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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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Answer:

Each pitcher has the same fraction of the other drink.

Step-by-step explanation:

After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).

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You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.

Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:

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3 years ago

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Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

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Drag the tiles to the correct boxes to complete the pairs.

Ne4ueva [31]

Answer:

Part 1) $-1.25$ -------> $2.75/(-2.2)$

Part 2) $-4\frac{1}{3}$ --------> $(-2\frac{3}{5}) / (\frac{3}{5})$

Part 3) $\frac{2}{3}$ ------> $(-\frac{10}{17}) / (-\frac{15}{17})$

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Step-by-step explanation:

Part 1) we have

$2.75/(-2.2)$

To calculate the division problem convert the decimal number to fraction number

$2.75=275/100\\ -2.2=-22/10$

$(275/100)/(-22/10)$

Remember that

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

$(275/100)/(-22/10)=(275/100)*(-10/22)=-(275*10)/(22*100)=-(275)/(220)$

Simplify

Divide by 22 both numerator and denominator

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Part 2) we have

$(-2\frac{3}{5}) / (\frac{3}{5})$

To calculate the division problem convert the mixed number to an improper fraction

$(-2\frac{3}{5})=-\frac{2*5+3}{5}=-\frac{13}{5}$

$(-\frac{13}{5}) / (\frac{3}{5})$

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

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Convert to mixed number

$-\frac{13}{3}=-(\frac{12}{3}+\frac{1}{3})=-4\frac{1}{3}$

Part 3) we have

$(-\frac{10}{17}) / (-\frac{15}{17})$

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

$(-\frac{10}{17}) / (-\frac{15}{17})=(-\frac{10}{17})*(-\frac{17}{15})=\frac{10*17}{17*15}=\frac{10}{15}$

Simplify

Divide by 5 both numerator and denominator

$\frac{10}{15}=\frac{2}{3}$

Part 4) we have

$(2\frac{1}{4}) / (\frac{3}{4})$

To calculate the division problem convert the mixed number to an improper fraction

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$(\frac{9}{4}) / (\frac{3}{4})$

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Answer:

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Step-by-step explanation:

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