 79.75
79.75/8 = 9.96875, SQRT(9.96875) = 3.1573
Standard Deviation = 3.1573
108.8 +/- 1.96 *(3.1573/sqrt(8) = 110.687 and 106.312
110.687 - 108.5 = 2.19
108.5 - 106.312 = 2.19
Margin of error = +/- 2.19
Answer:
Correct Answer: (8,2)
Step-by-step explanation:
<u>Dilation about the origin</u>
Most dilations in the coordinate plane use the origin, (0,0), as the center of the dilation.
In such cases, every point (x,y) dilated by a factor of k is mapped to the point (kx,ky).
The point R=(4,1) is dilated by a scale factor of 2 (k=2), thus the coordinates of its image are (2*4,2*1) = (8,2)
