jfan17

This is kind of nitpicky but "pie" is not correct mathematically speaking; that's the food pie(the one that you eat). The correct way to spell it mathematically is "pi" but that's just something on the side. Getting to the problem at hand:

the circumference given is 15pi centimeters. The definition of the circumference of a circle is equal to: 2pi * r , with r being the radius. If we use that in the context of our problem, that gives us:

2 * pi * r = 15 * pi. Dividing by pi on both sides, we get:

2r = 15

r = 15/2

Now that we have our radius, we can find the area. The area of a circle is equal to: pi * r^2

Since we already have the radius, the area of the circle is equal to:

pi * (15/2)^2, which expands out to:

225/4 * pi

First, there are 5 + 6 + 4 +3 + 2 = 20 marbles total in the bag.

the probability of getting a brown, an orange, and another orange is equivalent to:

the probability of a brown * the probability of 2 oranges.

The probability of a brown marble is just (5 choose 1), or 5 ways to choose it.

Next, the number of ways to get 2 orange marbles is just (2c2), or 1.

Finally, the total number of ways to choose three marbles(our divisor) is (20 choose 3), since you're picking 3 out of 20 total 

This gives us: 

(5c1) * (2c2) / (20c3) =

5 / 1140 = 

1/228

This is just combining like terms. Think about it. if you have a constant, you look for other constants, and then add or subtract as indicated in the problem. You do the same with linears and squares; it's just addition and subtraction. 

Start by looking at the constant terms of both equations, which are g and -16. We know that when we multiply the two polynomials together, the constant terms of the new equaion is only affected by the constant terms of the previous equations. In other words, g * (-8) = -16. This means that g = 2. Next, to find the value of h, we can look at the coefficient of "d" in the product. we know that the coefficient of d in the product comes from multiplying a linear "d" with a constant. That means that (-3d) * (-8) + hd * g = 14d. This expands to:

24d + hd*g = 14d, and subtracting on both sides, we get:

hd * g = -10 d

Remember that we already found that g = 2, giving us

hd * 2 = -10 d

hd = -5d 

h = -5.

Since the problem asks for g + h, we get :

2 - 5 = -3

Sorry I don't know if it's just me, but please check your formatting when you post a question. I can't see any values or numbers that are supposed to be in the problem.

First the problem states that nadia and olivia can clean a horse stable in 8 hours. That means that every hour, they complete 1/8 of the cleaning required for the stable. Next, the problem tells us that if Nadia cleans it herself, it would've taken her 12 hours to do it, meaning every hour, she completes 1/12 of the stable. From here on out, we can get how long olivia takes to clean the stable if we subtract the work efficiency of their combined cleaning and Nadia's cleaning alone. This is just 1/8 - 1/12, which is equal to 1/24. This means that every hour, Olivia cleans 1/24 of the stable, meaning she takes 24 hours to clean the stable by herself. (wow that's a lot of time)

Let's name the angle corresponding to one of the isosceles sides "x". With this, we have 2 base angles of "x" degrees(on the side of length 40), and a third angle of measurement 180-2x degrees. By dropping an altitude to side AC, we form two right triangles, both of which are congruent to each other AAS. Since the problem asks for the sin of ACB, we need only the opposite side of the right triangle, which is the altitude, divided by the hypotenuse. Because the two right triangles formed are congruent, the base of 40 is split into two halves of length 20. We then realize that this forms a 3 - 4 -5 triangle with a scale factor of 5:

Meaning that the length of the altitude of AC is 15 (3 * 5). Now that we have the opposite side, sine is just opposite / hypotenuse, which is 15 / 25 giving us our final answer of 3/5

First, let's define slope-intercept form: it's the form that's usually taught first in math with coordinates(at least in my experience):

y = mx + b, where m is the slope, and b is the y-intercept.

The problem already gives us a slope of -2, so we can already write part of our desired equation:

y = -2x + b

Next, the problem gives us a point of (-1, 8). Here, we can plug the point into the equation, with the respective x and y values, giving us:

8 = -2 * (-1) + b

This simplifies to

8 = 2 + b, or 

b = 6

Finally, we have our desired equation, which is y = -2x + 6!(not factorial)