Answer:
Z(-0.2, 2.2).
Step-by-step explanation:
We will use section formula when a point, say P, divides any segment ,say AB, internally in the ratio m:n.
![[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%2C%20y%3D%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5D)
We have been given the points of segment XY as X at (-2,1) and Y at (4,5) and ratio is 3:7.
Upon substituting coordinates of our given points in section formula we will get,
![[x=\frac{(3*4)+(7*-2)}{3+7}, y= \frac{3*5+7*1}{3+7}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B%283%2A4%29%2B%287%2A-2%29%7D%7B3%2B7%7D%2C%20y%3D%20%5Cfrac%7B3%2A5%2B7%2A1%7D%7B3%2B7%7D%5D)
![[x=\frac{12-14}{10}, y= \frac{15+7}{10}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B12-14%7D%7B10%7D%2C%20y%3D%20%5Cfrac%7B15%2B7%7D%7B10%7D%5D)
![[x=\frac{-2}{10}, y= \frac{22}{10}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B-2%7D%7B10%7D%2C%20y%3D%20%5Cfrac%7B22%7D%7B10%7D%5D)
![[x=-0.2, y= 2.2]](https://tex.z-dn.net/?f=%5Bx%3D-0.2%2C%20y%3D%202.2%5D)
Therefore, coordinates of point Z will be (-0.2, 2.2).
The correct answer is b; they are independent because the occurrence of one does not affect the occurrence of the other.
Answer:
Correct answer: F. graph F or x ∈ |-5 ; 5| (including endpoints)
Step-by-step explanation:
Let us first define the absolute value:
| x | = 1. { x with condition x ≥ 0 }
or 2. { - x with condition x < 0 }
This is a linear inequality
1. x ≤ 5 ∧ x ≥ 0 ⇒ 0 ≤ x ≤ 5 or interval x ∈ |0 ; 5| (including endpoints)
2. - x ≤ 5 when we multiply both sides of the equation by -1 we get:
x ≥ -5 ∧ x < 0 ⇒ -5 ≤ x < 0 or interval x ∈ |-5 ; 0) (including -5)
The solution to this linear inequality is the union of these two intervals:
x ∈ |-5 ; 0) ∪ |0 ; 5| ⇒ x ∈ |-5 ; 5| (including endpoints)
x ∈ |-5 ; 5| (including endpoints)
God is with you!!!
