For how many ordered pairs of positive integers (x,y) is 2x+3y<6
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For how many ordered pairs of positive integers (x,y) is 2x+3y<6
1
2
3
5
7
Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
okay thanks
Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
Passes through origin means line has form y= mx, where m is some real number.
Rearranging the perpendicular line, we get y = 4x + k, so this line has a slope of 4, so the inverse reciprocal slope is 1/4.
Which means, Line 1 has an equation of y = (1/4)x
Line 1: y = (1/4)x
Line 2: y = 4x + k
Since we know they intersect at (t, t+1), this must be a solution to both equations. Since Line 2 would have infinite solutions (since k is unknown), we choose Line 1 to solve for t.
t+1 = (1/4)t
1 = (3/4)t
(4/3) = t
So, t = 4/3
Hello, RK29;669895!
Quote:
$\displaystyle \text{For how many ordered pairs of }positive\text{ integers }(x,y)\text{ is }2x+3y \,<\, 6$
. . $\displaystyle (a)\,1 \qquad (b)\;2 \qquad (c)\;3 \qquad(d)\;5 \qquad (e) 7$
For positive integers, there is one pair: $\displaystyle (1,1)$
Ah, Plato beat me to it . . .Code:
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