Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
On this exercise is given that a triangle with vertices A(-6,-3), B(7,-7), and C(0,3) was dilated by a scale factor of 1.5, and it is asked to find the vertices of the image of the triangle after the dilation occurred.
Pre-image Image
A(-6,-3) --- (-6*1.5,-3*1.5) --- A'(-9,-4.5)
B(7,-7) ---- (7*1.5,-7*1.5) ---- B'(10.5,-10.5)
C(0,3) ----- (0*1.5,3*1.5) ----- C'(0,4.5)
The coordinates of the triangle's image after a dilation with a scale factor of 1.5 are represented by the points A'(-9,-4.5), B'(10.5,-10.5), and C'(0,4.5).
Answer:
The three consecutive integers are:
8, 9, 10
Step-by-step explanation:
Given:
There are three consecutive integers.
Three times the smallest is 14 more than the largest.
To find the three integers.
Solution:
Since the integers are consecutive , so each have a common difference of 1.
For example : -3,-2,-1
Let the integers be = ![x,(x+1),(x+2)](https://tex.z-dn.net/?f=x%2C%28x%2B1%29%2C%28x%2B2%29)
Three times the smallest is 14 more than the largest can be given as:
![3x=(x+2)+14](https://tex.z-dn.net/?f=3x%3D%28x%2B2%29%2B14)
Simplifying and solving for
.
![3x=x+2+14](https://tex.z-dn.net/?f=3x%3Dx%2B2%2B14)
![3x=x+16](https://tex.z-dn.net/?f=3x%3Dx%2B16)
Subtracting both sides by ![x](https://tex.z-dn.net/?f=x)
![3x-x=x-x+16](https://tex.z-dn.net/?f=3x-x%3Dx-x%2B16)
![2x=16](https://tex.z-dn.net/?f=2x%3D16)
Dividing both sides by 2.
![\frac{2x}{2}=\frac{16}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B16%7D%7B2%7D)
∴ ![x=8](https://tex.z-dn.net/?f=x%3D8)
Smallest integer = 8
Next integer = 9
Largest integer = 10
Answer:
x=6
y=3
Step-by-step explanation:
y(side)= x
x(side)=2x
3rd side (3
) = x![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
x=3;
x= 2(3)=6
y=(3)=3
Answer:
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).
Question #25:
One way to solve this is by multiplying the number of packages per serving by the number of guests.
1/4 * 16 = 4 packages to serve 16 guests. This means he doesn't have enough.
A second way to solve this is by diving the number of packages by the number of packages it takes to make on serving.
3 1/2 ÷ 1/4 = 14 guests he can serve. This means he doesn't have enough.
Question #26:
First, find common denominators.
2/3 = 8/12
1/4 = 3/12
Second, subtract.
8/12 - 3/12 = 5/12
Therefore, the tank is 5/12 full at the end of the trip.
Question #27:
1/2 is cut off then 1/3 is cut off. This means 3/6 was cut off to bundle newspapers, then 1/6 was cut off to make parcel. In all, 4/6 was cut off the original string. Afterwards, 2/6 was left over. So, just multiply; 2 * 3 = 6.
Therefore, the original string was as a total of 6 meters.
Best of Luck!