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Lilit [14]
3 years ago
12

Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive. What is the sum of the factors

?
Mathematics
1 answer:
statuscvo [17]3 years ago
7 0

Answer:

13

Step-by-step explanation:

Two factors of -48... that means two numbers which multiplied together give a result of -48, like -6 and 8 for example.

The difference of those two factors is -19.  There not that many possible factors for -48, so if we list them we'll be able to spot a pair with a difference of 19.

A first list of factors for -48 is: -1 and 48, -2 and 24, -3 and 16, -4 and 12, -6 and 8.

We can create another list by inverting the signs: 1 and -48, 2 and -24, 3 and -16, 4 and -12, 6 and -8.

The question says the difference of the two factors is 19...  can you spot in each list a pair of factors having a difference of 19?   I see -3 and 16 and also 3 and -16.

The question also say the one of the greatest absolute value is positive... so that  means it's a pair with +16, not -16.

The pair of factors we're looking for is then -3 and 16. They are factors of -18, they have a difference of 19, and the one with the greatest absolute value is positive.

The sum of -3 and 16 is 13.

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Answer: Kara should have written the proportion in step 1 as;

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Step-by-step explanation: The two similar triangles are given with the following dimensions;

Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.

For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures  1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.

Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;

VX = ZX

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What Kara did was as follows;

VX/ZY = VW/ZX

Which translates to 14/72 = 12/x

This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.

The correct step should therefore have been;

VW/ZY = VX/ZX

12/72 = 14/x (Step 1)

12x = (72) (14) {Step 2}

x = 1008/12 (Step 3)

x = 84 (Step 4)

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