Answer:
The vertex is (3,1)
Step-by-step explanation:
Hey Jackson!
-4x + 3y = 3
y = 2x + 1
Ok so what we need to do is solving y= 2x + 1 for y.
So let's start by using the substitution method :)
Substitute 2x + 1 for y in -4x + 3y = 3
-4x+ 3y = 3
-4x + 3(2x + 1) = 3
-4x + (3)(2x) + (3)(1) = 3
-4x + 6x + 3 = 3
2x + 3 = 3
Subtract 3 on both sides
2x + 3 - 3 = 3 - 3
2x = 0
x = 0/2
x = 0
So now since we find the number for x, we gonna use it to help us find the value for y.
To find y, we need to substitute 0 for x in y = 2x + 1
y = 2x + 1
y = 2(0) + 1
y = 0 + 1
y = 1
Thus,
The answer is: y = 1 and x = 0
How to graph?
You need to go on the thing where they put the numbers. y is located on top which has the positive numbers. So when you get there, make a line that comes from the top right side all the way to the bottom left sides. Remember that y = 1 so the line must pass through 1
I am not good with explanation. So I'll leave the graph down below then you'll see what I am talking about :)
Let me know if you have any questions. As always, it is my pleasure to help students like you!
x = 0.6x + 384
subtract .6x from each side
.4x = 384
divide both sides by .4
x = 960
Answer:
Option C. 12 by 15
Step-by-step explanation:
Let the length be L
Let the width be w
Area of rectangle = L x w
Perimeter of rectangular = 2 (L + w)
From the question given,
A = 180
P = 54
180 = L x w (1)
54 = 2(L + w) (2)
From equation (2),
54 = 2(L + w)
Divide both side by the 2
54/2 = L + w
27 = L + w
L = 27 — w (3)
Substituting the value of L into equation (1), we have:
180 = L x w
180 = w(27 — w)
180 = 27w — w^2
Rearrange the expression
w^2 — 27w + 180 = 0 (4)
Solving by factorization method:
Multiply the first term (i.e w^2) with the last term (i.e 180). This gives 180w^2. Now find two factors of 180w^2, such that their sum will result to the second (i.e —27w). These factors are —12w and —15w.
Now, substitute these factors (—12w and —15w) into equation (4)
w^2 — 27w + 180 = 0
w^2 — 12w —15w + 180 = 0
w(w — 12) — 15(w — 12) =0
(w — 12) (w — 15) = 0
w = 12 or w = 15.
Substituting the value of w into equation (3)
L = 27 — w
When w = 12
L = 27 — 12 = 15
When w = 15
L = 27 — 15 = 12
Since the length is longer than the width, the length is 15 and the width is 12.
Therefore the dimensions is 12 x 15