Answer:
h(x) = 3(x - 5)^2 + 6.
Step-by-step explanation:
g(x) = 3x^2 + 8
Shifting 5 units to the right gives:
3(x - 5)^2 + 8
Now 2 units down :
3(x - 5)^2 + 8 - 2
= 3(x - 5)^2 + 6.
Answer:
- Center = (3, 0)
- Radius = 3
- Graph = see below
Concept:
Here, we need to know the idea of the circle equation.
Circle equation: (x - h)² + (y - k)² = r²
(h, k) = center
r = radius
x = variable
y = variable
Solve:
<u>Given expression </u>
(x - 3)² + y² = 9
<u>Find the point of the center</u>
(h, k) = 
<u>Find the length of the radius</u>
r² = 9

Hope this helps!! :)
Please let me know if you have any questions
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
.
Rate x time = distance
25 x 35/60 = distance (35/60 is 35 minutes out of an hour- 60 minutes)
25/1 x 7/12 = distance (I put the 25 over 1 and reduced 35/60)
175/12 ≈ 14.58 miles
Notice that the time had to be in a fraction of an hour in order to do this.