Answer:
Point (1,8)
Step-by-step explanation:
We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.
When a point divides any segment internally in the ratio m:n, the formula is:
![[x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2Cy%3D%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5D)
Let us substitute coordinates of point P and Q as:
,
![[x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B%283%2A4%29%2B%281%2A-8%29%7D%7B3%2B1%7D%2Cy%3D%5Cfrac%7B%283%2A12%29%2B%281%2A-4%29%7D%7B3%2B1%7D%5D)
![[x=\frac{12-8}{4},y=\frac{36-4}{4}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B12-8%7D%7B4%7D%2Cy%3D%5Cfrac%7B36-4%7D%7B4%7D%5D)
![[x=\frac{4}{4},y=\frac{32}{4}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B4%7D%7B4%7D%2Cy%3D%5Cfrac%7B32%7D%7B4%7D%5D)
![[x=1,y=8]](https://tex.z-dn.net/?f=%5Bx%3D1%2Cy%3D8%5D)
Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.
The answer should be X>4
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
2*x+8-(5*x-4)<0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
-3x + 12 = -3 • (x - 4)
Equation at the end of step 1 :
Step 2 :
2.1 Divide both sides by -3
Remember to flip the inequality sign:
Solve Basic Inequality :
2.2 Add 4 to both sides
x > 4
So lets say that this salt and water solution consists of 100 liters.
Then that means 20 liters is salt, and 80 liters out of the 100 is water.
Now, we remove 25% of the water. 25% of 80 liters is 20 liters. So, we are left with 80-20, or 60 liters.
Now in all we have 20 liters of salt, and 60 liters of water.
The percentage of salt in the new mixture will be 20/(20+60) = 20/80 = 25%.
Your answer is 25%
