Answer: y = -1, y = 6 (choice D)
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Work Shown:
y - (6/y) = 5
y*(y - (6/y)) = y*5 <<--- see note 1 below
y^2 - 6 = 5y
y^2 - 5y - 6 = 0
(y+1)(y-6) = 0 <<--- see note 2 below
y+1 = 0 or y-6 = 0
y = -1 or y = 6 which are the two answers
note 1: I multiplied both sides by y to clear out the fraction (the LCD is y)
note 2: I factored the left side by asking myself "what two numbers multiply to -6 and add to +5?" the answer to that question is +1 and -6 which helps lead to the factorization. An alternative route instead factoring is to use the quadratic formula
2 x B + 4 = -8
-4 -4
2 x B = -12
divide by 2 on both sides
B = -6
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:
1.27388535028
Step-by-step explanation:
Simply using the formulas
They weigh the same --- One pound.
One pound of feathers = One pound of iron
