Math question

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1

<p>Can somebody help explain how they got the answer for this:
In the xy-plane, line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t, t+1), what is the value of t?</p>

<p>Answer: -4/3</p>

<p>Is there a shortcut for finding this answer:
If the average of x and y is k, which of the following is the average of x, y, and z?</p>

<p>Answer: (2k+z)/3</p>

<p>And are there shortcuts for problems like this:
When 15 is divided by the positive integer k, the remainder is 3. For how many different values of k is this true?</p>

<p>Answer: Three</p>

<p>these seem to be the only problems i get wrong on my practice tests, the last one i got right, but it took me a while because i plugged in numbers...any hints as to how to do these?
Thanks!!!!</p>

2

<p>1) First make the given equation look like y=kx+b => (y=-4x+k).
As you should know, a slope of a perpendicular line is negative reciprocal of the given line’s slope => (1/4).
As we are told, line 2 passes through origin (0,0), which means, that its y-intercept = 0, k=0.
So, the equation of line 2 is (y=x/4)
Plug in (t;t+1) to find t. => (t+1=t/4) => (4t+4=t) => (3t=-4) => (t=-4/3)</p>

<p>2) Write down the equation: ((x+y)/2=k) => (x+y=2k).
Now, calculate: ((x+y+z)/3) = ((2k+z)/3)</p>

<p>3) I’m not sure about shortcuts existing, but it should not take much time to plug-in. Because dividing 15 by smth gives a remainder, this something is less, than 15. You can logically exclude some numbers: 0 (no dividing by 0); 1,3,5 (those are 15’s factors).</p>

3

<p>thank you soo much, this is greatly appreciated</p>