Answer:
Step-by-step explanation:
Convert the equation of a circle in general form shown below into standard form. Find the center and radius of the circle. Group the x 's and y 's together. Consider the x2 and x terms only. Complete the square on these terms. Replace the x2 and x terms with a squared bracket.
-2 times -1 = positive 2
(two negatives cancel out to form a positive)
100 x 100 is also 100^2 and that equals 10,000
35 x 35 is also 35^2 and that equals 1,225
9 x 9 x 9 is also 9^3 and that equals 729
4 x 4 x 4 x 4 is also 4^4 and that equals 256
2 x 2 x 2 x 2 x 2 is also 2^5 and that equals 32
Answer:
all real numbers less than or equal to 4
Step-by-step explanation:
To obtain the range we require the value of the y- coordinate of the vertex.
Given
f(x) = - (x + 5)(x + 1) ← equate f(x) to zero to find the zeros, that is
- (x + 5)(x + 1) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 1 = 0 ⇒ x = - 1
The vertex lies on the axis of symmetry which is at the midpoint of the zeros
=
=
= - 3
Substitute x = - 3 into f(x) for y- coordinate of vertex
= - (- 3 + 5)(- 3 + 1) = - (2)(- 2) = 4
The vertex = (- 3, 4 )
and - (x + 5)(x + 1) = - (x² + 6x + 5) = - x² - 6x - 5
Since the coefficient of the x² term is - 1 < 0
then the vertex is a maximum ∩
Hence range is [ 4, - ∞ )
That is all real numbers less than or equal to 4
Area of the trapezium = 1/2(18 + 6) x 12
Area of the trapezium = 144 in²
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Answer: Area = 144 in²
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