So if x people were surveyed,
![\frac{7}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B8%7D%20)
people owned a bike and
![\frac{1}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B8%7D%20)
did not.
The difference between them is 72:
![\frac{7}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B8%7D%20)
x-\frac{1}{8} [/tex] =72
so this means that
![\frac{6}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B8%7D%20)
x=72
let's simplify:
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
x=72
and divide by 3:
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
x=24
and mupliply by 4:
x=96
so 96 people were surveyed
Percent increase/decrease formula
change/original * 100
(225-75)/75 * 100=
150/75 * 100 =
2 * 100 = 200% increase
Answer:
9 miles
Step-by-step explanation:
A 6+3 is nine
Answer:
Temperature.
Step-by-step explanation:
Temperature is a measure of the average kinetic energy of all the molecules in a gas. As the temperature, and therefore kinetic energy, of a gas changes the RMS speed of the gas molecules also changes. The RMS speed of the molecules is defined as the square root of the average of each individual velocity squared.
Answer:
The equation is: ![x^2-x+\frac{1}{2}](https://tex.z-dn.net/?f=x%5E2-x%2B%5Cfrac%7B1%7D%7B2%7D)
(A)![x^2-x+\frac{1}{2}=0](https://tex.z-dn.net/?f=x%5E2-x%2B%5Cfrac%7B1%7D%7B2%7D%3D0)
(B)![5x^2-5x+\frac{5}{2}=0](https://tex.z-dn.net/?f=5x%5E2-5x%2B%5Cfrac%7B5%7D%7B2%7D%3D0)
(C) ![-\frac{1}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D)
![-\frac{1}{2}x^2+\frac{1}{2}x-\frac{1}{4}=0](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B%5Cfrac%7B1%7D%7B2%7Dx-%5Cfrac%7B1%7D%7B4%7D%3D0)
d) √3
![(\sqrt{3}) x^2-x\sqrt{3}+\frac{\sqrt{3}}{2}=0](https://tex.z-dn.net/?f=%28%5Csqrt%7B3%7D%29%20x%5E2-x%5Csqrt%7B3%7D%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D0)
Step-by-step explanation:
If the roots of the quadratic equation are: ![\frac{\sqrt{3}+1}{2} and \frac{\sqrt{3}-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%2B1%7D%7B2%7D%20%20and%20%20%5Cfrac%7B%5Csqrt%7B3%7D-1%7D%7B2%7D)
This means:
x=
OR ![x= \frac{\sqrt{3}-1}{2}](https://tex.z-dn.net/?f=x%3D%20%20%5Cfrac%7B%5Csqrt%7B3%7D-1%7D%7B2%7D)
x-
=0 or x-
If a=0 or b=0, then ab=0
Therefore:
![(x-\frac{\sqrt{3}+1}{2})(x-\frac{\sqrt{3}-1}{2})=0\\x^2-\frac{x(\sqrt{3}-1)}{2}-\frac{x(\sqrt{3}+1)}{2}+(\frac{\sqrt{3}-1)}{2})(\frac{\sqrt{3}+1}{2})=0\\x^2-x+\frac{1}{2}=0](https://tex.z-dn.net/?f=%28x-%5Cfrac%7B%5Csqrt%7B3%7D%2B1%7D%7B2%7D%29%28x-%5Cfrac%7B%5Csqrt%7B3%7D-1%7D%7B2%7D%29%3D0%5C%5Cx%5E2-%5Cfrac%7Bx%28%5Csqrt%7B3%7D-1%29%7D%7B2%7D-%5Cfrac%7Bx%28%5Csqrt%7B3%7D%2B1%29%7D%7B2%7D%2B%28%5Cfrac%7B%5Csqrt%7B3%7D-1%29%7D%7B2%7D%29%28%5Cfrac%7B%5Csqrt%7B3%7D%2B1%7D%7B2%7D%29%3D0%5C%5Cx%5E2-x%2B%5Cfrac%7B1%7D%7B2%7D%3D0)
Therefore the coefficient of
here is 1.
b) To make 5 the coefficient of
Simply multiply
by 5
This gives: ![5x^2-5x+\frac{5}{2}=0](https://tex.z-dn.net/?f=5x%5E2-5x%2B%5Cfrac%7B5%7D%7B2%7D%3D0)
c) ![-\frac{1}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D)
To make
the coefficient of
Simply multiply
by ![-\frac{1}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D)
This gives: ![-\frac{1}{2}x^2+\frac{1}{2}x-\frac{1}{4}=0](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B%5Cfrac%7B1%7D%7B2%7Dx-%5Cfrac%7B1%7D%7B4%7D%3D0)
d) √3
To make
the coefficient of
Simply multiply
by ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
This gives: ![(\sqrt{3}) x^2-x\sqrt{3}+\frac{\sqrt{3}}{2}=0](https://tex.z-dn.net/?f=%28%5Csqrt%7B3%7D%29%20x%5E2-x%5Csqrt%7B3%7D%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D0)