Which gives 28 + 24 as a product of the GCF and a sum?
1 answer:
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To find the inverse of a function, we make the independent variable the subject of the formula.
Thus, the inverse of the given function is evaluated as follows.
From the work show, it can be seen that Talib's work is correct.
Thus, the inverse of the given function is evaluated as follows.
From the work show, it can be seen that Talib's work is correct.
Answer:
4. The equation of the perpendicular bisector is y = x -
5. The equation of the perpendicular bisector is y = - 2x + 16
6. The equation of the perpendicular bisector is y = x +
Step-by-step explanation:
Lets revise some important rules
- The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is
(reciprocal m and change its sign)
- The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
- The formula of the slope of a line is
- The mid point of a segment whose end points are
and
is
- The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept
4.
∵ The line passes through (7 , 2) and (4 , 6)
- Use the formula of the slope to find its slope
∵ = 7 and
= 4
∵ = 2 and
= 6
∴
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line =
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point =
∴ The mid-point =
- Substitute the value of the slope in the form of the equation
∵ y = x + b
- To find b substitute x and y in the equation by the coordinates
of the mid-point
∵ 4 = ×
+ b
∴ 4 = + b
- Subtract from both sides
∴ = b
∴ y = x -
∴ The equation of the perpendicular bisector is y = x -
5.
∵ The line passes through (8 , 5) and (4 , 3)
- Use the formula of the slope to find its slope
∵ = 8 and
= 4
∵ = 5 and
= 3
∴
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line = -2
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point =
∴ The mid-point =
∴ The mid-point = (6 , 4)
- Substitute the value of the slope in the form of the equation
∵ y = - 2x + b
- To find b substitute x and y in the equation by the coordinates
of the mid-point
∵ 4 = -2 × 6 + b
∴ 4 = -12 + b
- Add 12 to both sides
∴ 16 = b
∴ y = - 2x + 16
∴ The equation of the perpendicular bisector is y = - 2x + 16
6.
∵ The line passes through (6 , 1) and (0 , -3)
- Use the formula of the slope to find its slope
∵ = 6 and
= 0
∵ = 1 and
= -3
∴
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line =
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point =
∴ The mid-point =
∴ The mid-point = (3 , -1)
- Substitute the value of the slope in the form of the equation
∵ y = x + b
- To find b substitute x and y in the equation by the coordinates
of the mid-point
∵ -1 = × 3 + b
∴ -1 = + b
- Add to both sides
∴ = b
∴ y = x +
∴ The equation of the perpendicular bisector is y = x +