For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
Where:
m: Is the slope
b: Is the cut-off point with the y axis
According to the data of the statement we have two points through which the line passes:
![(x_ {1}, y_ {1}): (0,1)\\(x_ {2}, y_ {2}): (2,7)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%280%2C1%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%282%2C7%29)
We found the slope:
![m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {7-1} {2-0} = \frac {6} {2} = 3](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7By_%20%7B2%7D%20-y_%20%7B1%7D%7D%20%7Bx_%20%7B2%7D%20-x_%20%7B1%7D%7D%20%3D%20%5Cfrac%20%7B7-1%7D%20%7B2-0%7D%20%3D%20%5Cfrac%20%7B6%7D%20%7B2%7D%20%3D%203)
Thus, the equation is of the form:
![y = 3x + b](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%20b)
We substitute one of the points and find "b":
![1 = 3 (0) + b\\1 = b](https://tex.z-dn.net/?f=1%20%3D%203%20%280%29%20%2B%20b%5C%5C1%20%3D%20b)
Finally, the equation is:
![y = 3x + 1](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%201)
Answer:
![y = 3x + 1](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%201)
Lindsey has 25 inches long ribbons now.
Further explanation:
Simple addition and multiplication has to be used to solve this question.
Given
Ribbon Lindsey already has= 10 inches
Number of pieces she bought inches = 3
Length of each ribbon piece = 5 inches
So,
![The\ total\ length\ of\ piesces\ she\ bought\ later = 5*3\\=15\ inches](https://tex.z-dn.net/?f=The%5C%20total%5C%20length%5C%20of%5C%20piesces%5C%20she%5C%20bought%5C%20later%20%3D%205%2A3%5C%5C%3D15%5C%20inches)
As she already had 10 inches, now she has
![Total\ ribbon\ length=Ribbons\ she\ already\ had+New\ ribbon\ piesce\\=10+15\\=25\ inches](https://tex.z-dn.net/?f=Total%5C%20ribbon%5C%20length%3DRibbons%5C%20she%5C%20already%5C%20had%2BNew%5C%20ribbon%5C%20piesce%5C%5C%3D10%2B15%5C%5C%3D25%5C%20inches)
Lindsey has 25 inches long ribbons now.
Keywords: Addition, multiplication
Learn more about word problems at:
#LearnwithBrainly
Answer:
Tasha should mix 25 liters of 20% solution and 50 liters of 50%.
Step-by-step explanation:
Let x liters be the amount of 20% solution and y liters be the amount of 50% solution Tasha takes.
1. Tasha needs 75 liters of a 40% solution of alcohol. Then
x + y = 75
2. There are
liters of alcohol in x l of 20% solution
liters of alcohol in 50% solution
liters of alcohol in 75 liters of 40% solution
In total,
of alcohol that is 30 l, so
0.2x + 0.5y = 30
3. Solve the system of two equations:
![\left\{\begin{array}{l}x+y=75\\ \\0.2x+0.5y=30\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%2By%3D75%5C%5C%20%5C%5C0.2x%2B0.5y%3D30%5Cend%7Barray%7D%5Cright.)
From the first equation:
![x=75-y](https://tex.z-dn.net/?f=x%3D75-y)
Substitute it into the second equation
![0.2(75-y)+0.5y=30\\ \\15-0.2y+0.5y=30\\ \\0.3y=30-15\\ \\0.3y=15\\ \\3y=150\\ \\y=50\\ \\x=75-50=25](https://tex.z-dn.net/?f=0.2%2875-y%29%2B0.5y%3D30%5C%5C%20%5C%5C15-0.2y%2B0.5y%3D30%5C%5C%20%5C%5C0.3y%3D30-15%5C%5C%20%5C%5C0.3y%3D15%5C%5C%20%5C%5C3y%3D150%5C%5C%20%5C%5Cy%3D50%5C%5C%20%5C%5Cx%3D75-50%3D25)
Tasha should mix 25 liters of 20% solution and 50 liters of 50%.
Answer:
40
Step-by-step explanation: