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Basile [38]
3 years ago
11

In the answer space below, provide the larger of the two positive integers that add up to 60 and have the largest possible produ

ct.

Mathematics
1 answer:
MAXImum [283]3 years ago
5 0

Answer:

The two positive integers are 30 and 30

Step-by-step explanation:

Let

x------> the larger  positive integer

y-----> the smaller positive integer

P----> the product o the two positive integers

we know that

x+y=60

y=60-x -----> equation A

P=xy ----> equation B

substitute equation A in equation B

P=x(60-x)

P=60x-x^{2}

This is the equation of a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the largest possible product

Using a graphing tool

The vertex is the point (30,900)

That means------> For x=30 The largest possible product is 900

and

y=60-x ------> y=60-30=30

therefore

The two positive integers are 30 and 30

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gogolik [260]

Answer:

The factored form of this is (x - 7)(x -4)

Step-by-step explanation:

In order to factor quadratic equaitons with a 1 as the first coefficient, we look for two numbers that multiply to the last number (28), but add up to the middle number (-11). To do this, we often list the factors of the last number.

Factors of 28

1, 28

-1, -28

2, 14

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4, 7

-4, -7

The numbers -4 and -7 satisfy this requirement and are therefore the numbers we want. Now we stick them into parenthesis along with x terms in the front like this:

(x - 7)(x -4)

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3 years ago
A retail outlet offers a retention bonus for each shopping season an employee remains with the company. Samuel's starting pay is
miv72 [106K]

Answer:

Samuel's hourly rate after n seasons with the company is f(n)= 12.50 + 0.35*n.  After 18 seasons with the company, Samuel's hourly rate will be 18.8 $ /hr.

Step-by-step explanation:

You know that Samuel's starting pay is $12.50/hr and for each season Samuel remains with the company, he receives a $0.35/hr raise.

Samuel's hourly rate after n seasons at the company will then be:

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To determine the hourly rate after 18 seasons, you must replace the value n with 18:

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Solving you get:

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<u><em>Samuel's hourly rate after n seasons with the company is f(n)= 12.50 + 0.35*n.  After 18 seasons with the company, Samuel's hourly rate will be 18.8 $ /hr. </em></u>

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x = 0 : y = 0 - 4 = - 4 ⇒ (0, - 4 )

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Answer:

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