Suppose a parabola has vertex (6, -3) and also passes through the point (8,5).
Write the equation of the parabola in vertex form.
(Answers are given in photo)
10 points!!! Please help.
Answers
Answer: D. y = 2(x - 6)^2 - 3
Step-by-step explanation: see attachment. i hope this helped :)
The equation of the parabola that has vertex (6, -3) and also passes through the point (8,5) is [tex]y = 2(x - 6)^2-3\\[/tex]
The vertex form of the equation of a parabola is:
[tex]y = a(x - h)^2 + k[/tex]
where the vertex = (h, k)
The given vertex, (h, k) = (6, -3)
The line passes through the (8, 5)
x = 8, y = 5
Substitute x = 8, y = 5, h = 6, y = -3 into the equation to solve for a
[tex]y = a(x - h)^2 + k[/tex]
[tex]5 = a(8 - 6)^2 + (-3)\\5 = a(2^2)-3\\4a = 5 + 3\\4a = 8\\a = \frac{8}{4} \\a = 2[/tex]
Substitute a = 2, h = 6, k = -3 into [tex]y = a(x - h)^2 + k[/tex]
[tex]y = 2(x - 6)^2-3\\[/tex]
The equation of the parabola that has vertex (6, -3) and also passes through the point (8,5) is [tex]y = 2(x - 6)^2-3\\[/tex]
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Answer:
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Marge's plan costs .14 cents per minute plus a monthly fee of $24. Dan's plan costs .12 cents per minute plus a monthly fee of $28. How many minutes (m) are required for both plans to cost the same for the month?
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Answer:
6 min for Marge's and 7 for Dan's plan
Step-by-step explanation:
0.14x6=0.84
0.12x7=0.84
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Answer:
m = -4 3/5 or -4.6
Step-by-step explanation:
First, we need to isolate the variable, m. We subtract 1 3/5 on both sides of the equation, and then we should get -4 3/5 = m.
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Steve is turning half of his backyard into a chicken pen. His backyard is a 242424 meter by 454545 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?
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Answer:
51 meters
Step-by-step explanation:
The shape of the backyard is rectangular having a length, l=45 meters, and a width, w=24 meters as shown in the figure.
As wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. So,
The length of fencing = The length of the diagonal AC or BD
As the length of both the diagonals of a rectangle are equals, AC=BD.
The length of fencing [tex]=\sqrt{l^2+w^2}[/tex] [length of the diagonal]
[tex]=\sqrt{45^2+24^2}=51[/tex] meters
Hence, Steve needs 51 meters of fencing.
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Answer:
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Step-by-step explanation:
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A half of a number added to 7 gives 19. What is the number? *
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Answer:
24
Step-by-step explanation:
---------------
24÷2=12
12+7=19
---------------
a.What is the length of A’A?
b.What is the length of B’B
Both in units
Answers
Answer:
A'A = 18 units, B'B = 9 units
Step-by-step explanation:
Δ ACB and Δ A'CB' are similar triangles, thus the ratios of corresponding sides are equal, that is
[tex]\frac{AC}{A'C}[/tex] = [tex]\frac{AB}{A'B'}[/tex] , substitute values
[tex]\frac{AC}{12}[/tex] = [tex]\frac{20}{8}[/tex] ( cross- multiply )
8AC = 240 ( divide both sides by 8 )
AC = 30
Thus A'A = AC - A'C = 30 - 12 = 18 units
--------------------------------------------------------------------
and
[tex]\frac{CB}{CB'}[/tex] = [tex]\frac{AB}{A'B'}[/tex] , that is
[tex]\frac{CB}{6}[/tex] = [tex]\frac{20}{8}[/tex] ( cross- multiply )
8CB = 120 ( divide both sides by 8 )
CB = 15
Thus
B'B = CB - CB' = 15 - 6 = 9 units
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Step-by-step explanation:
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Answer:
The value of f(1 + g(2)) is 5
Step-by-step explanation:
Let us solve the question
∵ f(x) = 2x - 3
∵ g(x) = x + 1
We need to find the value of f(1 + g(2))
That means we will replace x in f(x) by 1 + g(2)
→ g(2) means substitute x in g by 2
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∵ x = 2
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images attached.
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Answer:
D
Step-by-step explanation:
Using the Sine rule in Δ QRS , that is
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Just got it using some brain cells >:)
Answer:
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Step-by-step explanation:
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