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Ronch [10]
3 years ago
13

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to find the largest or smallest possible values fo

r the sum of X and Y.

Mathematics
2 answers:
12345 [234]3 years ago
8 0

9514 1404 393

Answer:

  smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8

  largest: 1x -9 = 8; 2y +3 = 7. total = 19

Step-by-step explanation:

If we use variables to represent the box contents, we can write ...

  • ax -b = c
  • dy +e = f

Then the values of x and y are ...

  x = (c +b)/a

  y = (f -e)/d

For positive integer values of the variables, x will always be positive, and y may or may not be negative.

<h3>Smallest sum</h3>

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for

  • 8x -3 = 4   ⇒   x = 7/8
  • 1y +9 = 2   ⇒   y = -7

For these coefficients, the sum is -6 1/8 = -49/8.

(note that the values of 'b' and 'c' can be swapped with no net effect)

<h3>Largest sum</h3>

For the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for

  • 1x -9 = 8  ⇒   x = 17
  • 2y +3 = 7   ⇒   y = 2

For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.

_____

<em>Additional comment</em>

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

eimsori [14]3 years ago
6 0

Answer:

Smallest: <u>8</u><u>x</u><u>-</u><u>3</u><u>=</u><u>4</u><u>;</u><u> </u><u>1</u><u>y</u><u>+</u><u>9</u><u>=</u><u>2</u><u>.</u><u> </u><u> </u><u>total</u><u>=</u><u> </u><u>-</u><u>4</u><u>9</u><u>/</u><u>8</u>

Largest: <u> </u><u>1</u><u>x</u><u>-</u><u>9</u><u>=</u><u>8</u><u>;</u><u> </u><u>2</u><u>y</u><u>+</u><u>3</u><u>=</u><u> </u><u>7</u><u>.</u><u> </u><u> </u><u>total</u><u>=</u><u> </u><u>1</u><u>9</u>

Step-by-step explanation:

<h3>#CARRYONLEARNING</h3>

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Answer:

<h3>A. 1 hour</h3>

Step-by-step explanation:

If one cleaning company's cost can be calculated by the expression 75 + 50x, where x is the amount of hours they spend cleaning and another cleaning company's cost can be calculated using the expression 50 + 75x, then to calculate how long each company will have to clean to cost the same amount, we will equate both expression of the company cost and solve for x as shown;

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P divided by 28 = -26
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3 years ago
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7(8 + y) simplified?
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Factor out the equation

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Step-by-step explanation:

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3 years ago
Please help!! See the attachment, please!​
topjm [15]

Answer:

946

Step-by-step explanation:

we know that

The formula to find the sum is equal to

S=(a1+an)n/2

where

a1 is the first term

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In this problem we have

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an=(98-2(11))=76

substitute the values in the formula

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