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Mrac [35]
3 years ago
14

Using the digits 1 to 9 at most one time each, fill in the boxes to find the largest (or smallest) possible values for x.

Mathematics
1 answer:
Mice21 [21]3 years ago
8 0

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.

Smallest sum

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)

Largest sum

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.

_____

Additional comment

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

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Answer:

a)   n (A) = 7

Step-by-step explanation:

Here, set A =  {2,5,7,9,13, 25, 26)

Noe, for any set A,

n (A) is defined as he total number of elements in the set A.

or, n(A) = CARNALITY OF SET A

Here,the number of elements in set A = 7

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Jonah is going to the store to buy candles. Small candles cost $2.50 and large candles cost $7.00. He needs to buy at least 20 c
artcher [175]

<em><u>The system of linear inequalities are:</u></em>

a + b \geq 20\\\\2.50a + 7b\leq 80

<em><u>Solution:</u></em>

Let "a" be the number of small candles bought

Let "b" be the number of large candles bought

<em><u>He needs to buy at least 20 candles</u></em>

Therefore, number of small candles and number of large candles bought must be at least 20

Thus, we frame a inequality as:

a + b \geq 20

"at least" means greater than or equal to

Here, we used "greater or equal to" symbol because, he can buy 20 candles or more than 20 candles also

From given,

Cost of 1 small candle = $ 2.50

Cost of 1 large candle = $ 7

<em><u>He can spend no more than 80 dollars</u></em>

Which means, he spend maximum 80 dollars or less than 80 dollars also

So we have to use "less than or equal to" symbol

<em><u>Thus, we frame a inequality as:</u></em>

Number of small candles bought x Cost of 1 small candle + number of large candles bought x Cost of 1 large candle \leq 80

a \times 2.50 + b \times 7 \leq 80\\\\2.50a + 7b\leq 80

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a + b \geq 20\\\\2.50a + 7b\leq 80

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Nutka1998 [239]

Answer:

Table 1(red)

Step-by-step explanation:

A proportional relationship will have a constant of proportionality between y and x all through the data given.

Constant of proportionality, k = y/x

Table 1 (red):

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This doesn't have a constant of proportionality, k, that is the same all through in the given table of values. Therefore, it doesn't show any proportional relationship between x and y

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