(2 x 3.95) + (3 x 4.25) + (1 x 5.99) + ((2 x 3.95) + (3 x 4.25) + (1 x 5.99)) x 0.20
= 26.64 - 5.32
= 21.32
Answer: ? = 0.14
Step-by-step explanation:
So you need to find the value that fits the question mark. This means you have to get it by itself.
To start you subtract 0.4 from 0.546, which equals .146. Then you subtract 0.006 from 0.146 to get 0.14
What it looks like mathematically :
0.546 = 0.4 + ? + 0.006
0.146= ? + 0.006
0.14=?
Hopes this helps :)
Answer: ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Use the formula for calculate the distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Calculate the distance AB. Substitute the coordinates into the formula. Then:
![d_{AB}=\sqrt{(8-0)^2+(8-(-7))^2}](https://tex.z-dn.net/?f=d_%7BAB%7D%3D%5Csqrt%7B%288-0%29%5E2%2B%288-%28-7%29%29%5E2%7D)
![d_{AB}=17](https://tex.z-dn.net/?f=d_%7BAB%7D%3D17)
Calculate the distance A'B'. Substitute the coordinates into the formula. Then:
![d_{A'B'}=\sqrt{(2-6)^2+(1-5-(-6))^2}](https://tex.z-dn.net/?f=d_%7BA%27B%27%7D%3D%5Csqrt%7B%282-6%29%5E2%2B%281-5-%28-6%29%29%5E2%7D)
![d_{A'B'}=\frac{17}{2}](https://tex.z-dn.net/?f=d_%7BA%27B%27%7D%3D%5Cfrac%7B17%7D%7B2%7D)
As you can see, the distance A'B' is the distance AB multiplied by 1/2. Therefore, this is the scale factor.
Answer:
![(x,y) = \left(\dfrac{18}{5},\dfrac{67}{15}\right)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cleft%28%5Cdfrac%7B18%7D%7B5%7D%2C%5Cdfrac%7B67%7D%7B15%7D%5Cright%29)
Step-by-step explanation:
First rearrange all equations into this format:
![ax+by=c](https://tex.z-dn.net/?f=ax%2Bby%3Dc)
that will result in:
![3x-4y=-1](https://tex.z-dn.net/?f=3x-4y%3D-1)
![9x-7y=15](https://tex.z-dn.net/?f=9x-7y%3D15)
then we'll multiply an equation with a number such that we have same numbers on both equations (with only different signs). So we can add them
Here you can see that we've multiplied the first equation with (-3) so that we have -9x on one equation and 9x on the other. Now when we add the two equations the 9x and -9x terms will cancel out (or eliminate)
![\[\begin{array}{r@{}l@{\quad}l@{\quad}r@{}l@{}c}3x-4y&{}=-1&\xrightarrow{\times (-3)}&-9x +12y&{}=+3\\[\jot]9x -7y&{}=15&\xrightarrow{\phantom{\times (-3)}}&9x-y&{}=15&~\smash{\raisebox{.8\normalbaselineskip}{$+$}}\\\cline{4-5}&&&+5y&{}=18\\[\jot]&&&y&{}=\dfrac{18}{5}\\\end{array}\]\\](https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Barray%7D%7Br%40%7B%7Dl%40%7B%5Cquad%7Dl%40%7B%5Cquad%7Dr%40%7B%7Dl%40%7B%7Dc%7D3x-4y%26%7B%7D%3D-1%26%5Cxrightarrow%7B%5Ctimes%20%28-3%29%7D%26-9x%20%2B12y%26%7B%7D%3D%2B3%5C%5C%5B%5Cjot%5D9x%20-7y%26%7B%7D%3D15%26%5Cxrightarrow%7B%5Cphantom%7B%5Ctimes%20%28-3%29%7D%7D%269x-y%26%7B%7D%3D15%26~%5Csmash%7B%5Craisebox%7B.8%5Cnormalbaselineskip%7D%7B%24%2B%24%7D%7D%5C%5C%5Ccline%7B4-5%7D%26%26%26%2B5y%26%7B%7D%3D18%5C%5C%5B%5Cjot%5D%26%26%26y%26%7B%7D%3D%5Cdfrac%7B18%7D%7B5%7D%5C%5C%5Cend%7Barray%7D%5C%5D%5C%5C)
now that we've found the value of y
we'll use this value in any of the two equations to get the value of x.
let's put y in the first equation:
![3x-4y=-1](https://tex.z-dn.net/?f=3x-4y%3D-1)
![3x-4\left( \dfrac{18}{5}\right)=-1](https://tex.z-dn.net/?f=3x-4%5Cleft%28%20%5Cdfrac%7B18%7D%7B5%7D%5Cright%29%3D-1)
![3x=-1+4\left( \dfrac{18}{5}\right)](https://tex.z-dn.net/?f=3x%3D-1%2B4%5Cleft%28%20%5Cdfrac%7B18%7D%7B5%7D%5Cright%29)
![3x=-1+\dfrac{72}{5}](https://tex.z-dn.net/?f=3x%3D-1%2B%5Cdfrac%7B72%7D%7B5%7D)
![3x=\dfrac{67}{5}](https://tex.z-dn.net/?f=3x%3D%5Cdfrac%7B67%7D%7B5%7D)
![x=\dfrac{67}{3(5)}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B67%7D%7B3%285%29%7D)
![x=\dfrac{67}{15}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B67%7D%7B15%7D)
Answer:
![y=3(1-0.451)^t](https://tex.z-dn.net/?f=y%3D3%281-0.451%29%5Et)
The value of r is 0.451
The percentage decrease is about 45.1%
Step-by-step explanation:
The given exponential function is ![y=3e^{-0.6t}](https://tex.z-dn.net/?f=y%3D3e%5E%7B-0.6t%7D)
Using the exponent rule, ![(x)^{ab}=(x^a)^b](https://tex.z-dn.net/?f=%28x%29%5E%7Bab%7D%3D%28x%5Ea%29%5Eb)
![y=3(e^{-0.6})^t](https://tex.z-dn.net/?f=y%3D3%28e%5E%7B-0.6%7D%29%5Et)
Now the value of ![e^{-0.6}=0.5488](https://tex.z-dn.net/?f=e%5E%7B-0.6%7D%3D0.5488)
Thus, we can rewrite the function as
![y=3(0.5488)^t](https://tex.z-dn.net/?f=y%3D3%280.5488%29%5Et)
Therefore, the function in form ![y=a(1-r)^t](https://tex.z-dn.net/?f=y%3Da%281-r%29%5Et)
![y=3(1-0.451)^t](https://tex.z-dn.net/?f=y%3D3%281-0.451%29%5Et)
The value of r is 0.451
The percentage decrease is about 0.451 ×100 = 45.1%