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3 years ago

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Christian is helping Jay’s family build a rectangular deck in their backyard. On the blueprint, the deck is 7.5 inches long and

9 inches wide, and the given scale states that 1.5in =3ft Determine the length and width of the actual deck.

1 answer:

In-s [12.5K]3 years ago

6 0

Answer:

length=15ft width=18ft

Step-by-step explanation:

7.5÷1.5=5 5×3=15

9÷1.5=6 6×3=18

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Hello,how do I calculate the the volume of this compound shape?

Setler [38]

To calculate the volume, we can divide this figure into three shapes. Three rectangular prisms, like the following image

The volume of a rectangular prism is given by the product between its 3 different dimensions, width, length and height. The green prism is the easiest to see the its dimensions, it has a width equals to 3, a length equals to 3 and a height equal to 1/2, therefore, its volume is

$V_g=3\times3\times\frac{1}{2}=9\times\frac{1}{2}=\frac{9}{2}=4\frac{1}{2}$

Since the width of the green prism is 3 and the red prism is 1 1/2 apart from the corner of the green prism, the width of the red prism is the difference between those values.

$3-1\frac{1}{2}=\frac{6}{2}-\frac{3}{2}=\frac{6-3}{2}=\frac{3}{2}=1\frac{1}{2}$

The length and the height of the red prism are also easy to see on the image, both of those values are 1, which means the volume of the red prism is

$V_r=1\frac{1}{2}\times1\times1=1\frac{1}{2}$

Finally, the last prism is the blue prism. The height of the green prism and the blue prism combined is equal to 3/4. Since the height of the green prism is 1/2, the height of the blue prism is

$\frac{3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{2}{4}=\frac{3-2}{4}=\frac{1}{4}$

The length of the red prism and the blue prism combined is equal to 3, since the length of the red prism is 1, the length of the blue prism is

$3-1=2$

The width of the blue prism is given, it is equal to 1. With those dimensions, we can finally calculate the volume of the blue prism.

$V_b=\frac{1}{4}\times2\times1=\frac{1}{2}$

The total volume of the compound shape is the sum of all those volumes we calculated.

$V=V_g+V_r+V_b=4\frac{1}{2}+1\frac{1}{2}+\frac{1}{2}=6\frac{1}{2}$

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1 year ago

There will be 25 party guests. 8

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3 years ago

Read 2 more answers

If nine is X percent of 45, what is X percent of 5

antoniya [11.8K]

Answer:

x percent of 5 is 1

Step-by-step explanation:

Nine is x percent of 45

x = 20

20 % of 5 = 1

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3 years ago

What is the y value of the line when x = -1

sveticcg [70]

I cannot answer that question because I need to equation

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3 years ago

Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 14 hours. James can shingle the same

Snowcat [4.5K]

we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only? well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.

we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.

let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.

$\bf \stackrel{Bob}{\cfrac{1}{14}}~~+~~\stackrel{James}{\cfrac{1}{18}}~~=~~\stackrel{total~for~1~hour}{\cfrac{1}{t}} \\\\\\ \stackrel{\textit{using an LCD of 126}}{\cfrac{9+7}{126}=\cfrac{1}{t}}\implies \cfrac{16}{126}=\cfrac{1}{t}\implies 16t=126\implies t=\cfrac{126}{16} \\\\\\ \stackrel{\textit{7 hrs, 52 minutes and 30 seconds}}{t=\cfrac{63}{8}\implies t=7\frac{7}{8}}\implies \stackrel{\textit{rounded up}}{t=7.88}$

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3 years ago