4. A rock is thrown with a height equation of h = -16t2 + 64t + 5 (where h is the height of the rock in feet at any given time of t in seconds). Will it reach a height of 50 feet? Explain your answer.

Yes,  see below.

Step-by-step explanation:

Convert the equation to vertex form to find the maximum height:

h = -16t2 + 64t + 5

= -16(t^2 - 4t) + 5

= -16 [(t - 2)^2 - 4] + 5

= -16( t - 2)^2  + 64 + 6

= -16(t - 2)^2 + 69.

So the maximum height the rock reaches is 69 feet.

This height is reached at 2 time seconds.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

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