Answer:
a = 20
Step-by-step explanation:
The mean is calculated as
mean = 
=
= 
Then
= 27 ( multiply both sides by 5 to clear the fraction )
115 + a = 135 ( subtract 115 from both sides )
a = 20
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
<h3>Right angled triangle</h3>
A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.
For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.
Find the slopes of AB, BC and AC
Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5
Slope of BC = 0-5/7-1
Slope of BC = -5/6
Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11
Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
Learn more on right angle triangle here: brainly.com/question/22790996
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By solving a linear equation, we will see that the total cost for renting the bus is $90.
<h3>What was the total cost of renting the bus, in dollars?</h3>
Let's say that the total cost is C.
When there are 20 students, each student should pay:
p = C/20
When the other 10 students are added (for a total of 30) each student pays:
p' = C/30.
We know that the cost for each of the original 20 students decreased by $1.50, so:
p' = p - $1.50
Then we have 3 equations to work with:
p = C/20
p' = C/30.
p' = p - $1.50
Now we can replace the first and second equations into the third one:
C/30 = C/20 - $1.50
Now we can solve this linear equation for C:
C/20 - C/30 = $1.50
C*( 1/20 - 1/30) = $1.50
C*(30/600 - 20/600) = $1.50
C*(10/600) = $1.50
C*(1/60) = $1.50
C = 60*$1.50 = $90
So the total cost for renting the bus is $90.
If you want to learn more about linear equations:
brainly.com/question/1884491
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if the length is 8ft and the width is (7+x) then the area would be 56+8x, if x is unknown.
Each strip is 29 cm
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Change the m to cm
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6 m = 600 cm
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Find the number of strips for 1 6m-board
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Find the number of strips that can be cut from the 6m board.
600 ÷ 29 = 20 pieces remainder 20cm
So we can only cut 20 pieces of 29 strips from one 6m board.
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Find number of boards needed
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70 ÷ 20 = 3.5
We need 3.5 of the 6m boards.
Since she can't have half a board, she has to buy 4 pieces of the board.
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Answer: 4 pieces of the 6m board.
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