First we find the vertex of parabola
![f(x)=-12 x^{2} +7](https://tex.z-dn.net/?f=f%28x%29%3D-12%20x%5E%7B2%7D%20%2B7)
The vertex of parabola is
![( \frac{-b}{2a},f( \frac{-b}{2a}))](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B-b%7D%7B2a%7D%2Cf%28%20%5Cfrac%7B-b%7D%7B2a%7D%29%29%20%20)
Here,
b = coefficient of x term
a = coefficient of x² term
For given parabola, b = 0 , a = -12
So,
![\frac{-b}{2a}= \frac{0}{-24} =0](https://tex.z-dn.net/?f=%20%5Cfrac%7B-b%7D%7B2a%7D%3D%20%5Cfrac%7B0%7D%7B-24%7D%20%3D0%20)
And,
![f( \frac{-b}{2a} )=f(0) = -12(0)+7=7](https://tex.z-dn.net/?f=f%28%20%5Cfrac%7B-b%7D%7B2a%7D%20%29%3Df%280%29%20%3D%20-12%280%29%2B7%3D7)
Thus the vertex of parabola is (0, 7)
To find another point on parabola, substitute x by 1.
![f(1)=-12( 1^{2}) +7=-12+7=-5](https://tex.z-dn.net/?f=f%281%29%3D-12%28%201%5E%7B2%7D%29%20%2B7%3D-12%2B7%3D-5)
So the second point on parabola is (1,-5)
The plot of parabola is shown in image below:
since she already has 18 cups flour she needs 6 cups of sugar
Circumference= 2πr
Circumference= perimeter
14.28km= 2(3.14)r
14.28= 6.2831853072r
divide both sides by 6.2831853072
2.27= r
ANSWER: The radius is 2.27km
Hope this helps! :)
Answer:
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Step-by-step explanation:
Given:
The figure of a rhombus QRST.
To find:
A. The value of x.
B. The measure of angle RQP.
Solution:
A. We need to find the value of x.
We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.
[Right angle]
Divide both sides by 5.
Therefore, the value of x is 15.
B. We need to find the measure of angle RQP.
From the given figure, it is clear that
![m\angle RQP=(2x+3)^\circ](https://tex.z-dn.net/?f=m%5Cangle%20RQP%3D%282x%2B3%29%5E%5Ccirc)
Putting
, we get
![m\angle RQP=(2(15)+3)^\circ](https://tex.z-dn.net/?f=m%5Cangle%20RQP%3D%282%2815%29%2B3%29%5E%5Ccirc)
![m\angle RQP=(30+3)^\circ](https://tex.z-dn.net/?f=m%5Cangle%20RQP%3D%2830%2B3%29%5E%5Ccirc)
![m\angle RQP=33^\circ](https://tex.z-dn.net/?f=m%5Cangle%20RQP%3D33%5E%5Ccirc)
Therefore, the measure of angle RQP is 33 degrees.