Given:
A fraction is greater than
, is less than
.
The fraction has 6 as a denominator.
To find:
The fraction value.
Solution:
Let x be the required fraction.
According to the given information, we get
![\dfrac{3}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B12%7D%3Cx%3C%5Cdfrac%7B75%7D%7B100%7D)
![\dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%3Cx%3C%5Cdfrac%7B3%7D%7B4%7D)
We know that,
. So,
![x=\dfrac{2}{4}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B2%7D%7B4%7D)
![x=\dfrac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B1%7D%7B2%7D)
We need 6 as the denominator.
Multiply the numerator and denominator by 3.
![x=\dfrac{1\times 3}{2\times 3}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B1%5Ctimes%203%7D%7B2%5Ctimes%203%7D)
![x=\dfrac{3}{6}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%7D%7B6%7D)
Therefore, the required fraction is
.
The slope of (y=-3x+12) is -3 while the slope of (y=-6x+2) is -6. Therefore, it's Inconsistent.
Coincident is one line on the graph
Consistent is two parallel lines
Answer:
25 questions
Step-by-step explanation:
First set up the equation.
![\frac{20}{x} = \frac{80}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7Bx%7D%20%20%3D%20%5Cfrac%7B80%7D%7B100%7D)
To get from 20 to 80 you have to multiply by a scale factor of 4, so do the same to the bottom as well.
Do the inverse and divide 100 by 4 to get x = 25.
There were 25 questions on Victoria's test.
if we take 80 as the 100%, what is 110% of that?
![\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 80&100\\ x&110 \end{array}\implies \cfrac{80}{x}=\cfrac{100}{110}\implies \cfrac{80}{x}=\cfrac{10}{11}\implies 880=10x \\\\\\ \cfrac{880}{10}=x\implies 88=x](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccll%7D%20amount%26%5C%25%5C%5C%20%5Ccline%7B1-2%7D%2080%26100%5C%5C%20x%26110%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B80%7D%7Bx%7D%3D%5Ccfrac%7B100%7D%7B110%7D%5Cimplies%20%5Ccfrac%7B80%7D%7Bx%7D%3D%5Ccfrac%7B10%7D%7B11%7D%5Cimplies%20880%3D10x%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B880%7D%7B10%7D%3Dx%5Cimplies%2088%3Dx)
Answer:
![x=60](https://tex.z-dn.net/?f=x%3D60)
Step-by-step explanation:
![\frac{x}{6} =10](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B6%7D%20%3D10)
Times both sides by 6 to get x by itself
![x=60](https://tex.z-dn.net/?f=x%3D60)