The first method is substitution. This is when the x or y value that is known is substituted into one of the equations. This should be done when you can easily see or find the x or y value.
Example: x = 3, and x + 8y = 30.
The x was given in the first equation (x = 3), and can therefore be substituted into the other equation to find y.
The next method is elimination. This is when you add the two systems together and eliminate either the x values or the y values. This should be done when there are opposite signs of the same number in both equations.
Example: y - 3x = 24, and 2y + 3x = 7
In the first equation you have -3x, and in the second you have 3x. If you were to add the two equations, the x values would cancel out and you would be left with:
y + 2y = 24 + 7
And then you could solve for y.
The last method is to graph both equations and to see at which point the lines intersect.
True these are all equivalent.
Let me tell you a secret!
You know how the formula for Circumference is
<span>C = 2πr
</span>
Where r is the radius?
The reason why this formula works the way it does is because of what <span>π IS.
</span><span>π is the ratio of ANY circle's Circumference to it's Diameter.
So you can think of </span><span>π like this:
</span>
Circumference / Diameter.
2r is the same as the diameter. So what you are doing is canceling out the diameter. Similar to what you do in algebra I to solve for x. Then you are just left with the circumference. That's pretty neat!
So, let's get to it!
2<span>πr
</span>
Sadly, you'll most likely need to use a calculator for this problem, but if you are not permitted one then replace <span>π with 3.14.
</span>
What is r?
r = diameter / 2
r = 12 / 2
r = 6
2<span>π6
</span>
If you are allowed to use a calculator then plug it in to it. If not then start doing some long multiplication!
37.699ft
This is a neat little question. I don't think I've seen it before.
Step one
=======
Find c
3^2 + 4^2 = c^2
9 + 16 = c^2
c^2 = 25
c = 5
Step 2
====
Set up your first equation for b^2
a^2 + 4^2 = b^2 from triangle XWY
Step 3
=====
Set up your second equation for b^2
25 +b^2 = (a + 3)^2 from triangle XWZ
Step 4
=====
Put the results of Step 2 into step 3 and solve
25 + a^2 + 16 = (a + 3)^2 Collect the like terms on the left.
41 + a^2 = (a + 3)^2 Expand the brackets on the right
41 + a^2 = a^2 + 6a + 9 Transfer the 9 to the left.
32 + a^2 = a^2 + 6a Subtract a^2 from both sides.
6a = 32 Divide by 6
a = 32 / 6
a = 5 2/6
a = 5 1/3
Answer:
C is correct
Step-by-step explanation:
