Answer:
Part a) 
Part b) 
Part c) 
Part d) 
Step-by-step explanation:
see the attached figure to better understand the question
we know that
To find the length of the image after a dilation, multiply the length of the pre-image by the scale factor
Part a) we have
The scale factor is 5
The length of the pre-image is 3 cm
therefore
The length of the image AB after dilation is

Part b) we have
The scale factor is 3.7
The length of the pre-image is 3 cm
therefore
The length of the image AB after dilation is

Part c) we have
The scale factor is 1/5
The length of the pre-image is 3 cm
therefore
The length of the image AB after dilation is

Part d) we have
The scale factor is s
The length of the pre-image is 3 cm
therefore
The length of the image AB after dilation is

slope intercept form is: y = mx + b
m = slope
b = y-intercept
In the equation y = 1/4x + 8
m = 1/4 = slope
b = 8 = y-intercept
Answer:
69 feet
Step-by-step explanation:
we have

where
h(t) is the height of the ball
t is the time in seconds
we know that the given equation is a vertical parabola open downward
The vertex is the maximum
so
the y-coordinate of the vertex represent the maximum height of the ball
Convert the quadratic equation into vertex form
The equation in vertex form is equal to

where
(h,k) is the vertex of the parabola







the vertex is the point (2,69)
therefore
The maximum height is 69 ft
c. (x + 5)(x - 7) use the FOIL method.
x² + 5x - 7x - 35
x² + (5x - 7x) - 35 collect like terms.
x² - 2x - 35
hope that helps, God bless!