Answer:
The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64.
Step-by-step explanation:
Let L represents the Length of the cube before it's dilated.
Volume, V1 = Length * Length * Length
Volume, V1 = L * L * L
Volume, V1 = L³
When the cube is dilated by a factor of 4.
The new Length becomes 4L.
The new volume is calculated as thus.
New Volume, V2 = 4L * 4L * 4L
New Volume, V2 = 64L³
Dividing the new volume by the old volume gives the increment factor.
Factor = New Volume ÷ Old Volume
Factor = V2/V1
Factor = 64L³/L³
Factor = 64.
Hence, when the sides of the cube is dilated by 4, the volume increases by a factor of 64.
Filling the gap of the given sentence;
"The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64"
Answer:
C
Step-by-step explanation:
NQP is a triangle. It has 3 angles given.
We know
<em>sum of 3 angles in a triangle is 180 degrees</em>
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We are Given:
∠N = 2x
∠Q = 2x + 2
∠P = 134
THus, we can write and solve for x first:
∠N + ∠Q + ∠P = 180
2x + 2x + 2 + 134 = 180
4x + 136 = 180
4x = 180 - 136
4x = 44
x = 44/4
x = 11
Now, measure of ∠NQP is 2x + 2, so substituting the value of "x", we have:
2x + 2 = 2(11) + 2 = 22 + 2 = 24 degrees
So,
∠NQP = 24°
Correct answer is C
Answer:
true
Step-by-step explanation:
3/18=1/6
9/27=1/3
no one of these fractions is equivalent to 3/18
Answer: 30
Step-by-step explanation:
rs + 2s when r = 8 and s = 3
8(3) + 2(3)
8 * 3 = 24
2 * 3 = 6
24 + 6 = 30
