Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 24x + 16
Set equal to zero to find the x intercepts
0 = −16x^2 + 24x + 16
Factor out -8
0 = -8(2x^2 -3x-2)
Factor
0 = -8(2x +1) (x-2)
Using the zero product property
2x+1 =0 x-2 =0
x = -1/2 x=2
The x intercepts are -1/2 ,2
Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum
The x value of the maximum is 1/2 way between the zeros
(-1/2+2) /2 = 1.5/2 =.75
To find the y value substitute into the function
f(.75) = -8(2x +1) (x-2)
=-8(2*.75+1) (.75-2)
= -8(2.5)(-1.25)
=25
The vertex is at (.75, 25)
We have the zeros, and the vertex. We know the graph is symmetrical about the vertex
Answer: A
Step-by-step explanation:
To find the answer, we can first find the distance each of them have, then divide it by their speed to find the time needed.
Distance Steve need to travel: 300 feet
Distance Paula need to travel:
300+175(behind steve) = 475 feet
Time needed respectively:
Steve: 300 ÷ 9 = 33.33.. seconds
Paula: 475 ÷ 15 = 31.66... seconds
As we can see from the result, Paula would take less time to reach the goal (31.66<33.33),
therefore, Paula win the bike race by:
33.33-31.67
=1.66...
≈1.67 feet
Thus Paula won by 1.67 feet.
Hope it helps!
There are 204 teddy bears in the shipment.
Step-by-step explanation:
Total number of cases received = 17 cases
Numbers of bears per case = 12 bears
Total number of bears in the shipment = Cases received * Bears per case
Total number of bears = 
Total number of bears = 204
There are 204 teddy bears in the shipment.
Keywords: multiplication
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