Answer:
y = 2(x-3)^2 -12
y = -4/9(x-2)^2 +7 bonus
Step-by-step explanation:
The vertex form of a parabola is
y = a(x-h)^2 + k where (h,k) is the vertex
y = a(x-3)^2 - 12
We have one point given (0,6)
6 = a (0-3) ^2 -12
6 = a (-3)^2 -12
6 = 9a-12
Add 12 to each side
6+12 = 9a
18 = 9a
Divide each side by 9
18/9 = 9a/9
a=2
y = 2(x-3)^2 -12
We follow the same steps for the bonus
y = a(x-2)^2 +7
Substitute the point into the equation
3 = a (-1-2)^2 +7
3 =a (-3)^2 +7
3 = 9a +7
subtract 7 from each side
3-7 = 9a +7-7
-4 = 9a
Divide by 9
-4/9 =a
y = -4/9(x-2)^2 +7
Answer: 410 square km
Step-by-step explanation:
The area of each of the triangles with their base on the 10 km side is 
, so their combined area is 
.
The area of each of the triangles with their base on the 12 km side is 
, so their combined area is 
.
The area of the bottom rectangular face is 
.
So, the total surface area is 
Use this equation: A=3.14159r^2
Answer:
Step-by-step explanation:
Annual gross salary = $28000
Income tax = 20% on anything above $15000
So she's taxable for $5000
Rent loan = $140 per month = $140 * 12= $1680 per annum
Tax deductible per annum = 20% of $5000
20 / 100 * $5000 = $1000
Total amount she takes home per annum =
Gross salary per annum - tax - loan =
($28000 - $1000 - $1680) = $25,320
Ayesha takes home $25,320 home annually.
Answer:
102
Step-by-step explanation:
The least common multiple of 6 and 17
For us to determine the L.C.M of 6 and 17,
First find the prime factors of 6 and 17
Prime Factor of 6
6 = 2 × 3
Prime factor of 17
17 = 1 × 17
Secondly;
Multiply all the factors together to find the L.C.M:
L.C.M = 1 × 2 × 3 × 17
L.C.M = 102
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