Answer:
![\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B4%7D%7B5%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B5%7D-%5Cfrac%7B3%7D%7B5%7D%7D%3D-12)
Step-by-step explanation:
Considering the expression
![\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B4%7D%7B5%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B5%7D-%5Cfrac%7B3%7D%7B5%7D%7D)
Solution Steps:
![\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B4%7D%7B5%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B5%7D-%5Cfrac%7B3%7D%7B5%7D%7D)
as
![\mathrm{Combine\:the\:fractions\:}\frac{1}{5}-\frac{3}{5}:\quad -\frac{2}{5}](https://tex.z-dn.net/?f=%5Cmathrm%7BCombine%5C%3Athe%5C%3Afractions%5C%3A%7D%5Cfrac%7B1%7D%7B5%7D-%5Cfrac%7B3%7D%7B5%7D%3A%5Cquad%20-%5Cfrac%7B2%7D%7B5%7D)
so
![\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%7Ba%7D%3D%5Cfrac%7Bb%7D%7Bc%5C%3A%5Ccdot%20%5C%3Aa%7D)
![=\frac{4}{5\left(\frac{1}{3}-\frac{2}{5}\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B5%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B2%7D%7B5%7D%5Cright%29%7D)
join ![\frac{1}{3}-\frac{2}{5}:\quad -\frac{1}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B2%7D%7B5%7D%3A%5Cquad%20-%5Cfrac%7B1%7D%7B15%7D)
so
![=\frac{4}{5\left(-\frac{1}{15}\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B5%5Cleft%28-%5Cfrac%7B1%7D%7B15%7D%5Cright%29%7D)
![\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a](https://tex.z-dn.net/?f=%5Cmathrm%7BRemove%5C%3Aparentheses%7D%3A%5Cquad%20%5Cleft%28-a%5Cright%29%3D-a)
![=\frac{4}{-5\cdot \frac{1}{15}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B-5%5Ccdot%20%5Cfrac%7B1%7D%7B15%7D%7D)
![\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7Ba%7D%7B-b%7D%3D-%5Cfrac%7Ba%7D%7Bb%7D)
![=-\frac{4}{5\cdot \frac{1}{15}}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7B4%7D%7B5%5Ccdot%20%5Cfrac%7B1%7D%7B15%7D%7D)
![\mathrm{Multiply\:}5\cdot \frac{1}{15}\::\quad \frac{1}{3}](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3A%7D5%5Ccdot%20%5Cfrac%7B1%7D%7B15%7D%5C%3A%3A%5Cquad%20%5Cfrac%7B1%7D%7B3%7D)
so
![=-\frac{4}{\frac{1}{3}}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7B4%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![\mathrm{Simplify}\:\frac{4}{\frac{1}{3}}:\quad \frac{12}{1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D%5C%3A%5Cfrac%7B4%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%3A%5Cquad%20%5Cfrac%7B12%7D%7B1%7D)
so
![=-\frac{12}{1}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7B12%7D%7B1%7D)
![\mathrm{Apply\:rule}\:\frac{a}{1}=a](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Arule%7D%5C%3A%5Cfrac%7Ba%7D%7B1%7D%3Da)
![=-12](https://tex.z-dn.net/?f=%3D-12)
Therefore
![\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B4%7D%7B5%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B5%7D-%5Cfrac%7B3%7D%7B5%7D%7D%3D-12)
Answer:
<h2>
V ≈ 628.3 cm³</h2>
Step-by-step explanation:
Volume of cylinder: V = π×r² × h
diameter = 20 cm ⇒ r = 10 cm
h = 2 cm
Volume:
V = π×(10)²×2 = 200π cm³ = 628.318.... cm³ ≈ 628.3 cm³
Answer:
B
Step-by-step explanation:
The equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
h= 9, k = -7
r = 2, so r^2 = 4.
We now know that the equation must equal 4, so we can rule out answers A and C.
Plug in the values for h and k to get
(x-9)^2 + (y+7)^2 = 4
Choice B is correct!
Answer:
The answer is B
Step-by-step explanation:
For these equations, the number inside the parenthesis has to be greater than 1 in order to increase. You also have to multiply what is inside the parenthesis with what is outside.
It equals -1
you have collect like terms the -7w+w
which give you -6w then you have to divide both sides by -6
which gives you -1