The exact form is: 64/5
The decimal from is: 12.8
And the Mixed number form is: 12 4/5
To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c.
We are given two different solutions of the equation.
First, (2, 0).
![0=(2)^2+2b+c\\-4=2b+c](https://tex.z-dn.net/?f=0%3D%282%29%5E2%2B2b%2Bc%5C%5C-4%3D2b%2Bc)
Second, (0, 14).
![14=(0)^2+0b+c\\c=14](https://tex.z-dn.net/?f=14%3D%280%29%5E2%2B0b%2Bc%5C%5Cc%3D14)
So we have a value (14) for c. We can substitute that into our first equation to find b.
![-4=2b+c\\-4=2b+14\\-18=2b\\b=-9](https://tex.z-dn.net/?f=-4%3D2b%2Bc%5C%5C-4%3D2b%2B14%5C%5C-18%3D2b%5C%5Cb%3D-9)
We can now plug in our values for b and c into the equation to get its standard form.
![y=x^2-9x+14](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B14)
To find the vertex, we can convert this equation to vertex form
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
by completing the square.
![y=x^2-9x+14](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B14)
![y=x^2-9x+(-4.5)^2+14-(-4.5)^2](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B%28-4.5%29%5E2%2B14-%28-4.5%29%5E2)
![y=x^2-9x+20.25+14-20.25](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B20.25%2B14-20.25)
![y=(x-4.5)^2-6.25](https://tex.z-dn.net/?f=y%3D%28x-4.5%29%5E2-6.25)
Thus, the vertex is (4.5, –6.25).
We can confirm the solution graphically (see attachment).
<u>Answer:</u>
(i) Total cost of the flat is Rs. 540000.
(ii) Expenditure incurred on labour is Rs. 150000
<u>Step-by-step explanation:</u>
According to the question, cement cost is Rs. 112500, which represents 75° in the pie chart.
(i) The total cost of the flat is represented by the total 360° in the pie chart.
∴ Using unitary method
75° represents Rs. 112500
⇒ 360° represents =
× 360
= Rs. 540000
∴ Total cost of flat = Rs. 540000
(ii) Similarly, to calculate the cost of labour, represented by 100° in the pie chart, we can use the unitary method:
75° represents Rs. 112500
⇒ 100° represents =
× 100
= Rs. 150000
∴ Cost of labour = Rs. 150000
The given table is
x 2 3 4;
f(x): 10 28 82
Note:
The equations were mistyped. They should read as follows:
A)
![f(x) = 2^{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%5E%7Bx%7D)
B)
![f(x)=2^{x}+1](https://tex.z-dn.net/?f=f%28x%29%3D2%5E%7Bx%7D%2B1)
C)
![f(x)=3^{x}](https://tex.z-dn.net/?f=f%28x%29%3D3%5E%7Bx%7D)
D)
![f(x)=3^{x}+1](https://tex.z-dn.net/?f=f%28x%29%3D3%5E%7Bx%7D%2B1)
Answer:
The correct answer is D.
Verify the answer.
When x=2,
![3^{2}+1 =9+1=10](https://tex.z-dn.net/?f=3%5E%7B2%7D%2B1%20%3D9%2B1%3D10)
CORRECT
When x=3,
![3^{3}+1=27+1=28](https://tex.z-dn.net/?f=3%5E%7B3%7D%2B1%3D27%2B1%3D28)
CORRECT
When x=4,
![3^{4}+1=81+1=82](https://tex.z-dn.net/?f=3%5E%7B4%7D%2B1%3D81%2B1%3D82)
CORRECT
There are infinity of fractions equal to 1/2, it just means half of a number, so for example, 3/6, 4/8, 5/10, 6/12 are all equal to 1/2 and so on