Find all points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10
1 answer:
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Answer:
x = - , x =
Step-by-step explanation:
Given
x² - x - = 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
You can do this one simply just by plugging in the values of x and y for each answer.
Note: (0,5) is just a way to right x=0 and y=5
Try answer A (0,5)
This is not true. 5 is not bigger than 5 so A is not the answer
Try answer B (1,7)
This is true so answer B works!
Might as well try answer C (7,1)
1 is obviously not greater than 12 so C does not work
The answer is B (1,7)
Note: (0,5) is just a way to right x=0 and y=5
Try answer A (0,5)
This is not true. 5 is not bigger than 5 so A is not the answer
Try answer B (1,7)
This is true so answer B works!
Might as well try answer C (7,1)
1 is obviously not greater than 12 so C does not work
The answer is B (1,7)