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2 years ago

Determine a and k so the given points are on the graph of the function.

Mathematics

1 answer:

Margarita [4]2 years ago

3 0

Answer:

y = -7(x +1)² +35

Step-by-step explanation:

The given quadratic equation has two parameters you are asked to find. When you fill in the given point values, the result is two linear equations in the two unknown parameters. You can solve these equations in any of the usual ways.

<h3>equation for point (1, 7)</h3>

y = a(x +1)² +k

7 = a(1 +1)² +k

7 = 4a +k

<h3>equation for point (2, -28)</h3>

-28 = a(2 +1)² +k

-28 = 9a +k

<h3>solution</h3>

The first equation can be subtracted from the second equation to eliminate the k variable. (This is solving by <em>elimination</em>.)

(-28) -(7) = (9a +k) -(4a +k)

-35 = 5a . . . . . . . . simplify

-7 = a . . . . . . . . divide by 5

Using the first equation, we can find k.

7 -4a = k . . . . . subtract 4a

7 -4(-7) = k . . . . substitute for 'a'

35 = k

The parameter values are a = -7, and k = 35. The quadratic equation is ...

y = -7(x +1)² +35

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A pet store sells goldfish and hermit crabs,

Elis [28]

Answer:

$Cost = \$28$

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

$7g + 3h = 26$

The second statement, we have:

$4g + 5h = 28$

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

$7g + 3h = 26$ --- (1)

$4g + 5h = 28$ --- (2)

Make g the subject in (2)

$4g + 5h = 28$

$4g = 28 - 5h$

Divide both sides by 4

$g = \frac{1}{4}(28 - 5h)$

Substitute $\frac{1}{4}(28 - 5h)$ for g in (1)

$7g + 3h = 26$

$7(\frac{1}{4}(28 - 5h)) + 3h = 26$

$\frac{7}{4}(28 - 5h) + 3h = 26$

Multiply through by 4

$4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4$

$7(28 - 5h) + 4*3h = 26*4$

Open bracket

$196 - 35h + 12h = 104$

$196 -23h = 104$

Collect Like Terms

$-23h = 104-196$

$-23h = -92$

Make h the subject

$h = \frac{-92}{-23}$

$h = \frac{92}{23}$

$h = 4$

Substitute 4 for h in $g = \frac{1}{4}(28 - 5h)$

$g = \frac{1}{4}(28 - 5*4)$

$g = \frac{1}{4}(28 - 20)$

$g = \frac{1}{4}(8)$

$g = 2$

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

$Cost = 6g + 4h$

$Cost = 6*\$2 + 4*\$4$

$Cost = \$12 + \$16$

$Cost = \$28$

5 0

3 years ago

how much money has to be invested at 5.9% interest compounded continuously to have 15,000 after 12 years?

Scrat [10]

Hi there

The formula is
A=pe^rt
We need to solve for p where
A future value 15000
P present value?
E constant
R interest rate 0.059
T time 12 years
So when you solve for p you get
P=A÷e^rt
P=15,000÷e^(0.059×12)
P=7,389.43

Hope it helps

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3 years ago

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Leviafan [203]

Answer:

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Step-by-step explanation:

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2 years ago

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Fittoniya [83]

15$ is the answer! :)

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3 years ago

If the racetrack publishes that the odds in favor of a horse winning a race are 5 to 9, what is probability that the horse will

crimeas [40]

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3 years ago

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