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Mathematics

1 answer:

lara31 [8.8K]3 years ago

5 0

One's a parabola, one's a line, so they should intersect in two places.

Table of values:

for x = 1,2,3,4,5,6
f(x) = 3,0,-1,0,3,8
g(x) = -1,0,1,2,3,4

Now all you need to do is look where they have the same (x,y) values.

This is at (2,0) and (5,3).

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Find two numbers whose sum is 25 and the sum of whose reciprocals is 1/6

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Answer:

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Step-by-step explanation:

Let 'x' and 'y' are the numbers we need to find.

x + y = 25 (two numbers whose sum is 25)

(1/x) + (1/y) = 1/6 (the sum of whose reciprocals is 1/6)

The solutions of the this system of equations are the numbers we need to find.

x = 25 - y

1/(25 - y) + 1/y = 1/6 multiply both sides by 6(25-y)y

6y + 6(25-y) = (25-y)y

6y + 150 - 6y = 25y - (y^2)

y^2 - 25y + 150 = 0 quadratic equation has 2 solutions

y1 = 15

y2 = 10

Thus we have :

First solution: for y = 15, x = 25 - 15 = 10

Second solution: for y = 10, x = 25 - 10 = 15

The first and the second solution are in fact the same one solution we are looking for: the two numbers are 10 and 15 (since the combination 10 and 15 is the same as 15 and 10).

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Step-by-step explanation:

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