I could only figure out one... sorry! Good luck
The answer is: 21x-28
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.
Answer:
A. (x + 2)^2 = 31.
Step-by-step explanation:
x^2 + 4x = 27
x^2 + 4x - 27 = 0
A. (x + 2)^2 = 31
x^2 + 4x + 4 - 31 = 0
x^2 + 4x - 27 = 0
This option corresponds to the given equation, so it is correct.
B. (x + 2)^2 = 43
x^2 + 4x + 4 - 43 = 0
x^2 + 4x - 39 = 0
This does not correspond to the equation.
C. (x + 4)^2 = 31
x^2 + 8x + 16 - 31 = 0
x^2 + 8x - 15 = 0
This does not correspond to the equation.
D. (x+4)^2 = 43
x^2 + 8x + 16 - 43 = 0
x^2 + 8x - 27 = 0
This does not correspond to the equation.
So, your answer is A. (x + 2)^2 = 31.
Make sure to SUBMIT and check your PREVIOUS answers to make sure they are right! XD Also, hope this helps!
Answer: 1/24
Step-by-step explanation:
1/2 divided by 12
