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professor190 [17]
3 years ago
10

4. A rectangular back yard ice rink is to have an area of 1200m, and will be surrounded by boards. [6]

Mathematics
1 answer:
tamaranim1 [39]3 years ago
7 0

Answer:

<h2>20 meters by 60 meters.</h2><h2>80 boards.</h2>

Step-by-step explanation:

We know that the ice rink is 1200 square meters, which means to enclose the rink we need dimensions of 20 meters by 60 meters, to have 1200 square meters of area.

Now, the boards are on the perimeter of the ice rink with dimensiosn 20 meters times 60 meters. So, its perimeter is

P=2(l+w)=2(60+20)=2(80)=160m

If each board is 2.0 meter long, that means we can divide to find the total number of boards we can have on the ice rink:

n=\frac{160}{2} =80

Therefore, with those dimensions, we can have 80 boards surrounding the ice rink.

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Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
blagie [28]
A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;5x-4=-2 \times 3x-2 \times 2 \\&#10;5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\&#10;11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\&#10;11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\&#10;x=0

B.
3(2x-4)=5x-1 \\&#10;6x-12=5x-1 \\&#10;\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\&#10;11x=11 \\&#10;\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\&#10;x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\&#10;x=11
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Step-by-step explanation:

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Step-by-step explanation:

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B

Step-by-step explanation:

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