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Fed [463]
3 years ago
8

Plz do because I have been struggling with this homework

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
3 0

Answer:

  1332 m³

Step-by-step explanation:

The volume of a prism is the product of its length (12 m) and the area of its base. This base is a ∩ - shape whose overall dimensions are 11 m high and 15 m wide. The "tunnel" is shown as 6 m high, but we need to calculate how wide it is.

The two "legs" are each 3 m wide, so total 6 m in width. Then the width of the "tunnel" is the difference between that and the overall width of 15 m:

  tunnel width = 15 m -6 m = 9 m

__

One way to compute the base area is to subtract the tunnel area from the overall area:

  base area = B = (15 m)(11 m) -(9 m)(6 m) = 165 m² -54 m² = 111 m²

The volume of the prism is ...

  V = Bl = (111 m²)(12 m) = 1332 m³

The volume of the prism is 1332 m³.

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Problem 13

10p+10q factors to 10(p+q). If we apply the distributive property, we can distribute the 10 to each term inside (p and q) to get

10(p+q) = (10 times p)+(10 times q) = 10*p + 10*q = 10p+10q

so we get the original expression again. Here 10 is the GCF of the two terms.

--------------------------------------------------------------

Plug p = 1 and q = 2 into the factored form

10*(p+q) = 10*(1+2) = 10*(3) = 30

As a check, let's plug those p,q values into the original expression

10*p+10*q = 10*1+10*2 = 10+20 = 30

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