Bill's Responses in WyzAnt Answers

The 13th Amendment to the US Constitution outlaws slavery and involuntary servitude, except as punishment for a crime. 

Hi Mercedes!  Try to write down what you know...  

First, name things with single letters.  For example, let's name each side of the square as "s", and each side of the triangle as "t" (easy to remember t=triangle and s=square :-)

Now translate "side of an equilateral triangle is 2 inches shorter than the side of a square":

t = s-2  (triangle side t is 2" less than square side s)

And, "perimeter of the square is 30 inches more than the perimeter of the triangle":

Perimeter of a square = 4s (add all 4 sides together, and since all sides are the same, = 4s)

Perimeter of a triangle = 3t (add all 3 sides together, and since all sides are the same, = 3t)

So now we have 4s = 3t + 30 (square perimeter is 30" longer than triangle perimeter)

We have two unknowns, s and t.  But we also have two equations (in bold, above).  So we fix that by substituting one unknown with its counterpart using the other unknown:

into 4s = 3t + 30, we can substitute  T = s - 2, so 4s = 3(s-2) + 30;  4s = 3s - 6 + 30,

so 4s - 3s = 3s - 3s + 30 - 6, or s = 24

Now put that 24 back into t = s - 2; t = 24 - 2;   t = 22.

Let's check, is that correct?

triangle side of 22 is 2" shorter than the square side of 24 - check.

The triangle perimeter = 3t = 3(22) = 66, and the square perimeter = 4s = 4(24) = 96;  96 - 66 = 30 - check.

You don't need to cite a copyright date for a website or link - it's perpetual and continual.  Just cite the link URL and the date you obtained the info, plus the name of the tutor who provided it.

Hi Kiona, as I bet you already know, point coordinates (locations on the X and Y axes of a graph) are listed as X first, then Y.  The first set (5,3) means at that point, X=5 and Y=3.  The second set (5,-3) means that X=5 and Y=-3

Usually the X-axis is a horizontal line, and the Y-axis is vertical, crossing the X-axis perpendicular (at right angles).  The point (0,0) is where the X and Y axes meet each other (cross).  

Since both points have X=5, both points are equally distant (+5) from the Y-axis, and therefore a line through those two points is a straight line parallel (same direction as) the Y-axis, crossing the X-axis at X=+5.  Draw it yourself so you can see it - makes it much easier to understand!

One point is +3 above the X-axis, and the other point is -3 below the X-axis.  Therefore, the total distance must be 6.

Another way, using Simultaneous Equations:

Numbers of tickets: Student (s) tickets + General Admission (g) tickets = 450, or s + g = 450

Numbers of dollars: 4s + 6g = 2340

4s + 6g = 2340

s + g = 450. Multiply the bottom equation by -4: -4s - 4g = -1800

Now we have:

4s + 6g = 2340

-4s - 4g = -1800

=========== (add them together)

+2g = 540

or g = 270, the number of General Admissions tickets sold

s + g = 450; s = 450 - g; s = 450 - 270, so s = 180, the number of Student tickets sold

Check the dollar amounts:

4s + 6g = 2340

4(180) + 6(270) = 2340; 720 + 1620 = 2340, and 2340 = 2340, so we know we are correct.