Vertex form: y = a(x - h)² + k
h = 2
k = -1
y = 0
x = 5
0 = a(5 - 2)² - 1
0 = 9a - 1
a = 1/9
Answer:
x = 240 feet
Step-by-step explanation:
It is given that,
The angle of depression is 30 degrees from the bottom of the boat to a deep sea diver at the depth of 120 ft.
We need to find the distance x the diver must swim up to the boat. It can be calculate by applying trigonometry as follows :
So, the distance the diver must swim up to the boat is 240 feet.
We have the function 
and we want to find a function that has the same y-intercept than the previous function.
First, let's find the y-intercept by subtituting 0 for 'x'.
Now that we found that y-intercept =-3, any lineal function of the type: 
will have the same y-intercept. Where 'a' can take all the real values.
Also, any quadratic function of the type: 
will have the same y-intercept. Where 'a' and 'b' can take all the real values.
2.
We have a transversal across parallel lines so we get the usual array of congruent and supplementary angles. We just have to figure out which is which, and the diagram, even though not to scale, makes it pretty obvious.
Angle x isn't the same as the 40° angle so it must be its supplement.
Answer: C 140°
3.
r=1.2, h=2.9, V = (1/3) πr²h
Nothing hard here, we just plug in the numbers,
V = (1/3) π (1.2)² (2.9) ≈ 4.37310
Answer: B. 4.4 cubic inches
4.
Dilation by .5 makes a similar triangle, and reflection is an isomorphism (i.e. it doesn't change the size or shape) so the answer is
Answer: B similar not congruent
5.
The corresponding interior and exterior angles of a triangle form a linear pair, so supplementary angles. x=180-110 = 70°
Answer: A 70°
