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Answer: 5x-2y = 16</h3>
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Explanation:
Consider the standard form Ax+By = C
Anything perpendicular to this is Bx-Ay = D. We swapped the positions of A and B, and changed the plus sign to a minus. This will ensure we get a negative reciprocal slope needed for the perpendicular line. The slope of the first line is -B/A, while the slope of the second line is A/B. The two slopes multiply to -1 assuming neither A nor B are zero.
Also, I've introduced the constant D. There may be cases when C = D, but that isn't always the case.
The given equation is 2x+5y = 10. This tells us A = 2, B = 5, C = 10.
The perpendicular line will be of the form 5x-2y = D, based on the template I mentioned above.
Plug the coordinates (2,-3) into 5x-2y = D to find the value of D
5x-2y = D
5(2)-2(-3) = D
10+6 = D
16 = D
D = 16
So 5x-2y = D updates to 5x-2y = 16
Therefore, 5x-2y = 16 is perpendicular to the original line, and this new line goes through (2,-3)
Answer:
Step-by-step explanation:
Solution
The distributive property is one of the handiest tools when factoring. You can't use it all the time, but it makes this problem so much easier. Use the distributive property to factor out the 2 from all three terms.
2(x^2 - 4x - 5)
Notice how much easier the problem got. There are only 2 integers that divide into 5. One of them is 5 and the other is one. So the solution is going to look like this
2(x 5) (x 1)
But what do you put in the space? Your choice is between a plus or a minus. Look to the middle term to find out. It is a minus 4. That means that the 5 must be minus because 5 is bigger than 1.
2(x - 5)(x 1 )
So what about the second bracket? It has to be plus. An odd number of minus signs always gives a minus. We used up the one minus we had so the one must have a plus in front of it.
2(x - 5)(x + 1 )
5x + 18y = 23
x + 3y = 2 .....multiply by -5
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5x + 18y = 23
-5x - 15y = -10 (result of multiplying by -5)
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3y = 13 <=== the resulting equation
