Let g = graph paper and r = ruler
1st equation: 5g + 30r = 40
2nd equation: 12g + 20r = 44
Multiply the 2nd equation by -1.5 to cancel out the r's
2nd equation: 12g + 20r = 44 x -1.5 = -18g - 30r = -66
Now add the 1st equation to that:
-18g + 5g = -13g
30r -30r = 0
40 -66 = -26
The new equation becomes -13g = -26
Divide both sides by -13
g = -26 / -13
g = 2
This means each pack of graph paper cost $2.
Now replace g with 2 in the first equation to solve for the cost of a rule:
5(2) + 30r = 40
Simplify:
10 + 30r = 40
Subtract 10 from each side:
30r = 30
Divide both sides by 30:
r = 30 / 30
r = 1
Each rule cost $1.
Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
-16 + 5n = -7(-6 + 8n) + 3 Given
-16 + 5n = 42 - 56n + 3 Distribute
-16 + 5n = 45 - 56n Collect like terms
61n = 61 Add 56n to the left side and add 16 to the right side
n = 1 Divide 61 from both sides
The answer is n = 1. Remember that when you have a number beside two or more numbers in parentheses, you have to distribute, or multiply the number outside the parentheses by each number inside the parentheses.
Hope this helps!
Answer:
A
Step-by-step explanation:
x | y
0 0
1 4
2 n -> 8
3 12
I've rewritten the x-y table so it's easier to read.
Take a point: 2,8. 2 times 4 is 8.
Take another point: 3,12. 3 times 4 is 12.
Ooh, looks like we have a pattern! After testing all the points (which you should always do in case there's an outlier) each x is multiplied by 4 to get the y. The formula for this is <u>y=kx,</u> where k is the constant of proportionality. So the equation is <u>y=4x.</u> This means x and y are directly proportional.
(They would be inversely proportional if in the form y=k/x; jointly proportional if they were in the form z=kxy, and nonproportional if there was no relationship at all.)
