Answer:
A and B are the correct
Step-by-step explanation:
= 3(8 - 4x)
= 24 - 12x
so, A . 24 - 12x
B . 2(12 - 6x)
24 - 12x
Answer:
![\begin{cases}y=-5x+1\\y=5x-4 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dy%3D-5x%2B1%5C%5Cy%3D5x-4%20%5Cend%7Bcases%7D)
Step-by-step explanation:
Slope-intercept form of a <u>linear equation</u>:
![\boxed{y=mx+b}](https://tex.z-dn.net/?f=%5Cboxed%7By%3Dmx%2Bb%7D)
where:
- m is the slope.
- b is the y-intercept (where the line crosses the y-axis).
<u>Slope formula</u>
![\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctextsf%7Bslope%7D%5C%3A%28m%29%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%7D)
<u>Equation 1</u>
<u />
Define two points on the line:
<u>Substitute</u> the defined points into the slope formula:
![\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7Bslope%7D%5C%3A%28m%29%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cdfrac%7B1-6%7D%7B0-%28-1%29%7D%3D-5)
From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
![y=-5x+1](https://tex.z-dn.net/?f=y%3D-5x%2B1)
<u>Equation 2</u>
<u />
Define two points on the line:
<u>Substitute</u> the defined points into the slope formula:
![\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7Bslope%7D%5C%3A%28m%29%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cdfrac%7B-4-1%7D%7B0-1%7D%3D5)
From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
![y=5x-4](https://tex.z-dn.net/?f=y%3D5x-4)
<u>Conclusion</u>
Therefore, the system of linear equations shown by the graph is:
![\begin{cases}y=-5x+1\\y=5x-4 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dy%3D-5x%2B1%5C%5Cy%3D5x-4%20%5Cend%7Bcases%7D)
Learn more about systems of linear equations here:
brainly.com/question/28164947
brainly.com/question/28093918
Y=1x-8
Slope intercept form: y=mx+b
Slope of the line: 1/1 (rise/run) or 1
Y-intercept: -8
![ln(T- \frac{20}{200})=-0.11t \\ e^{ln(T- \frac{20}{200})}=e^{-0.11t} \\ T- \frac{20}{200} =e^{-0.11t} \\ T-0.1=e^{-0.11t} \\ T=e^{-0.11t}+0.1](https://tex.z-dn.net/?f=ln%28T-%20%5Cfrac%7B20%7D%7B200%7D%29%3D-0.11t%20%5C%5C%20e%5E%7Bln%28T-%20%5Cfrac%7B20%7D%7B200%7D%29%7D%3De%5E%7B-0.11t%7D%20%5C%5C%20T-%20%5Cfrac%7B20%7D%7B200%7D%20%3De%5E%7B-0.11t%7D%20%5C%5C%20T-0.1%3De%5E%7B-0.11t%7D%20%5C%5C%20T%3De%5E%7B-0.11t%7D%2B0.1)
Then, now that we have solved for T, we can evaluate and solve for t=20 minutes.