The straight line ℓ is perpendicular to the line y + 2x = 9 and passes through the point p(4, 3). find the x-intercept of ℓ.

1 answer:

8 0

The slope of the line l is the opposite reciprocal of y+2x=9. Rearranged the equation to y=9-2x and we get a slope of -2. The opposite reciprocal of -2 is 1/2.

y-y=m(x-x)
y-3=.5(x-4)
y=.5x+1

At the x-intercept, y=0, so
0=.5x+1
-1=.5x
x=-2

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There are exactly 20 students currently enrolled in a class. How many different ways are there to pair up the 20 students, so th

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Answer:

The students can be paired up in 654,729,075 ways

Step-by-step explanation:

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If the two people in a pair swap positions. In mathematics, it is considered as a different arrangement. This can be done $2^{10} ways$ since there are 10 pairs We will have to divide by this.

If the 10 pairs can swap places with each other, it will form another pair. As a matter of fact, the 10 pairs can swap pairs with each other all they like. This can be done in 10! ways. we will also have to divide by this.

Hence the total number of ways = $\frac{20!}{2^{10}\times 10! } = 654,729,075 ways$