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3 years ago

Which statements about this prism partially packed with unit cubes are true? Check all that apply.

Mathematics

2 answers:

Gre4nikov [31]3 years ago

8 0

Answer:

We have that the dimensions are:

height = 3

length = 3

width = 4

so in each layer of cubes, we have 3*4 = 12 cubes, and we have 3 layers.

1) The middle layer of cubes is missing 7 unit cubes.

In this layer, we have 5 cubes, and in each layer, we should have 12.

12 - 5 = 7

so this statement is true.

2) There are 9 unit cubes stacked in the prism.

Only in the bottom layer, we have 9 cubes, 5 in the second and 2 in the third one, a total of 16 cubes. this statement is false.

3) There are 7 unit cubes that are hidden from view inside the prism.

We have 16 cubes inside, and we can see 9 of them, so the ones we can not see are:

16 - 9 = 7

This statement is true

4) The volume of the prism can be found by because there are 12 cubes in each layer and there are 3 layers of cubes.

This is true, the volume of the prism is equal to 3*12 = 36 cubes

5) The volume of the prism can be found by doubling the number of cubes in the prism because it is half full.

inside the prism, we have 16 cubes, and the full prism would have 36 cubes, so it is not half full, this statement is false.

AVprozaik [17]3 years ago

4 0

Answer:

The middle layer of cubes is missing 7 unit cubes

There are 7 unit cubes that are hidden from view inside the prism

The volume of the prism can be found by because there are 12 cubes in each layer and there are 3 layers of cubes.

Step-by-step explanation:

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Circle C has a center at (-2,10) and contains the point P(10,5). Which equation represents circle C?

Rina8888 [55]

Answer:

The equation that represents circle C is $(x+2)^2+(y-10)^2=169$ .

Step-by-step explanation:

A circle is the set of all points in the plane which maintains a fixed finite distance r from a fixed point O = (a, b). Here O is called the center, and r is called the radius of that circle.

The standard equation for a circle with center (a, b) and radius r is

$(x-a)^2+(y-b)^2=r^2$

We are told that the center of this circle is (-2, 10), so

$(x+2)^2+(y-10)^2=r^2$

We are also told that the circle contains the point (10, 5), so we will use that information to find the radius r.

$(10+2)^2+(5-10)^2=r^2\\\\r^2=\left(10+2\right)^2+\left(5-10\right)^2\\\\r^2=12^2+5^2\\\\r^2=144+25\\\\r^2=169\\\\r=\sqrt{169}=13$

Therefore, the equation that represents circle C is

$(x+2)^2+(y-10)^2=13^2\\\\(x+2)^2+(y-10)^2=169$

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