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topjm [15]
3 years ago
7

Susie has 8/9 cup of ice cream. How many 1/4 cup servings can she make?

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
5 0

Answer:

8 cups of ice cream

Step-by-step explanation:

1/4×8=8 cups

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Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha
Pavel [41]

Answer:

(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14.

(Expand to obtain an equivalent expression for the sphere: x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0)

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}.

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}.

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between \left(x_1, \, y_1, \, z_1\right) and \left(x_2, \, y_2, \, z_2\right) would be:

\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right).

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}.

The equation for a sphere of radius r and center \left(x_0,\, y_0,\, z_0\right) would be:

\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2.

In this case, the equation would be:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2.

Simplify to obtain:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56.

Expand the squares and simplify to obtain:

x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0.

8 0
3 years ago
GIVING BRAINLIEST HELP NEEDED
xenn [34]

The volume of the prism given its dimensions is equal to 160 cubic units.

<h3>What is the volume of the prism?</h3>

The given prism is made up of two prisms. The volume of the prism is the volume of the two shapes.

  • One of the prisms have the dimensions: 4 x 4 x 5.

Volume = 80

  • The other prism has the dimensions: 8 x 2 x 5.

Volume = 80

Volume of the prism = 80 x 2 = 160 cubic units.

To learn more about rectangular prisms, please check: brainly.com/question/8890358

8 0
2 years ago
Which equation matches the graph?
Iteru [2.4K]

Answer:

D

Step-by-step explanation:

intercept is -4 and slope is rise over run which is 3/1 = 3

put into slope intercept form to achieve answer D

7 0
3 years ago
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Triangle ABC is reflected to form Triangle A’B’C
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Answer:

I believe it is reflection across the x axis.

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Callie

P..S Are you in k12

Step-by-step explanation:

4 0
3 years ago
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What is the Greatest Common Factor of x^4 and x^3?
hammer [34]
Judging by the question I noticed that the two both share x^3 in common. You can divide x^4 by x^3 and get x as a result, and x^3 can still divide into itself.

Thus your answer should be C, x^3
5 0
3 years ago
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