Answer:
and
Step-by-step explanation:
The standard equation of a circle is 
where the coordinate (h,k) is the center of the circle.
Second Problem:
- We can start with the second problem which uses this info very easily.
- (h,k) in this problem is (-2,15) simply plug these into the equation.
. - We can also add the radius 3 and square it so it becomes 9. The equation.
- This simplifies to .
First Problem:
- The first problem takes a different approach it is not in standard form. But we can convert it to standard form by completing the square.
first subtract 37 from both sides so the equation is now 
.- by adding
to both the x and y portions of this equation you can complete the squares. 
and 
which equals 49 and 4. - Add 49 and 4 to both sides and the equation is now:
You can simplify the y and x portions of the equations into the perfect squares or factored form 
and 
. - Finally put the whole thing together. .
I hope this helps!
The value of any number multiplied by 1 stays exactly the same, right? Well, as it turns out, 1 can be written as the fraction 7/7, or the fraction 8/8, or 9/9, 10/10, 11/11... I could go on and on to infinity, but there's a pattern there. 1 simply means "1 whole," or "all of it." "All of it" looks different in different denominators, but the core idea is the same: if we split something into n pieces, "all of it" means we have all n of those pieces. The numerator and denominator will always been the same, no matter how we want to represent 1.
What does this have to do with our problem? Well, we don't want to change the <em>value </em>of our fraction, we just want to change its <em>label</em>. So what we're going to do is multiply it by 1, but we're going to make sure to pick the right <em>label</em> for that 1.
7/12 x 1 = 7/12. This will be true no matter what. Let's see which of these options actually fit the bill:
Can we get this fraction by multiplying 7/12 from some form of 1? Well, 14 = 7 x 2, so let's see what we get if we pick the form 1 = 2/2:
Nope, not quite. 14/28 is <em>not </em>equivalent to 7/12.
What about 21/36? 21 = 7 x 3, so let's give the form 1 = 3/3 a shot:
There we go! All we did there was <em>relabel </em>7/12 by multiplying by form of 1. Since we never changed its value, we can stop our search here and conclude that 21/36 is equivalent to 7/12.
Answer:
The answer is 9/20
Step-by-step explanation:
If you do order of operations, you divide 6 and 2 getting 3. Add 42 and 3. 45 is the answer.
Given the literal equation, a/e - d = c:
To solve for "a", add "d" to both sides:
a/e - d + d = c + d
a/e = c + d
Next, multiply both sides by "e" to isolate "a"
(e) a/e = [c + d] (e)
Distribute "e" into the bracket to arrive at the final answer:
a = ce + de
