Answer:
The area of one slice of pizza is 18 in²
Step-by-step explanation:
First we have to know that the 360 ° representing the circle expressed in radians are expressed as 2π
Now we must calculate the area of the circle
a = π * r²
a = π * (12in)²
a = 144π in²
Now that we have the area of the circumference we multiply it by (π/4) / (2π)
144π in² * (π/4) / (2π) =
144 in² * 1/8 =
18 in²
The area of one slice of pizza is 18 in²
You start with: (assuming x equals the cost to enter and y the cost of going on the rollercoasters.)
x+5y=35
x+11y=59. Multiply the top equation by -1, and subtract the equations, giving you -6y=-24, divide by -6 into both sides of the equation, to get y=4. Now replace y in one of the original equations (I recommend x+5y=35) and solve for x, giving you x=15
The cost for entering is 15 dollars, while each coaster is 4 dollars more. You could simplify this by changing y into x and making it slope-intercept form, to track your cost. y=4x+15, so it has a slope of 4, and a y-intercept of 15. This answer should give you a good grade on a test.
![5ab^{3} +7-3a^{2} b ^{2} +a^{3}b+10](https://tex.z-dn.net/?f=5ab%5E%7B3%7D%20%2B7-3a%5E%7B2%7D%20b%20%5E%7B2%7D%20%2Ba%5E%7B3%7Db%2B10)
can be simplified to by adding the 7 and 10 to get
![a^{3}b-3a^{2} b ^{2}+ 5ab^{3} + 17](https://tex.z-dn.net/?f=a%5E%7B3%7Db-3a%5E%7B2%7D%20b%20%5E%7B2%7D%2B%205ab%5E%7B3%7D%20%2B%2017)
.
![5ab^{3}+3a^{2}b^{2}+a^{3}b -10](https://tex.z-dn.net/?f=5ab%5E%7B3%7D%2B3a%5E%7B2%7Db%5E%7B2%7D%2Ba%5E%7B3%7Db%20-10)
cannot be simplified any more by combining like terms.
By distributing the 2b into the parentheses, you can simplify the expression:
![5ab^{3}+2b(3ab^{2})+a^{3}b-10\\ 5ab^{3}+6ab^{3}+a^{3}b-10\\ 11ab^{3}+a^{3}b-10](https://tex.z-dn.net/?f=5ab%5E%7B3%7D%2B2b%283ab%5E%7B2%7D%29%2Ba%5E%7B3%7Db-10%5C%5C%0A5ab%5E%7B3%7D%2B6ab%5E%7B3%7D%2Ba%5E%7B3%7Db-10%5C%5C%0A11ab%5E%7B3%7D%2Ba%5E%7B3%7Db-10)
Here you can just add:
![5a^{3}b^{3}+3a^{2}b^{2}+a^{3}b^{3}-10ab\\ 6a^{3}b^{3}+3a^{2}b^{2}-10ab](https://tex.z-dn.net/?f=5a%5E%7B3%7Db%5E%7B3%7D%2B3a%5E%7B2%7Db%5E%7B2%7D%2Ba%5E%7B3%7Db%5E%7B3%7D-10ab%5C%5C%0A6a%5E%7B3%7Db%5E%7B3%7D%2B3a%5E%7B2%7Db%5E%7B2%7D-10ab)
Thus, the only expression that cannot simplify any more using adding like terms is the second,
![5ab^{3}+3a^{2}b^{2}+a^{3}b -10](https://tex.z-dn.net/?f=5ab%5E%7B3%7D%2B3a%5E%7B2%7Db%5E%7B2%7D%2Ba%5E%7B3%7Db%20-10)
.
Answer:
50
Step-by-step explanation:
50 / 10 = 5
5 x 3 = 15