Answer:
5.656854249 cm
Step-by-step explanation:
Use the Pythagorean theorem to solve this (assuming that the bottom of the cup is a right angle). 
. a and b are sides, and c is the hypotenuse.
The length of the pencil would be the hypotenuse (c), and how tall the cup is (7 cm) would be one of the sides (a). The diameter of the cup, would be the other side (b).
Plug this into the Pythagorean theorem to get the equation: 
. From here, we can find the diameter of the cup by isolating b - remove everything from the left side, but remember, what you do to one side you must do to the other.
First, solve all of the exponents: 
Second, subtract 49 from both sides: 
This cancels out the 49 on the left.
Lastly, square root both sides: 
This cancels out the exponent on the left.
In conclusion, the diameter of the cup is 5.656854249 centimeters.
Answer:
x² + 23x + 49
Step-by-step explanation:
Since the area of a rectangle is: A = l x w, where l = length and w = width, we can find the overall area of the shaded region by multiplying the entire area and subtracting the smaller area of the unshaded square:
(2x + 5)(x + 10) - (x + 1)² or (2x + 5)(x + 10) - (x² + 2x + 1)
Distribute/FOIL:
2x² + 20x + 5x + 50 - x² - 2x -1
Combine like terms:
x² + 23x + 49
2x - 5 + 3x = 3 (collect like terms)
2x + 3x = 3 + 5 (add the like terms)
5x = 8 (divide by 5 both sides to get x)
x = 8,5
X = 1.6
6,000,000,000+400,000,000+30,000,000+5,000,000+900,000,20,000+100+70+8
The answer should be 3x^2 -13x+7.
