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Vlad [161]
2 years ago
12

You must calculate the number of sheets of plywood needed for subflooring. Each sheet of plywood measures 4'by 8. The measuremen

ts of the house are 28 by 30' and there is a 12 by 4' hole for the stairs to come up from the basement. How many sheets of plywood will be needed? Round up to the nearest sheet
Mathematics
1 answer:
snow_lady [41]2 years ago
8 0

Answer:

25 sheets of plywood will be needed

Step-by-step explanation:

Each sheet of plywood measures 4ft*8ft=32ft^{2}.

We have to cover the surface of the house, minus the surface of the hole of the stairs.

Surface _{to cover} = Surface _{house} -Surface _{hole}= (28ft*30ft)-(12ft*4ft)= 840ft^{2}-48ft^{2}=792ft^{2}

To know how many sheets will be needed, we divide the surface to be covered by the surface of each sheet

Sheets_{needed} =\frac{Surface _{house}}{Surface _{sheet}} =\frac{792ft^{2}}{32\frac{ft^{2}}{sheet} } = 24,75 sheets

As we can't buy 0,75 of a sheet, we round it up, i.e. we will need 25 sheets of plywood for subflooring.

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1 year ago
The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers
sergejj [24]
Assume the first even integer is x.
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The reciprocals of these two even integers can be written as \frac{1}{x} and \frac{1}{x+2} respectively.

The sum of their reciprocals is 7/24. So we can set up the equation as:

\frac{1}{x}+ \frac{1}{x+2}= \frac{7}{24}

Taking LCM on left hand side:

\frac{x+2+x}{x(x+2)}= \frac{7}{24} \\  \\ &#10; \frac{2x+2}{ x^{2} +2x}= \frac{7}{24}

Cross Multiplying the denominators:

24(2x+2)=7({ x^{2} +2x}) \\  \\ &#10;48x+48=7 x^{2} +14x \\  \\ &#10;7 x^{2} +14x-48x-48=0 \\  \\ &#10;7 x^{2} -34x-48=0 \\  \\ &#10;&#10;

Using the quadratic formula to solve the above equation:
7 x^{2} -34x-48=0 \\  \\ &#10;x= \frac{34+- \sqrt{1156+1344} }{14} \\  \\ &#10;x= \frac{34+- \sqrt{2500} }{14} \\  \\ &#10;x=\frac{34+-50 }{14} \\  \\ &#10;x=6 \\ x=- \frac{8}{7} &#10;

Since, the value of x can only be an integer, we discard the fractional value and keep x=6

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Find the point p where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0
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solution:

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