proyaop

e = amount of cholestrol in an egg

c = amount of cholestrol in a cupcake

p = amount of cholestrol in a slice of pizza

e + c + p = 300

Since cupcakes is plural, I will assume cupcakes = 2 "cupcake"

2c + p = 82

2e + c = 568

Adding both of those two equations together, we get

2e + 3c + p = 650

Subtracting the first equation from our new equation, I obtain

e + 2c = 350.

Using elimination, I get

3e = 786

e = 262 

c = 44

We can plug the values of -7 and 2 into the equation and we get -7a + 2b = 3. The slope of a standard form equation is -a/b, and the sloper of x + 3y = -5 is -1/3, so a/b = 1/3, 3a = b. -7a + 2(3a) = 3. -a = 3, a = -3. b = -9.

Thus the value of B - A = -6.

First combine like terms:

x^2 + 9x + 18 = 0 -> (x + 6)(x + 3) = 0.

Either x + 6 or x + 3 = 0 (not both), so x = -6 and x = -3. 

If -6 and -3 are the values of u and v, plugging in we have u/v + v/u, -6/-3 + -3/-6 = 2 + 1/2 = 2.5

Take the average of the x1 and x2 coordinates, and the average of the y1 and y2 coordinates:

Midpoint of PQ = (-1, -6)

First we combine like terms: (I will not be using quadratic formula or a calculator)

x^2 + 6x + 6 = 0 

First we can use sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2). Then we can see by using Vieté's Formula, it will be easy to solve.

The sum of the roots = -6 = a + b

The product of the roots = 6 = ab

a^2 + b^2 = (a + b)^2 - 2ab

a^3 + b^3 = (a + b)[(a + b)^2 - 2ab - ab]

Plugging in the values, we have:

(-6)[(-6)^2 - 2(6) - (6)]

-6(36 - 18)

-6(18)

a^3 + b^3 = -108

Well... the parenthesis are pretty useless, if we remove them it turns from +(-66) to -66. The first and last terms of the expression are 75 and -75. The common difference is 3. So the middle term will be 0. Then we can deduce that every term cancels out, and then the answer is ZERO!!!

The formula for compound interest is A = P(1 + r/100)^nt where A is the answer, P is the principle amount which is 300$, r is the compounded rate, n is the amount of times compounded per year, and t is the number of years.

Plugging in our values we have A = 300(1 + 0.05)^4. The answer is 364.65$

If the three youngest students in the class are triplets, then I think the problem is implying we can assume they are identical. If that is so, we can group those 3 into "1 person" or 1 variable, named "a". The other 3 students will be "b, c, d". Now it is stars and bars and we can do how to distribute 13 stickers among 4 people. a + b + c +d = 13, and a, b, c, and d are nonnegative, we do (13 + 4 - 1 choose 4 - 1)

The answer is 16 choose 3 or 560.

:)

First, we use the distribution property by opening the parenthesis around x + 7. Since 5 has to multiply both x and 7, we have 5x + 35 = 42

Then you want to isolate the variable so we subtract 35 from both sides of the equation, and we obtain 5x = 7. Dividing both sides by 5 we achieve x = 7/5 or 1.4.

:)

We want to try to minimize the cases to minimize mistakes. We have 4 cases:

Case1 = no touchdowns

Case2 = 1 touchdown

Case3 = 2 touchdowns

Case4 = 3 touchdowns

Case4: If there are 3 touchdowns, then that means there is one possible way since you must have 3 touchdowns and one field goal. 

Case4 = 1 way

Case3: If there are 2 touchdowns, we are left with 10 points. 3x + 2y = 10. If x = 0, then y = 5. If x = 1, then y is invalid. If x = 2, then y = 2. If x = 3, y is invalid. Thus, there are 2 ways if for Case3.

Case3 = 2 ways

Case2: If there is 1 touchdown, we are left with 17 points. 3x + 2y = 17. If x = 0, then y is invalid. If x = 1, then y = 7.  If x = 2, then y is invalid. If x = 3, then y = 4. (We notice that x has to be odd) If x = 5, then y = 1. If x = 7, then y is negative --- impossible...

Case2 = 3 ways.

Case1: If there are no touchdowns, we have to make do with 24 points, 3x + 2y = 24. x = 0, y = 12. (x must be even) x = 2, y = 9. x = 4, y = 6. x = 6, y = 3. x = 8, y = 0. Case1 has 5 cases (x = 0, 2, 4, 6, 8). 

Case1 = 5 ways.

Hence, we have 1 + 2 + 3 + 5 ways = 11 ways.

proyaop :)