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max2010maxim [7]
2 years ago
5

The sum of two positive integers is 97 and their difference is 37. What is their product?

Mathematics
1 answer:
LuckyWell [14K]2 years ago
8 0

Answer:

  2010

Step-by-step explanation:

If the numbers are x and y, you have ...

  x +y = 97

  x -y = 37

Adding these two equations gives ...

  2x = 134

  x = 67

  y = 67 -37 = 30

The product is then ...

  xy = (67)(30) = 2010

__

<em>Alternate solution</em>

There is no need to find the actual numbers. We can go directly to their product.

  (x+y)² = x² +2xy +y² = 97² = 9409

  (x-y)² = x² -2xy +y² = 37² = 1369

Subtracting the second equation from the first gives ...

  4xy = 9409 -1369 = 8040

  xy = 8040/4 = 2010

Of course the difference of squares can be factored, so we could compute ...

  (97² -37²)/4 = (97 +37)(97 -37)/4 = 134(60)/4 = 134(15) = 2010

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five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amou
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9514 1404 393

Answer:

Youngest to oldest:

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Step-by-step explanation:

At 9% interest per year, the present value of 1 at age 20 is ...

  p(a) = 1.09^(a-20)

Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.

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<em>Additional comment</em>

This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.

(We assume the bank <em>pays</em> 9% per year, rather than <em>charges</em> 9% per year.)

6 0
3 years ago
Which expression is equivalent to the given expression? Assume the denominator does not equal zero
rusak2 [61]

Answer:

Step-by-step explanation:

This question is based on the of expression. Therefore, the correct option is (A) that is, .

Given:

Expression :

We have to determined the expression is equivalent to the given expression.

According to the question,

It is given, to be assume that denominator does not equal zero.

Now by given expression, i.e.

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Answer:

1 50.1253%decrease

Step-by-step explanation:

\frac{399-199}{399}

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Find the slope of the line passing through the points (4,4) and (6, -5)
Verdich [7]
I not sure if you mean the gradient of the line or the equation, so here is both.

Gradient (=m) :

( 4, 4 ) ( 6, 5 )
( x1 , y1) ( x2, y2 )

m = y2-y1 / x2-x1
= -5-4 / 6 - 4

= -9 / 2 (as a fraction)
= -4.5 (as a decimal)

Equation of the line :

m = -9/2

( 4, 4 )
( a, b )

y - b =m (x - a)
y - 4= -9/2 (x - 4)
(Multiply both sides by 2 to get rid of fraction)
2y - 4 = -9 (x - 4)
2y - 4 = -9x + 36
2y = -9x + 36 + 4
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Please feel free to ask if you have any questions
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3 years ago
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