3/4 would have to be a answer
Step-by-step explanation:
5 gallons 3 quarts +4 gallons 2 quarts
5.3
+
4.2
=9.5 gallons
D is your answer.
Hope this helps & good luck. :)
Answer:
New image will have (2,1) , (-2,0) and (-2,-2) as new vertex.
Below is the graph.
Step-by-step explanation:
Given the triangle with points (4,7) , (-8,4) and (-8,-2) having dilation center at (1,-2) .
We have to dilate using a factor of 1/3 and graph the new image.
Let us find all the three points,
Formula,
New point = [old point - dilation center]* scale factor + dilation center
So,
For (4,7)
![[(4,7)- (1,-2)]*\frac{1}{3} + (1,-2)](https://tex.z-dn.net/?f=%5B%284%2C7%29-%20%281%2C-2%29%5D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B%20%281%2C-2%29)
![[3,9]*\frac{1}{3} +(1,-2)](https://tex.z-dn.net/?f=%5B3%2C9%5D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B%281%2C-2%29)
![[1,3]+(1,-2)= (2,1)](https://tex.z-dn.net/?f=%5B1%2C3%5D%2B%281%2C-2%29%3D%20%282%2C1%29)
For (-8,4)
![[(-8,4)- (1,-2)]*\frac{1}{3} + (1,-2)](https://tex.z-dn.net/?f=%5B%28-8%2C4%29-%20%281%2C-2%29%5D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B%20%281%2C-2%29)
![[-9,6]*\frac{1}{3} +(1,-2)](https://tex.z-dn.net/?f=%5B-9%2C6%5D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B%281%2C-2%29)
![[-3,2]+(1,-2)= (-2,0)](https://tex.z-dn.net/?f=%5B-3%2C2%5D%2B%281%2C-2%29%3D%20%28-2%2C0%29)
For (-8,-2)
![[(-8,-2)- (1,-2)]*\frac{1}{3} + (1,-2)](https://tex.z-dn.net/?f=%5B%28-8%2C-2%29-%20%281%2C-2%29%5D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B%20%281%2C-2%29)
![[-9,0]*\frac{1}{3} +(1,-2)](https://tex.z-dn.net/?f=%5B-9%2C0%5D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B%281%2C-2%29)
![[-3,0]+(1,-2)= (-2,-2)](https://tex.z-dn.net/?f=%5B-3%2C0%5D%2B%281%2C-2%29%3D%20%28-2%2C-2%29)
Therefore these (2,1) , (-2,0) and (-2,-2) are the new vertices after dilation.
Answer:
x = 8
x = 21/14
x = 8
x = 15/21
x = 1/4
x = 7
Step-by-step explanation:
(For all instances of number, let it be x)
Double the sum of a number and 15. The result is the same as the product of 23 and the number.
2x + 15 = 23 + x
2x - x + 15 = 23 + x - x
x + 15 = 23
x + 15 - 15 = 23 - 15
x = 8
Multiply a number by 15 and add 2. The result is the same as the sum of 23 and the number.
15x + 2 = 23 + x
14x + 2 = 23
14x = 21
x = 21/14
Double a number and add 15. The result is the same as the sum of 23 and the number.
2x + 15 = 23 + x
x + 15 = 23
x = 8
Double a number and add 15. The result is the same as the product of 23 and the number. (This time we will move the x to the other side as the right side has a larger x than the left side)
2x + 15 = 23x
15 = 21x
x = 15/21
Multiply a number by 15 and add 2. The result is the same as the product of 23 and the number.
15x + 2 = 23x
2 = 8x
2/8 = x
x = 1/4
Double the sum of a number and 15. The result is the same as the sum of 23 and the number.
2(x + 15) = 23 + x
2x + 30 = 23 + x
x + 30 = 23
x = 7
