Mathematics, 18.01.2020 01:31 seraphina05

Which statements are true about a rectangular pyramid with a height of 15 inches and a base with the dimensions of 12 inches
and 9 inches? select three options.

Answers: 3

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Answers

Answer from: genyjoannerubiera

Question:

Which statements are true about a rectangular pyramid with a height of 15 inches and a base with the dimensions of 12 inches and 9 inches? Check all that apply.

1.The area of the base of the pyramid, B, is 36 in3

2.The area of the base of the pyramid, B, is 108 in3

3.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid.

4.The volume of this pyramid is 540in 3

5.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid

The statements that are true about a rectangular pyramid

2.The area of the base of the pyramid, B, is 108 in3

4.The volume of this pyramid is 540in 3

5.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid.

Step-by-step explanation:

The area of the base of the pyramid, B

The area of the base of the pyramid is equal to

$B=(12)(9)=108\ in^{2}$ ----------------------(1)

The volume of the pyramid

Substituting the values

$V=\frac{1}{3}(108)(15)=540\ in^{3}$ ------------------------(2)

The volume of the rectangular prism

V=BH

Substituting the values

$V=(108)(15)=1,620\ in^{3}$ ------------------(3)

Now,

(1) From(1) ,The area of the base of the pyramid, B, is 36 in^3 is false, because we have found the volume as 108 in^3

(2).From (2),The area of the base of the pyramid, B, is 108 in^3 is true

(3) From (2) and (3) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid is false

because $540 in^3 \neq 1620 in^3$

4. From(2) The volume of this pyramid is 540in 3 is true

5. From(2) and (3) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid is true

$540 \times 3 = 1620$

Answer from: Quest

for this case we must apply distributive property to the following expression:

$-2 (2.1x + 3y-0.8)$

the distributive property states that:

$(a + b) (c + d) = ac + ad + bc + bd$

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

$-4.2x-6y + 1.6$

Answer from: Quest

1. supplementary angles

2. acd and bcd

step-by-step explanation:

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