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 answerB: is The AnswerC: There's y at all. It's wrongD: 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 %
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 (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.
