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For the first question, the answer is B. I feel like a picture will help explain my answer the most.
178 is equal to the area of the pen minus the area of the doghouse. For the area of the pen, we turn to the problem which said that the pen is three feet wider than it is long, making the width x+3 and the length x since the problem said that x represent the length of the pen. Now, you can find the area of the pen by multiplying x+3 by x, giving us a answer of x^2+3x. Lastly, subtract by y, giving us an equation of 178=x^2+3x-y. Looking at the answer choice, I only see one answer that wrote that, answer choice B, so I don't even have to confirm the second part of the answer (the one with positive/negative 6 equals to 4x minus 3y).

For the second question the answer is C since .15% is equal to 0.0015 and .37% is equal to 0.0037. Since it is decaying, it must be negative, so the answer is C.
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jcherry99

Problem One

If you start with the perimeter equation, you find that the perimeter of the dog house (y) is one third the size of the pen. Or the perimeter of the pen is 3 times the doghouse.

The perimeter of the pen is

2(x + 3 + x) = 3y           combine terms on the left

2(2x + 3) = 3y               remove the brackets

4x + 6 = 3y                    Subtract 3y and 6 from both sides

4x - 3y = - 6                   AB and C each have this answer. D does not D is gone.

Now we look at the area parameters

x(x + 3) - y = 178

  • A: y should be minus, not plus: not the answer
  • B: is The Answer
  • C: There's y at all. It's wrong
  • D: 3x is added not subtracted.

Problem Two

There are two things you need to interpret in this question.

  • The number of zeros in 0.15% and 0.37%
  • Whether the %s are plus or minus

Check the second one first. You need to know what happens to e when it's power is plus or minus. The easiest way to determine that is just to try it. Suppose you have y = 400e^-2 and y = 400e^2. Which condition will make y go down (which is what we want for your question)? y = 400*e-2 = 54.2 This is definitely going down. What happens to the other condition? y = 2955 which is definitely going up. This is a decay question. The answer must go DOWN.  A and D are both wrong. Their answers are going up.

So now we are left with what to do about 0.15% and 0.37%. To get these percents in decimals they should be written as 0.15/100 = 0.0015 and 0.0037

The answer needs 2 zeros for the %

Answer: C

In 232 years, they will have the same mass.

Problem 3

Of all the 3 problems this one is the worst because you have to set up everything before you can really answer the question. And some of it is not clear.

Start with the cost factor. She can only spend 500 dollars and she is getting each tree for 5.25. How many trees can she buy?

500 / 5.25 = 95.24 trees. So the inequality is 5.25*y ≤ 95

The number of tomatoes she gets from these plants is 25 * 95 = 2375

That means that the rest of the tomatoes must come from last year's tomatoes. 5000 - 2375 = 2625

How many plants does she need? Each plant produces 35 tomatoes.

2625 / 35 = 75

What is the total number of plants? 75 + 95 = 170

Now comes the ugly part of the problem

The number of plants in each Column = C

The number of plants in each Row = R

These are related by R = C + 5

R*C = 170

R*(R - 5) = 170

R^2 - 5R - 170 = 0

So R = 15.8

or R = - 10.8. Of course this won't work.

So what are the choices.

It looks to me like A is the answer. You have 1 viable solution. I have never seen a linear Algebra problem until I started contributing to Brainly (so we all learn something being here). I know that you can juggle the numbers around to get an answer that is more refined, but I'm not able to do it. A should still be right.


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