The tables below represent the profits earned by a merchandiser from four new consignments of t-shirts. Each consignment contain
ed t-shirts of five different sizes. If we were to plot each of the t-shirt sizes and the profit earned on each new size, we would get a different graph for each consignment. Almost all the graphs showed some association between the two variables, except one consignment, which showed no association. Which of the following consignments shows no association?
2 answers:
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There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question. I do the first two ways.
Step One
Graph the two equations.
The graph is below.
Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D
Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6
Step 4
Solve
6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x Pull the 2 terms on the left over to the right.
6x - 5x = -x^2
x = - x^2
x^2 + x = -x^2 + x^2
x^2 + x = 0 Factor
x(x + 1) = 0
That means that
x = 0
or
x + 1 = 0
x = - 1
Step 3
Find the ys
y = 6x + 6
if x = -1
y = 6(-1) + 6
y = -6 + 6
y = 0
One of the answers is
(-1,0) <<<<<<<< Answer
Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6
The other point is (0,6) answer <<<<<<<
D <<<<<< Total answer
There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question. I do the first two ways.
Step One
Graph the two equations.
The graph is below.
Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D
Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6
Step 4
Solve
6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x Pull the 2 terms on the left over to the right.
6x - 5x = -x^2
x = - x^2
x^2 + x = -x^2 + x^2
x^2 + x = 0 Factor
x(x + 1) = 0
That means that
x = 0
or
x + 1 = 0
x = - 1
Step 3
Find the ys
y = 6x + 6
if x = -1
y = 6(-1) + 6
y = -6 + 6
y = 0
One of the answers is
(-1,0) <<<<<<<< Answer
Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6
The other point is (0,6) answer <<<<<<<
D <<<<<< Total answer
Answer:
Step-by-step explanation:
The given equations are:
1st: -3x=42-16y
2nd: 14x=76-16y
Subtract the first equation from the second one:
14x--3x=76-42-16y--16y
14x+3x=34-16y+16y
17x=34
We plug in x-value into the second equation to get:
14(2)=76-16y
14x=76-32
28-76=-16y
-48=-16y
Divide both sides by -16
y=3