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ra1l [238]
3 years ago
8

Line a and b are perpendicular lines.If line a is represented by y=s/t x+10 and line b is represented by y=q/r -4 where s,t,q an

d r are integers and t and r are not equal to zero which statement is always true
Mathematics
1 answer:
alekssr [168]3 years ago
7 0

Answer:

The options are not shown, so i will answer in a general way.

First, for a line of the form:

y = a*x + b

All the perpendicular lines will have a slope of -(1/a), then we can write a general perpendicular line as:

y = -(1/a)*x + c.

In this problem we have the perpendicular lines:

y=(s/t)*x+10

y = (q/r)*x - 4

Because those lines are perpendicular, we must have that:

(q/r) = -(1/(s/t)) = -(t/s)

q/r = -t/s

and we knew that s, t, q and r are integers (where t and r can not be equal to zero), and because of this relation, where we can see that in the denominator at the right we have the integer s, we can conclude that s can not be zero (we can not divide by zero).

And we know that t and s are both different than zero, then:

-t/s ≠ 0.

This means that:

q/r ≠ 0

And from this, we can conclude that q is different than zero.

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Answer:

465

Step-by-step explanation:

Since we are looking for the the number of combinations to have 2 different flavors in the ice cream, we can use the formula for combination.

_{n}C_{k}=\dfrac{n!}{k!(n-k)!}

Our variables are:

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_{31}C_{2}=\dfrac{31!}{2!(31-2)!}

_{31}C_{2}=\dfrac{31!}{2!29!}

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_{31}C_{2}=465

The number of possible combinations of having 2 different flavors out of 31 different flavors is 465.

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Step-by-step explanation:

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