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Isolate the constant: \(x^2 + y^2 + 5x - 5y = 18\)

Rearrange as follows: \((x^2 + 5x) + (y^2 - 5y) = 18\)

Add 6.25 to complete the square on x, and add another 6.25 to complete the square on y. 

This gives: \((x+2.5)^2 + (y-2.5)^2 = 30.5\).

Note that the constant (30.5) is \(r^2\), meaning the area of the circle, in terms of pi, is \(\color{brown}\boxed{{30.5 \pi}}\)

Note that \((x+b)^2 = x^2 + b^2 + 2xb\)

This means that \(a = -6\)

Also, note that \(-6 \times 2xb = 72x\), because it is the only term with x. 

This means \(b = -6\)

Expanding what we have gives us: \(-6x^2 + 72x -216\), so we add 432, to make the constant positive. 

This means \(a + b + c = \color{brown}\boxed{420}\)

nvm I got it its 8 4/7 or 60/7.

1  -  [3/4 + 1/10] ==3/20 - Cranberry juice portion

The ratios are: 3/20 : 3/4 : 1/10 - in their simplest form. OR:

3/20 : 15/20 : 2/20 ==3 : 15 : 2

what do you think?

How could you start it?

I have already answered another part of this question so look at what I did.

You are welsome to get back with your thoughts.

Assume all the marbels are different.  

the number of ways that three blues can be chosen is   6C3 

the number of ways that three white can be chosen is    5C3

the number of ways that three red can be chosen is      4C3

the number of ways any 3 can be chosen is   18C3

Can you finish it?

Where are points D and E?

The area is 47*pi

DE = 21/2

 (2x+10)(x+3)<(3x+9)(x-8).

So what have you done towards solving this???

I might start by expanding both sides.

Do something yourself and get back to us if you still have problems.

Here:  https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus   

Read it for yourself.  I have no idea what it means. 

101 = 1.01e2 = 101

101^2 = 10201

101^3 = 1030301

101^9 = 1093685272684360901

101^10 = 110462212541120451001

We seem to have a pattern here, based on the pattern   the last 3 digits are most likely  201

You question is poorly presented and makes no sense.

what has a cone got to do with anything?

101^202 % 10^10==8603030201 - these are the last 10 digits.

\(\displaystyle g(x)=\sqrt[3]{\frac{x+3}{4}}\), for what value of x will g(2x) = g(x)? x=0

Adding everything gives us: \(3(w+x+y+z) = 37\)

This means \(w + x + y + z = {37 \over 3}\).

Now, you can use this to solve for w, x, y, and z, and compute the answer. 

Can you take it from here?

The blue area represents the successes (areas where the sum of x and y is less than or equal to 5)

The big rectangle represents all the possibilities. 

So, the probability is \(\text{area of blue shaded region} \over \text{area of total black rectangle}\). 

Can you take it from here?

The 

47.4

Area 1 = 8 * 6 = 48

It's 48 square centimeters

Area 2 = 6 * 4 = 24

Its 24 square centimeters

Area 3 = 1/2 * 13 * 5 = 32.5

It's 32.5 square centimeters

48 + 24 + 32.5 = 104.5

104.5 square centimeters

Area 1 = 9 * 3 = 27

It's 27 square inches
Area 2 = 7 * 5 = 35

It's 35 square inches

Area 3 = 1/2 * 9 * 4 = 18

It's 18 square inches

27 + 35 + 18 = 80 square inches

Cross multiply: \(3(a+2) = b(a+5)\)

Simplify: \(3a + 6 = ab + 5b\)

Isolate the constant: \(3a -ab-5b= -6\)

Factor out a: \(a(3-b) - 5b = -6\)

Add 15 to both sides: \(a(3-b) - 5b + 15 = 9\)

Factor out b: \(a(3-b) + 5 (3 - b) = 9\)

Combine like terms: \((a+5)(3-b) = 9\)

Note that \(a + 5\) must equal 1, 3, or 9, so \(3- b\) can equal the other factor of 9.

Thus, there are \(\color{brown}\boxed{3}\) cases that work.

Note that the cases are (4, 2), (-2, 0), and (-4, -6)

Original number of students==5

5 C 4 ==5 committees

5+1 ==6 students

6 C 4 ==15 committees [or 3x when there were only 5 students]