The vertices for the dilated image can be found by multiplying the coordinates of the original image by the scale factor. In this problem, the scale factor is 1/3.
(0,0) ⇒ 0 x 1/3 = 0 ; 0 x 1/3 = 0 ⇒ (0,0)
(27,0) ⇒ 27 x 1/3 = 9 ; 0 x 1/3 = 0 ⇒ (9,0)
(36,30) ⇒36 x 1/3 = 12 ; 30 x 1/3 = 10 ⇒ (12,10)
(9,30) ⇒ 9 x 1/3 = 3 ; 30 x 1/3 = 10 ⇒ (3,10)
Answer is choice D. (3,10)
Answer:
Step-by-step explanation:
Let the number of cars be x and buses be y
<u>Then we have below inequalities as per given:</u>
- 5x + 32y ≤ 1310
- x + y ≤ 135
It is easy to notice that cars occupy 6 times less area than buses but cost of parking is 3 times less. So we would need maximum number of cars and minimum number of buses to maximize income
<u>Let's assume there are 135 cars and buses, then from the second inequality:</u>
<u>Substitute it in the first one:</u>
- 5(135 - y) + 32y ≤ 1310
- 675 - 5y + 32y ≤ 1310
- 27y ≤ 1310 - 675
- 27y ≤ 635
- y ≤ 635/27
- y≤ 23.5
The greatest number of buses is 23
Option D. 23 is correct
Answer:

Step-by-step explanation:
Given a function:

To find:
Function
whose graph is a reflection in the y -axis for the given function = ?
Solution:
First of all, let us learn about the reflection of a point (
) in y axis.
For example, let us consider a point (3, 2) on the coordinate axis.
The reflection of this point in y axis will be (-3, 2)
OR
In other words, <em>To find the image of a point in y axis</em>:
the x coordinate is made of negative sign and y coordinate remains the same.
A line is nothing but a number of points joined together.
So, if we want to find reflection of a line or linear function in y axis, we just make the sign of x as negative.
Given that 
We can write it as:

To find its reflection:

Please refer to the attached graphs of
and
.
So, the answer is:

9/12=1/2+1/4 hope this helps
<h3>
Answer: (x,y) = (-2, 5)</h3>
======================================================
Explanation:
4x-3y = -23 is the same as 12x-9y = -69 when we multiply both sides by 3
-3x-2y = -4 is the same as -12x-8y = -16 when we multiply both sides by 4
Our updated system looks like this

Notice how we have 12x and -12x. They combine to 0x allowing the x terms to go away.
The y terms combine to -9y+(-8y) = -17y and the right hand sides combine to -69+(-16) = -85
After doing those three sets of additions, we get the new equation -17y = -101 which solves to y = -85/(-17) = 5
The last step is to use this y value to find x
4x-3y = -23
4x-3(5) = -23
4x-15 = -23
4x = -23+15
4x = -8
x = -8/4
x = -2
So the solution is (x,y) = (-2, 5)
-------------------------------------------
Check:
Let's plug the solution into the first equation
4x-3y = -23
4(-2)-3(5) = -23
-8-15 = -23
-23 = -23
We get a true result. Let's do the same for the second equation
-3x-2y = -4
-3(-2) - 2(5) = -4
6 - 10 = -4
-4 = -4
This result is true as well. So we've confirmed both equations to fully confirm the solution of this system.