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SIZIF [17.4K]
3 years ago
10

Is -8 - 2(3+2n)+7n equivalent to -30 - 13n​

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Answer:

The terms are not equivalent

Step-by-step explanation:

-8 - 2(3+2n)+7n

Distribute the 2

-8 -6-4n+7n

Combine like terms

-14 +3n

That is not equal to -30 -13n

The terms are not equivalent

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Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
Natali [406]

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.

5 0
2 years ago
What is (6p+15)+(10p-9)
Yuliya22 [10]
6p+10p+15-9

16p+6 will be your final answer
6 0
3 years ago
Read 2 more answers
Solve by graphing <br><br> u=v and 6u=2v-24
Vadim26 [7]

Answer:

u=-6 \\ \\ v=-6

Step-by-step explanation:

In this exercise, we have two equations, namely:

u=v \ and \ 6u=2v-24

And we are asked to solve this problem by graphing. In this way, we can write a system of linear equations in two variables, but first of all, let's rewrite:

u=y \\ \\ v=x

Then:

\left\{ \begin{array}{c}y=x\\6y=2x-24\end{array}\right.

So here we have two lines.

The first one is:

\boxed{y=x}

This line passes through the origin and has a slope m=1

The second one is:

6y=2x-24 \\ \\ \therefore y=\frac{2x-24}{6} \\ \\ \therefore \boxed{y=\frac{1}{3}x-4}

This line has a slope m=\frac{1}{3} and cuts the y-axis at b=-4

By using graph tools, we get the graph shown below, then:

x=-6 \\ \\ y=-6 \\ \\ \\ Since \ u=y \ and \ v=x, then: \\ \\ u=-6 \\ \\ v=-6

8 0
3 years ago
Frank solved an equation and got the result x=x Sarah solved the same equation and got 12=12 Frank says that one at one of them
babymother [125]
You can get the different results for the same equation if one of the results is a variable. This is because, in this problem, x=12.
5 0
3 years ago
A student thinks that the regular pentagon in the diagram
Nadya [2.5K]

Answer:

A

Step-by-step explanation:

The student must have thought that every single arrowhead is a line of symmetry, so since there are 10 arrowheads, there must be 10 lines of symmetry. This is incorrect because if you look closely at the diagram, each line has 2 arrowheads, so the student is overcounting by a factor of 2. They should have just counted the number of lines, not arrowheads. Therefore, there must be 10/2 = 5 lines of symmetry, not 10. Hope this helps!

4 0
2 years ago
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