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LUCKY_DIMON [66]
3 years ago
11

-4x^2 (3x^2 + 25x - 7)

Mathematics
1 answer:
disa [49]3 years ago
6 0
In the instructions for this problem I am told to distribute -4x^2. Why?
the order of operations is the order in which to simlify
if you look inside the parenthases, all like terms have been combined so the inside of parenthasees have already been simlified
expanding the exponents won't make it any easier so we move to distriubiting (or mulitplying)
so then the next step is mulitply -4x^2 by the trinomial


<span>In the order of operations you must do problems inside parentheses first. Why does multiplying monomials by polynomials change this? </span>multiplying monomails by polynomials does not change this

<span>Would the answer come out different if I did the work according to the order of operations?
no because distributing first is what you should do if you follow order of operations
</span>



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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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  • Total equation:  x+y = 80
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====================================================

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...

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  • 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

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x = -72/(-2)

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There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

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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