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Alina [70]
2 years ago
13

The volume of a rectangular prism can be found by multiplying the base area, B, times the height. If the volume of the prism is

represented by 15x2 + x + 2 and the height is x2, which expression represents B, the area of the base? 15x + + 15x + + 15 + + 15 + +
Mathematics
1 answer:
PSYCHO15rus [73]2 years ago
4 0

Answer:

Base (B) = /frac{15x² + 1 + 2}{x}

Step-by-step Explanation:

==>Given:

Dimensions of a rectangular prism are expressed as follow:

Volume (V) = 15x² + x + 2

Height (h) = x²

==>Required:

Expression of the Base area (B)

==>Solution:

Volume (V) = Base (B) × Height (h)

15x² + x + 2 = B × x²

Divide both sides by x²

\frac{15x² + x + 2}{x²} = B[tex]Base (B) = /frac{15x² + 1 + 2}{x}

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Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
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Answers:

  • Total equation:  x+y = 80
  • Legs equation:  2x+4y = 248
  • How many ducks? 36
  • How many cows? 44

====================================================

Further explanation:

  • x = number of ducks
  • y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

  • 2x = number of legs from all the ducks only
  • 4y = number of legs from all the cows only
  • 2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

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

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

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x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

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There are 44 cows.

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

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

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