Answer:
Vertex ( 5 ,8) .
Step-by-step explanation:
Given : f(x) = 2(x − 5)² + 8.
To find : Determine the vertex of the function .
Solution : We have given
f(x) = 2(x − 5)² + 8.
Vertex form of parabola : f (x) = a(x - h)² + k, where (h, k) is the vertex.
On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.
a = 2 , h = 5 , k = 8 .
Vertex ( 5 ,8) .
Therefore, Vertex ( 5 ,8) .
Answer:
.625 to get .875
Step-by-step explanation:
what is a rational number
Answer:
The answer to your question is: L = 30 ft
Step-by-step explanation:
Data
man = 6 ft
man shadow = 5 ft
lamppost shadow = 25 ft
lamppost height = ? = L
Process
![\frac{6}{5} = \frac{L}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B5%7D%20%3D%20%5Cfrac%7BL%7D%7B25%7D)
![L = \frac{6 x 25}{5}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B6%20x%2025%7D%7B5%7D)
![L = \frac{150}{5}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B150%7D%7B5%7D)
L = 30 ft
If
![u](https://tex.z-dn.net/?f=u)
and
![v](https://tex.z-dn.net/?f=v)
are <span>supplementary angles, then
![u+v=180^{\circ}~~~~~\mathbf{(i)}](https://tex.z-dn.net/?f=u%2Bv%3D180%5E%7B%5Ccirc%7D~~~~~%5Cmathbf%7B%28i%29%7D)
The ratio of
![u](https://tex.z-dn.net/?f=u)
and
![v](https://tex.z-dn.net/?f=v)
is
![\dfrac{7}{13}:](https://tex.z-dn.net/?f=%5Cdfrac%7B7%7D%7B13%7D%3A)
<span>
![\dfrac{u}{v}=\dfrac{7}{13}\\\\\\ u=\dfrac{7v}{13}~~~~\mathbf{(ii)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bu%7D%7Bv%7D%3D%5Cdfrac%7B7%7D%7B13%7D%5C%5C%5C%5C%5C%5C%20u%3D%5Cdfrac%7B7v%7D%7B13%7D~~~~%5Cmathbf%7B%28ii%29%7D)
Substitute
![\mathbf{(ii)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28ii%29%7D)
into
![\mathbf{(i)}:](https://tex.z-dn.net/?f=%5Cmathbf%7B%28i%29%7D%3A)
![\dfrac{7v}{13}+v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+1 \right )\cdot v=180^{\circ}\\\\\\ \left(\dfrac{7}{13}+\dfrac{13}{13} \right )\cdot v=180^{\circ}\\\\\\ \dfrac{20}{13}\cdot v=180^{\circ}\\\\\\ v=180^{\circ}\cdot \dfrac{13}{20}\\\\\\ \boxed{\begin{array}{c} v=117^{\circ} \end{array}}](https://tex.z-dn.net/?f=%5Cdfrac%7B7v%7D%7B13%7D%2Bv%3D180%5E%7B%5Ccirc%7D%5C%5C%5C%5C%5C%5C%20%5Cleft%28%5Cdfrac%7B7%7D%7B13%7D%2B1%20%5Cright%20%29%5Ccdot%20v%3D180%5E%7B%5Ccirc%7D%5C%5C%5C%5C%5C%5C%20%5Cleft%28%5Cdfrac%7B7%7D%7B13%7D%2B%5Cdfrac%7B13%7D%7B13%7D%20%5Cright%20%29%5Ccdot%20v%3D180%5E%7B%5Ccirc%7D%5C%5C%5C%5C%5C%5C%20%5Cdfrac%7B20%7D%7B13%7D%5Ccdot%20v%3D180%5E%7B%5Ccirc%7D%5C%5C%5C%5C%5C%5C%20v%3D180%5E%7B%5Ccirc%7D%5Ccdot%20%5Cdfrac%7B13%7D%7B20%7D%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B%5Cbegin%7Barray%7D%7Bc%7D%20v%3D117%5E%7B%5Ccirc%7D%20%5Cend%7Barray%7D%7D)
From
![\mathbf{(i)},](https://tex.z-dn.net/?f=%5Cmathbf%7B%28i%29%7D%2C)
we find the measure of
![u:](https://tex.z-dn.net/?f=u%3A)
![u=180^{\circ}-v\\\\ u=180^{\circ}-117^{\circ}\\\\ \boxed{\begin{array}{c} u=63^{\circ} \end{array}}](https://tex.z-dn.net/?f=u%3D180%5E%7B%5Ccirc%7D-v%5C%5C%5C%5C%20u%3D180%5E%7B%5Ccirc%7D-117%5E%7B%5Ccirc%7D%5C%5C%5C%5C%20%5Cboxed%7B%5Cbegin%7Barray%7D%7Bc%7D%20u%3D63%5E%7B%5Ccirc%7D%20%5Cend%7Barray%7D%7D)
</span></span>