Answer:
B. 0.025
Step-by-step explanation:
Answer: Abigail can make about 16 candles because 0.4 of a candle would not make an entire candle.
Step-by-step explanation:
For the Wax, it’s
V=Bh
V= l*w*h
= 15 cm * 11cm * 18 cm
= 2,970 cm^3
For the Mold, it’s
V=Bh
= r^2h
= * (3.1 cm)^2 * 6
= about 181 cm^3
Then you divide to find out how many candles you can make.
2,970 cm^3/181= 16.4
Hope this helps!
7
Hope this helped hope you have a good day
Consider the expression
![\frac{x^{2} -x-6}{ x^{2} -4}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%5E%7B2%7D%20-x-6%7D%7B%20x%5E%7B2%7D%20-4%7D%20)
To factorize the expression in the denominator we use difference of squares:
![x^{2} -4=x^{2} - 2^{2} =(x-2)(x+2)](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-4%3Dx%5E%7B2%7D%20-%202%5E%7B2%7D%20%3D%28x-2%29%28x%2B2%29)
To factorize
![x^{2} -x-6](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-x-6)
we use the following method:
![x^{2} -x-6=(x-a)(x-b)](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-x-6%3D%28x-a%29%28x-b%29)
where a, b are 2 numbers such that a+b= -1, the coefficient of x,
and a*b= -6, the constant.
such 2 numbers can be easily checked to be -3 and 2
(-3*2=6, -3+2=-1)
So
![x^{2} -x-6=(x-a)(x-b)=(x+3)(x-2)](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-x-6%3D%28x-a%29%28x-b%29%3D%28x%2B3%29%28x-2%29)
![ \frac{x^{2} -x-6}{ x^{2} -4}= \frac{(x+3)(x-2)}{(x-2)(x+2)}= \frac{x+3}{x+2}](https://tex.z-dn.net/?f=%0A%20%5Cfrac%7Bx%5E%7B2%7D%20-x-6%7D%7B%20x%5E%7B2%7D%20-4%7D%3D%20%5Cfrac%7B%28x%2B3%29%28x-2%29%7D%7B%28x-2%29%28x%2B2%29%7D%3D%20%5Cfrac%7Bx%2B3%7D%7Bx%2B2%7D%20)
![\frac{x+3}{x+2}= \frac{x+2+1}{x+2}= \frac{x+2}{x+2}+ \frac{1}{x+2}=1+ \frac{1}{x+2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B3%7D%7Bx%2B2%7D%3D%20%5Cfrac%7Bx%2B2%2B1%7D%7Bx%2B2%7D%3D%20%5Cfrac%7Bx%2B2%7D%7Bx%2B2%7D%2B%20%5Cfrac%7B1%7D%7Bx%2B2%7D%3D1%2B%20%5Cfrac%7B1%7D%7Bx%2B2%7D)
for x>2
![\frac{1}{x+2}\ \textless \ \frac{1}{2+2}= \frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%2B2%7D%5C%20%5Ctextless%20%5C%20%20%5Cfrac%7B1%7D%7B2%2B2%7D%3D%20%5Cfrac%7B1%7D%7B4%7D%20%20)
thus
for x>2,
![1+ \frac{1}{x+2}\ \textless \ 1+ \frac{1}{4}= \frac{5}{4}](https://tex.z-dn.net/?f=1%2B%20%5Cfrac%7B1%7D%7Bx%2B2%7D%5C%20%5Ctextless%20%5C%201%2B%20%5Cfrac%7B1%7D%7B4%7D%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20)
Answer:
for x>2
![\frac{x^{2} -x-6}{ x^{2} -4} = \frac{x+3}{x+2} \ \textless \ \frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%20-x-6%7D%7B%20x%5E%7B2%7D%20-4%7D%20%3D%20%20%5Cfrac%7Bx%2B3%7D%7Bx%2B2%7D%20%5C%20%5Ctextless%20%5C%20%20%5Cfrac%7B5%7D%7B4%7D%20)
, (but the expression is never 0)