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mixas84 [53]
3 years ago
6

Convert the line into slope intercept form: 3x + 5y =-15

Mathematics
1 answer:
kipiarov [429]3 years ago
3 0
3x-5y=-15
move the x to the other side
-5y=-3x-15
divide all by -5
y= 3/5x+3
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What is the slope of the line parallel to y= 5x+2.<br><br> A. -1/5<br> B. -5<br> C. 5<br> D. 1/5
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slope = 5

Step-by-step explanation:

Parallel lines have the same slope

Equation: y = mx + b

So, slope m = 5

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If 8 identical blackboards are to be divided among 4 schools,how many divisions are possible? How many, if each school mustrecei
MAXImum [283]

Answer:

There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.

Step-by-step explanation:

Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.

 The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is {11 \choose 3} = 165 . As a result, we have 165 ways to distribute the blackboards.

If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is {7 \choose 3} = 35. Thus, there are only 35 ways to distribute the blackboards in this case.

4 0
3 years ago
To win the carnival game Ring Ding, you must toss a wooden ring onto a grid of rectangles so that it lands without touching any
guapka [62]

Answer:

5in x 10in

Step-by-step explanation:

Solution:

1.  You have to assume that the ring will land on the board and as a result, just focus on one rectangle of the board since they are all the same size.  

 

2.  For the ring to land entirely inside the rectangle, the center of the ring needs to be 1.5 inches inside the border (radius is 1.5 inches), so the "winning rectangle" will have dimensions:

                               L = (x - 2(1.5)) = x - 3

                              w = (2x - 2(1.5)) = 2x-3.

 

3.  Now, we will set up and solve our geometric probability equation.  The winning rectangle's area of (x-3)*(2x-3) divided by the total rectangle's area of x*(2x) = 28%

 

                                (2x-3)*(x-3)/(2x^2) = .28

                                2x^2 - 9x + 9 = .56x^2

                                1.44x^2 - 9x + 9 = 0

 

4 .  Now you can plug that in the quadratic formula and get the solutions x = 1.25 or 5.  However, it cannot by 1.25 because that is too small of a dimension for the the circle with diameter of 3 to fit in, the answers has to be 5.

 

5. As a result, the dimensions of the rectangles are 5in x 10in.  

6 0
3 years ago
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