Answer:
Please see attachment
Step-by-step explanation:
Please see attachment
Answer:
X= 8
Y= 130
(8, 130)
Step-by-step explanation:
I used a graphing calculator to see where the two equations intersected.
Hope this helped :)
Answer:
nope it is equal to 84/100 though
Step-by-step explanation:
cross multiply
21 x
-------- -----------
25 100
21*100= 2100
2100/25= 84
x=84
I hope this helped!
Answer:
![\textsf{A)} \quad \left(-\dfrac{1}{2} , 0\right) \textsf{ and } (2, 0)](https://tex.z-dn.net/?f=%5Ctextsf%7BA%29%7D%20%5Cquad%20%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D%20%2C%200%5Cright%29%20%5Ctextsf%7B%20and%20%7D%20%282%2C%200%29)
![\textsf{B)} \quad \left(\dfrac{3}{4},25 \right)](https://tex.z-dn.net/?f=%5Ctextsf%7BB%29%7D%20%5Cquad%20%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%2C25%20%5Cright%29)
C) see explanation
Step-by-step explanation:
Given function:
![f(x) =-16x^2 + 24x + 16](https://tex.z-dn.net/?f=f%28x%29%20%3D-16x%5E2%20%2B%2024x%20%2B%2016)
<h3><u>Part A</u></h3>
To find the <u>x-intercepts</u>, set the function to zero, factor and solve for x:
![\implies f(x)=0](https://tex.z-dn.net/?f=%5Cimplies%20f%28x%29%3D0)
![\implies -16x^2 + 24x + 16=0](https://tex.z-dn.net/?f=%5Cimplies%20-16x%5E2%20%2B%2024x%20%2B%2016%3D0)
![\implies -8(2x^2-3x-2)=0](https://tex.z-dn.net/?f=%5Cimplies%20-8%282x%5E2-3x-2%29%3D0)
![\implies 2x^2-3x-2=0](https://tex.z-dn.net/?f=%5Cimplies%202x%5E2-3x-2%3D0)
![\implies 2x^2-4x+x-2=0](https://tex.z-dn.net/?f=%5Cimplies%202x%5E2-4x%2Bx-2%3D0)
![\implies 2x(x-2)+1(x-2)=0](https://tex.z-dn.net/?f=%5Cimplies%202x%28x-2%29%2B1%28x-2%29%3D0)
![\implies (2x+1)(x-2)=0](https://tex.z-dn.net/?f=%5Cimplies%20%282x%2B1%29%28x-2%29%3D0)
Therefore:
![\implies 2x+1=0 \implies x=-\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%202x%2B1%3D0%20%5Cimplies%20x%3D-%5Cdfrac%7B1%7D%7B2%7D)
![\implies x-2=0 \implies x=2](https://tex.z-dn.net/?f=%5Cimplies%20x-2%3D0%20%5Cimplies%20x%3D2)
Therefore, the x-intercepts of the graph of f(x) are
![\left(-\dfrac{1}{2} , 0\right) \textsf{ and } (2, 0)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D%20%2C%200%5Cright%29%20%5Ctextsf%7B%20and%20%7D%20%282%2C%200%29)
<h3><u>Part B</u></h3>
As the leading coefficient is negative, the parabola will open downwards. Therefore, the vertex of the graph of f(x) will be a <u>maximum</u>.
The x-coordinate of the vertex is the midpoint of the x-intercepts:
![\implies \sf midpoint=\dfrac{2+\left(-\frac{1}{2}\right)}{2}=\dfrac{3}{4}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20midpoint%3D%5Cdfrac%7B2%2B%5Cleft%28-%5Cfrac%7B1%7D%7B2%7D%5Cright%29%7D%7B2%7D%3D%5Cdfrac%7B3%7D%7B4%7D)
To find the y-coordinate of the vertex, substitute the x-value into the function:
![\implies f\left(\dfrac{3}{4}\right)=-16\left(\dfrac{3}{4}\right)^2 + 24\left(\dfrac{3}{4}\right) + 16](https://tex.z-dn.net/?f=%5Cimplies%20f%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%3D-16%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E2%20%2B%2024%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%20%2B%2016)
![\implies f\left(\dfrac{3}{4}\right)=-9+18+16](https://tex.z-dn.net/?f=%5Cimplies%20f%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%3D-9%2B18%2B16)
![\implies f\left(\dfrac{3}{4}\right)=25](https://tex.z-dn.net/?f=%5Cimplies%20f%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%3D25)
Therefore, the <u>coordinates of the vertex</u> are:
![\left(\dfrac{3}{4},25 \right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%2C25%20%5Cright%29)
<h3><u>Part C</u></h3>
Find the y-intercept by substituting x = 0 into the function:
![\implies f(0) =-16(0)^2 + 24(0) + 16=16](https://tex.z-dn.net/?f=%5Cimplies%20f%280%29%20%3D-16%280%29%5E2%20%2B%2024%280%29%20%2B%2016%3D16)
Therefore, the y-intercept is (0, 16)
To graph f(x)
- Plot the vertex
- Plot the x-intercepts
- Plot the y-intercept
- Draw a parabola opening downwards with the vertex as the maximum point.
The axis of symmetry is the x-value of the vertex. Use this to help ensure the curve is symmetrical.
The length of AD is 75. Since opposite sides have the same length, 63 plus 63 is 126. The perimeter is 276, so 276 minus 126 is 150. 150 divided by 2 is 75.