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Tom [10]
3 years ago
11

2 to the Third power -(30÷5) +9

Mathematics
1 answer:
OLga [1]3 years ago
8 0

Answer:

11

Step-by-step explanation:

2^3-(30/5)+9

First, you divide 30/5 because it is in parentheses and we are following this rule for order of operations:

P- parentheses

E- exponents

M- multiplication

D- division

A- addition

S- subtraction

so 30/5 = 6 and plugged in is:

2^3-(6)+9

Next, we do exponents:

2^3 = 2x2x2 = 8

plugged back in:

8-(6)+9

Now, we do the math from left to right so:

8-6=2

2+9=11

11 is your answer

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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

-2x = -72

x = -72/(-2)

x = 36

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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Answer:

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