Which of the following correctly identifies the set of outputs?
1 answer:
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There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.
Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.
We are required to find the number of ways in which the volunteers can be assigned.
Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.
n=n!/r!(n-r)!
Number of ways in which the volunteers can be assigned is equal to the following:
Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.
Number of ways =14
=14!/12!(14-12)!
=14!/12!*2!
=14*13/2*1
=91 ways
Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.
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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 +