What are the solutions of 4x2 - 16X = 16x - 39
1 answer:
Answer:
x = , x =
Step-by-step explanation:
Given
4x² - 16x = 16x - 39 ( subtract 16x - 39 from both sides )
4x² - 32x + 39 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is
product = 4 × 39 = 156 and sum = - 32
The factors are - 26 and - 6
Use these factors to split the x- term
4x² - 26x - 6x + 39 = 0 ( factor the first/second and third/fourth terms )
2x(2x - 13) - 3(2x - 13) = 0 ← factor out (2x - 13) from each term
(2x - 13)(2x - 3) = 0
Equate each factor to zero and solve for x
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
2x - 13 = 0 ⇒ 2x = 13 ⇒ x =
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Answer:
Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.
Step-by-step explanation:
Let B, C, F and R represent Braeburn apples, Cortland apples, Fuji apples, and Rome apples respectively.
We have been given that Morgan family picked a total of 360 apples. We can represent this information in an equation as:
We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:
We are told that Morgan family picked twice as many Cortland as Rome, that is:
We are told that Morgan family picked 50% more Fuji than Rome, that is:
Upon substituting equation (4) in equation (2), we will get:
Now, each apple in in terms of Rome apples, so we will get:
Let us solve for R.
Therefore, Morgan family picked 48 Rome apples.
Upon substituting in (3), we will get:
Therefore, Morgan family picked 96 Cortland apples.
Upon substituting in (4), we will get:
Therefore, Morgan family picked 72 Fuji apples.
Upon substituting in (2), we will get:
Therefore, Morgan family picked 144 Braeburn apples.