Answer: The scale factor is 1.3 .
Step-by-step explanation:
Given: The first hexagon is dilated to form the second hexagon.
The side length of first hexagon=5 units.
The side-length of second hexagon= 6.25 units
When a shape having measure x is dilated by using a scalar factor of k, then the side measure (y) of the image is given by:-
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Substitute, y=6.5 and x=5 to find the value of k we get
![6.5=5k\\\Rightarrow\ k=\frac{6.5}{5}=1.3](https://tex.z-dn.net/?f=6.5%3D5k%5C%5C%5CRightarrow%5C%20k%3D%5Cfrac%7B6.5%7D%7B5%7D%3D1.3)
Hence, the scale factor is 1.3
Answer:
0.000385
Step-by-step explanation:
The exponent is -4, making it 10 to the power of negative 4. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 4 times
Answer:
8i and -8i
Step-by-step explanation:
Move everything into the left-hand side to get a quadratic equation:
![\frac{1}{2}(x^2+40)=-12\\\frac{1}{2}x^2+20=-12\\\frac{1}{2}x^2+32=0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28x%5E2%2B40%29%3D-12%5C%5C%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B20%3D-12%5C%5C%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B32%3D0)
Solve for x using the quadratic formula:
![\frac{1}{2}x^2+32=0\\x=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\x=\frac{-(0)\±\sqrt{0^2-4(\frac{1}{2})32}}{2(\frac{1}{2})}\\x=\±\sqrt{-64}\\x=\±8i](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B32%3D0%5C%5Cx%3D%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5Cx%3D%5Cfrac%7B-%280%29%5C%C2%B1%5Csqrt%7B0%5E2-4%28%5Cfrac%7B1%7D%7B2%7D%2932%7D%7D%7B2%28%5Cfrac%7B1%7D%7B2%7D%29%7D%5C%5Cx%3D%5C%C2%B1%5Csqrt%7B-64%7D%5C%5Cx%3D%5C%C2%B18i)
The two imaginary solutions for the equation are 8i and -8i.
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