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
Mia walked 7km/h so after 1 hour, she is 7 km north of the house of Julia
Samantha walked 11km/h so after 1 hour, she is 11 km west of the house of Julia.
The points where Mia and Samantha are after 1 hour , and the house of Julia form a right triangle with sides 7 and 11 km. The distance between the girls, is the hypotenuse of his triangle.
by the pythagorean theorem:
Answer: 13 km
36.00 will be enough to pay for fuel because if you multiply the 8.8 gallons of diesel needed by the fuel cost per gallon you get 35.112
Compatible numbers are those closest to these numbers- 65 rounded to the nearest tens is 70, and adding that to 150 we get B. 210.
---
Hope this helps!
First, we are going to find the sum of their age. To do that we are going to add the age of Eli, the age Freda, and the age of <span>Geoff:
</span>
The combined age of Eli, Freda, and Geoff is 40, so the denominator of each ratio will be 40.
Next, we are going to multiply the ratio between the age of the person and their combined age by <span>£800:
For Eli: </span>
For Freda: 
For Geoff: 
<span>
We can conclude that
Eli will get </span>
£180,
Freda will get £260, and
Geoff will get <span>
£360.</span>
