Dilation means maximization/minimization of the shape without any deflection nor rotation.
Therefore, the dilated line D'E' will be parallel to the original line DE
Choice: A
Remark
The easiest way to do this is to find the radius of both spheres . That gives you the scale factor. The answer to the next two parts might surprise you.
Step one
Find the volume of the small sphere.
V = 4/3 pi r^3
V = 250 yards^3
pi = 3.14
r = ???
Sub and solve
250 = 4/3 pi * r^3 Multiply both sides by 3/4 to get rid of the fraction on the right.
250 * 3/4 = pi * r^3
187.5 = pi r^3 Divide by pi
187.5 / pi = r^3
59.71 = r^3 Take the cube root of both sides.
cube root (59.71) = cube root(r^3)
r = 3.91
Step 2
find the radius of the large sphere.
I'm just going to give you the answer. Follow the above steps to confirm it.
V = 686 cubic yards
pi = 3.14
r = ??
r = cube root (514.5/3.14)
r = 5.472
Step 3
Find the ratio
r_large/r_small = 5.472/3.91 = 1.3995
I'm going to leave the Area calculations to you
The area ratios should come to 1.96 (about)
The volume ratios should come to 1:2.74
Answer:
Step-by-step explanation:
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Good evening ,
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394 384÷2
=197 192
197 192÷2
=98 596
98 596÷2
=49 298
49 298÷2
=24 649
24 649÷157
=157
157÷157
=1
Then 394 384 = 2⁴ × 157² = 4² × 157² = 628²
So 394 384 = 628²
So √(394 384) = 628
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:)
Answer:
D. 80
Step-by-step explanation:
Given:
f(x) = 5x - 4,
g(x) = x² - 1
Required:
(g o f)(-1)
SOLUTION:
(g o f)(-1) = g(f(-1))
Plug in -1 for x into the function, f(x) = 5x - 4:
g(f(-1)) = g(5(-1) - 4)
= g(-5 - 4)
= g(-9)
Plug in -9 for x in the function, g(x) = x² - 1
g(-9) = (-9)² - 1
= 81 - 1
= 80.
Therefore, (g o f)(-1) = g(f(-1)) = 80
D. 80 is the correct answer.
Let Y be amount of times beat
let X be amount of time in seconds
the slope intercept form is y=mx+b
fill in the variables: y=30x
The correct answer is y=30x