Answer:
The coordinates of E are
.
Step-by-step explanation:
The triangle ABC represents a right triangle as both sides AB and AC are orthogonal to each other. The side AB is in the y axis, whereas the side AC is in the x axis. The triangle is dilated with respect to the origin, in which point A is set.
Vectorially speaking, dilation is defined by the following operation:
(1)
Where:
- Point of reference.
- Original point.
- Dilated point.
- Dilation factor.
By applying this operation, point B becomes point D:
, 
![D(x,y) = (0,0) + k\cdot [(0,4)- (0,0)]](https://tex.z-dn.net/?f=D%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20k%5Ccdot%20%5B%280%2C4%29-%20%280%2C0%29%5D)




Lastly, we transform point C into point E by applying the same operation:
,
and 
![E(x,y) = (0,0) + \frac{3}{2}\cdot [(3,0)-(0,0)]](https://tex.z-dn.net/?f=E%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5Ccdot%20%5B%283%2C0%29-%280%2C0%29%5D)

The coordinates of E are
.
Answer:
volume of cube share box = 67.92 inch²
Step-by-step explanation:
given data
soccer ball volume = 85.3π cubic inches
solution
we know that ball will fit inside the box when box length will be equal to diameter of ball
and here soccer ball volume will be express as
soccer ball volume =
.................1
85.3π =
solve it we get
r³ = 69.9765
r = 4.12 inch
so diameter = 2 × 4.12 = 8.24 inch
diameter = length of box side
volume of cube share box = a²
volume of cube share box = 8.24²
volume of cube share box = 67.92 inch²
F(g(x))= -4(10x-6) + 7
f(g(x))= -40x + 24 +7
f(g(x))= -40x +31
Answer:
"10"
Step-by-step explanation:
This is rather thinking "pictorially". Picture it.
You can match it with a round clock that has numbers 1 - 12 written on it.
So,
32 and 16 would be opposite of each other [top and bottom]. And, 1 - 15 would be on right side and 17 - 31 would be on left side.
Now,
Going counter-clockwise from 32, 26 would be the 6th number. Going counter-clockwise from 16, 10 would be the 6th number.
Hence, they would be opposite of each other.
10 would be opposite of 26
Answer:
21
Step-by-step explanation: