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poizon [28]
3 years ago
5

A right rectangular prism is packet with cubes of side length 1/3 inch. If the prism is packed with 6 cubes along the leght, 4 c

ubes along the width and 8 cubes along the hight what is the volume of the prism
Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0

Answer:

7.11 inches^3

Step-by-step explanation:

Firstly calculate the number of the cubes;

6 × 4 × 8 = 192 cubes

;Therefore there are 192 cubes of 1/3inch side length

;Then for the volume of the prism

;Volume of one cube = (1/3)^3 = 1/27inches^3

;Then multiply the volume of one cube by the number of cubes in the prism

(1/27) × 192 = 7.11 inches^3

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Help me please, this is really hard.
Snowcat [4.5K]

The points of new triangle is (3,-2), (6,-3) and (2,-5).

<u>Step-by-step explanation:</u>

The given points in the triangle A(-3,7), B(9,3) and C(-7,-5).

The scale factor is \frac{1}{4} and centered at point (5,-5).

The formula to dilate a point that is not centered on a origin is given by,

D(x,y)=(h+t(x-h),k+t(y-t)).

where (h,k) is the center point.

To find A',

D(-3,7)=(5+\frac{1}{4}(-3-5),-5+\frac{1}{4}(7+5)).

D(-3,7)=(5+\frac{1}{4}(-8),-5+\frac{1}{4}(12)).

D(-3,7)=(5-2, -5+3).

D(-3,7)=(3,-2).

To find B',

D(9,3)=(5+\frac{1}{4}(9-5),-5+\frac{1}{4}(3+5)).

D(9,3)=(5+\frac{1}{4}(4),-5+\frac{1}{4}(8)).

D(9,3) = (5+1,-5+2).

D(9.3)=(6,-3).

To find C',

D(-7,-5)=(5+\frac{1}{4}(-7-5),-5+\frac{1}{4}(-5+5)).

D(-7,-5)=(5+\frac{1}{4}(-12),-5+\frac{1}{4}(0)).

D(-7,-5)=(5-3,-5+0).

D(-7,-5)=(2,-5).

∴ The points of new triangle is (3,-2), (6,-3) and (2,-5).

8 0
3 years ago
The weight of animal hearts can range widely. An African bull elephant's heart can weigh as much as 61.73 pounds. A blue whale's
Bogdan [553]
The difference between a blue whale's heart and a African bull elephant heart is 2963.27 lbs. it will take 49 African bull elephant's heart to equal one blue whale's heart.
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3 years ago
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If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fo
amm1812

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

(f \circ g)(x) = f(g(x))

In this case:

f(x) = 4x^2 - 8x - 20

g(x) = 2x + a

So

(f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when x = 0, f(g(x)) = 25. So

4a^2 - 8a - 20 = 25

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Solving a quadratic equation, by Bhaskara:

\Delta = (-8)^2 - 4(4)(-45) = 784

x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5

x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5

The possible values are a = -2.5 or a = 4.5.

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Mandarinka [93]

Answer:

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Step-by-step explanation:

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3 years ago
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