09.03.2020

The expressions 2(x^2 – 4x– 21) - (x – 7)(x + 77) and ( x– 7)(x + k) are equivalent. What must be the value of k?

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17.12.2021, solved by verified expert
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Answer: k = -71
Explanation:
2(x^2 – 4x– 21) - (x – 7)(x + 77) = ( x– 7)(x + k)
2(x^2 – 4x– 21) - (x – 7)(x + 77) = ( x– 7)(x + k)
2x^2 −8x−42−(x−7)(x+77) = ( x– 7)(x + k)
2x^2−8x−42−(x^2+70x−539) = ( x– 7)(x + k)
2x^2−8x−42−x^2-70x+539 = ( x– 7)(x + k)
x^2−8x−42−70x+539 = ( x– 7)(x + k)
x^2−78x+497 = ( x– 7)(x + k)
x^2−78x+497 = x^2+kx-7x-k*7
−78x+497 = kx-7x-k*7
-71x+71*7 = k(x-7)
-71(x-7) = k(x-7)
-71 = k
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Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
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