44 - 1 + 7q = 106
43 + 7q = 106
7q = 63
q = 9
Answer:
(-4, 5)
Step-by-step explanation:
The problem is a system of equations where you have two variables and can use the method of eliminate (eliminating one of the variables) to solve. In this case, you will need to multiply one of the fractions by a factor to eliminate a variable. It seems easiest to multiply the first equation by a factor of -5:
-5(x - 3y) = -24 (distribute) -5x + 15y = 120
Add the equations:
-5x + 15y = 120
<u>+5x + 8y = -5</u>
23y = 115 (divide by 23)
y = 5
Solve for 'x': x - 3(5) = -24 or x - 15 = 24 (add 15) x = -4
Ordered pair: (-4, 5)
54 shots. 9 out of 12 means she is making 75% of her shots. 75% of 72 is 54.
Answer:
We conclude that the constant of proportionality between the number of shirts and how much they cost is:
k = 8
Hence, option 'D' is correct.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get
y ∝ x
y = kx
k = y/x
where k is called the constant of proportionality
Given the points
For (10, 80)
substituting y = 80 and x = 10 in the equation
k = y/x
k = 80/10 = 8
For (20, 160)
k = y/x
k = 160/20 = 8
For (50, 400)
k = y/x
k = 400/50 = 8
It is clear that the value of k is the same for all the points.
Thus, the value of k = 8
Therefore, we conclude that the constant of proportionality between the number of shirts and how much they cost is:
k = 8
Hence, option 'D' is correct.
