![\text{ The vertex of } y = 4x^2 - 2 \text{ is (h, k) = (0, -2)}](https://tex.z-dn.net/?f=%5Ctext%7B%20The%20vertex%20of%20%7D%20y%20%3D%204x%5E2%20-%202%20%5Ctext%7B%20is%20%28h%2C%20k%29%20%3D%20%280%2C%20-2%29%7D)
<em><u>Solution:</u></em>
Given that we have to find the vertex
<u><em>The vertex form of equation is written as:</em></u>
![y = a(x-h)^2+k](https://tex.z-dn.net/?f=y%20%3D%20a%28x-h%29%5E2%2Bk)
Where, (h, k) is the vertex
Given equation is:
![y = 4x^2 - 2](https://tex.z-dn.net/?f=y%20%3D%204x%5E2%20-%202)
Convert to vertex form
![y = 4x^2 -2\\\\x^2\ can\ be\ written\ as\ (x+0)^2\\\\Thus\ above\ equation\ becomes\\\\y = 4(x+0)^2 - 2](https://tex.z-dn.net/?f=y%20%3D%204x%5E2%20-2%5C%5C%5C%5Cx%5E2%5C%20can%5C%20be%5C%20written%5C%20as%5C%20%28x%2B0%29%5E2%5C%5C%5C%5CThus%5C%20above%5C%20equation%5C%20becomes%5C%5C%5C%5Cy%20%3D%204%28x%2B0%29%5E2%20-%202)
The above equation is of vertex form
On comparing vertex form with above equation,
![y = a(x-h)^2+k\\\\y = 4(x+0)^2 -2](https://tex.z-dn.net/?f=y%20%3D%20a%28x-h%29%5E2%2Bk%5C%5C%5C%5Cy%20%3D%204%28x%2B0%29%5E2%20-2)
On comparing we get,
h = 0
k = -2
Thus vertex is (h, k) = (0, -2)
This value is very different from the other values
Answer:
![x=-\frac{9}{4} \\ or \:\\x = -2\frac{1}{4}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B9%7D%7B4%7D%20%5C%5C%20or%20%5C%3A%5C%5Cx%20%3D%20-2%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
![-2 (x + 1/4)+1=5\\\\-2\left(x+\frac{1}{4}\right)+1=5\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\-2\left(x+\frac{1}{4}\right)+1-1=5-1\\\\Simplify\\-2\left(x+\frac{1}{4}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+\frac{1}{4}\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x+\frac{1}{4}=-2\\\\\mathrm{Subtract\:}\frac{1}{4}\mathrm{\:from\:both\:sides}\\\\x+\frac{1}{4}-\frac{1}{4}=-2-\frac{1}{4}\\\\Simplify\\x=-\frac{9}{4}\\\\x = -2\frac{1}{4}](https://tex.z-dn.net/?f=-2%20%28x%20%2B%201%2F4%29%2B1%3D5%5C%5C%5C%5C-2%5Cleft%28x%2B%5Cfrac%7B1%7D%7B4%7D%5Cright%29%2B1%3D5%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D1%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C-2%5Cleft%28x%2B%5Cfrac%7B1%7D%7B4%7D%5Cright%29%2B1-1%3D5-1%5C%5C%5C%5CSimplify%5C%5C-2%5Cleft%28x%2B%5Cfrac%7B1%7D%7B4%7D%5Cright%29%3D4%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D-2%5C%5C%5Cfrac%7B-2%5Cleft%28x%2B%5Cfrac%7B1%7D%7B4%7D%5Cright%29%7D%7B-2%7D%3D%5Cfrac%7B4%7D%7B-2%7D%5C%5C%5C%5CSimplify%5C%5Cx%2B%5Cfrac%7B1%7D%7B4%7D%3D-2%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D%5Cfrac%7B1%7D%7B4%7D%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5Cx%2B%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%3D-2-%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5CSimplify%5C%5Cx%3D-%5Cfrac%7B9%7D%7B4%7D%5C%5C%5C%5Cx%20%3D%20-2%5Cfrac%7B1%7D%7B4%7D)
Answer:
C. 138°
Step-by-step explanation:
< ABC = 1/2 ( ac + de)
90 = 1/2 (ac +42)
multiply each side by 2
2*90 = 2*12/ (ac+42)
180 = ac+42
subtract 42 from each side
180-42 = ac
138 = ac
Answer:
200 fruits
Step-by-step explanation:
The questions states that 50% of the fruits were ripe, and that 100 fruits were ripe
Therefore: 100 = 50%
Which makes the total amount of fruits 200
Don't believe me? Reverse work:
200 / 2 = 100
200 = 100%, 100 = 50%