Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?
Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).
Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:
x + y = 80 . . . 1)
Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:
0.65x + 0.9y = 68 . . . 2)
We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:
0.65x + 0.65y = 52 . . . 3)
Subtract equation 3 from 2 and solve for y:
0.25y = 16
y = 16/0.25 = 64
y = 64 pints
Put y = 64 in equation 1:
x + 64 = 80
x = 80 - 64 = 16
x = 16 pints
Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.
If you're looking for the gradient then it will be y=4x otherwise please write the question!
The factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)
<h3>Factoring a Quadratic expression </h3>
From the question, we are to determine the each of the factors of the given quadratic expression
The given quadratic expression is
2x² - 4x - 16
Factoring
2x² - 4x - 16
First, factor out 2
That is,
2(x² - 2x - 8)
Now, we will factor x² - 2x - 8
x² - 2x - 8
x² - 4x + 2x - 8
x(x - 4) +2(x -4)
(x +2)(x -4)
Thus,
2x² - 4x - 16 = 2(x +2)(x -4)
Hence, the factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)
Learn more on Factoring a quadratic expression here: brainly.com/question/52959
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