Answer:
2.537 x 10¹⁵ miles
Step-by-step explanation:
We are given the following:
1 light year = 5.9 x 10¹² miles
Distance of the star = 4.3 x 10² light years
To get this we just convert the distance of the star in light years into miles.
![4.3\times10^2\hspace{2}lightyears\times\dfrac{5.9\times10^{12}miles}{1\hspace{2}lightyear}](https://tex.z-dn.net/?f=4.3%5Ctimes10%5E2%5Chspace%7B2%7Dlightyears%5Ctimes%5Cdfrac%7B5.9%5Ctimes10%5E%7B12%7Dmiles%7D%7B1%5Chspace%7B2%7Dlightyear%7D)
We cancel out the light years and then we are left with:
![(4.3\times10^2)\times(5.9\times10^{12}miles)](https://tex.z-dn.net/?f=%284.3%5Ctimes10%5E2%29%5Ctimes%285.9%5Ctimes10%5E%7B12%7Dmiles%29)
In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.
Coefficients:
4.3 x 5.9 = 25.37
Exponents of 10:
10² x 10¹² = 10⁽²⁺¹²⁾=10¹⁴
Then we combine them again to form a scientific notation:
25.37 x 10¹⁴
But since the standard in writing a scientific notation, the coefficient needs to be a number from 1-9, we need to move the decimal. When we move the decimal to the right or left, we change the exponent of the power of 10. Since we will move it once to the left, we add 1.
The answer will then be:
2.537 x 10¹⁵ miles
Answer:
![y=\frac{1}{2}x-3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx-3)
Step-by-step explanation:
<u><em>The question is</em></u>
Find the equation of the line for points (-2,-4) and (4,-1)
step 1
Find the slope
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
we have
(-2,-4) and (4,-1)
substitute
![m=\frac{-1+4}{4+2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%2B4%7D%7B4%2B2%7D)
![m=\frac{3}{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B6%7D)
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
step 2
Find the equation if the line in point slope form
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
![point\ (4,-1)](https://tex.z-dn.net/?f=point%5C%20%284%2C-1%29)
substitute
![y+1=\frac{1}{2}(x-4)](https://tex.z-dn.net/?f=y%2B1%3D%5Cfrac%7B1%7D%7B2%7D%28x-4%29)
step 3
Convert to slope intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
we have
![y+1=\frac{1}{2}(x-4)](https://tex.z-dn.net/?f=y%2B1%3D%5Cfrac%7B1%7D%7B2%7D%28x-4%29)
isolate the variable y
![y+1=\frac{1}{2}x-2](https://tex.z-dn.net/?f=y%2B1%3D%5Cfrac%7B1%7D%7B2%7Dx-2)
![y=\frac{1}{2}x-2-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx-2-1)
![y=\frac{1}{2}x-3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx-3)
Answer:
3.8
Step-by-step explanation:
5% times 20 is 100% and that is the number we are trying to find so of we multiply .19 by 20 we should get 3.8 wich is promotional to the 100%
S= (pi times r times l) + (pi times radius squared)
Factor out the pi times r
S= (pi times r) l + r
Divide
S/(pi times r)= l + r
Find common denominator and subtract
(S- pi times r)/(pi times r) = l
The answer therefore is A
She gave her friend 6 pieces, just multiply 14 by 3/7! hope it helped