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.
<h3>
Answer:</h3>
x = 1
<h3>
Step-by-step explanation:</h3>
<em>The only solution is an extraneous solution</em>, which is to say the equation has no solution.
The rational expression reduces to -1 (for x≠1), which makes the equation ...
1 = 1/x
The only solution to this is x=1, which is specifically disallowed.
___
If you subtract the right side, the equation becomes ...
((-x+1)(x) +2(x)(x -1) -(x -1))/(x -1) = 0
(-x^2 +x +2x^2 -2x -x +1)/(x -1) = 0 . . . . eliminate parentheses in the numerator
(x^2 -2x +1)/(x -1) = 0 . . . . . . . . . . . . . . . collect terms
(x -1)^2/(x -1) = 0 . . . . . . . . . . . . . . . . . . . factor
This is undefined for the only value of x that could possibly be a solution, x=1.
Answer:
first one: yes
second one: yes
third one: no
fourth one: yes
Step-by-step explanation:
Answer:
x > -6.
Step-by-step explanation:
16x - 33x < -12x + 30
Add 12x to both sides:
16x - 33x + 12x < 30
-17x + 12x < 30
-5x < 30
x > 30/-5
x > -6
(Note the inequality signs flips because we are dividing by negative 5).
Answer:
4x +1 is your answer.
Step-by-step explanation:
What you do is you add f(x) and g(x) together.
<em>3x - 1 + (x + 2)</em>
4x +1 is your answer.
