Step-by-step explanation:
In this given figure vertical opposite angles are equal
6x+7=8x-17
2x=24
X=12
Answer:

Step-by-step explanation:
Start by finding the slope of the given line.

Slope of given line




A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.




, where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

Midpoint of given line


= (0, 2)

When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is
.
Answer:
A.
= 
Step-by-step explanation:
of the students wore shorts.
of the students wore jeans.
Converting the fractions of the students who wore shorts and jeans respectively;
= 0.25
= 0.25
This means that the ratio of students who wore shorts is the same as that of students who wore jeans.
i.e
= 
Answer:
5r^2+2
Step-by-step explanation:
(4r^2 – 3r + 2) – (-r^2 – 3r) =
Distribute the minus sign
(4r^2 – 3r + 2) +r^2 + 3r =
Combine like terms
(4r^2 + r^2 – 3r+ 3r + 2) =
5r^2+2
Answer:
A. 1/5k - 2/3j and -2/3j +1/5k
Step-by-step explanation:
A. 1/5k - 2/3j and -2/3j +1/5k
B. 1/5k - 2/3j and -1/5k +2/3j
There is a change in the signs of each term
1/5k changed to -1/5k
-2/3j changed to +2/3j
Not equivalent
C. 1/5k - 2/3j and 1/5j - 2/3k
There is a change in the variables
1/5k changed to 1/5j
-2/3j changed to -2/3k
D. 1/5k - 2/3j and 2/3j - 1/5k
The is a change in the signs of each term
1/5k changed to -1/5k
-2/3j changed to +2/3j
The only equivalent expression is
A. 1/5k - 2/3j and -2/3j +1/5k