Answer:
3) Midpoint is (-4,0.5)
Option A is correct.
4) Midpoint is (2.5,0)
Option B is correct.
5) The factors are (x+4)(x-7)
Option C is correct.
6) The factors are (x+4)(x+2)
Option A is correct.
Step-by-step explanation:
Question 3
Find midpoint of the following:
(2,-7), (-10,8)
The formula used to find midpoint is: [tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]
We have [tex]x_1=2, y_1=-7, x_2=-10,y_2=8[/tex]
Putting values and finding midpoint
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\\Midpoint=(\frac{2-10}{2},\frac{-7+8}{2} )\\Midpoint=(\frac{-8}{2},\frac{1}{2} )\\Midpoint=(-4,0.5 )[/tex]
So, Midpoint is (-4,0.5)
Option A is correct.
Question 4
Find midpoint of the following:
(2,-10), (3,10)
The formula used to find midpoint is: [tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]
We have [tex]x_1=2, y_1=-10, x_2=3,y_2=10[/tex]
Putting values and finding midpoint
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\\Midpoint=(\frac{2+3}{2},\frac{-10+10}{2} )\\Midpoint=(\frac{5}{2},\frac{0}{2} )\\Midpoint=(2.5,0 )[/tex]
So, Midpoint is (2.5,0)
Option B is correct.
Question 5
Factor each completely
[tex]x^2-3x-28[/tex]
We will break the middle term and find factors
[tex]x^2-3x-28\\=x^2-7x+4x-28\\Taking\:common\\=x(x-7)+4(x-7)\\=(x+4)(x-7)[/tex]
So, the factors are (x+4)(x-7)
Option C is correct.
Question 6
Factor each completely
[tex]x^2+6x+8[/tex]
We will break the middle term and find factors
[tex]x^2+6x+8\\=x^2+4x+2x+8\\=x(x+4)+2(x+4)\\=(x+4)(x+2)[/tex]
So, the factors are (x+4)(x+2)
Option A is correct.
