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Bumek [7]
3 years ago
14

Simplify each expression as much as possible, and rationalize denominators when applicable. . √54x^2=?

Mathematics
1 answer:
JulijaS [17]3 years ago
3 0

Answer:

\sqrt{54x^{2}} = 3x\sqrt{6}

Step-by-step explanation:

We have

\sqrt{54x^{2}} this equals to

\sqrt{3.3.3.2.x^{2} }  now we try to agrupate to have exponent of 2 that we can cancel

\sqrt{3^{2}.3.2x^{2}}  we can take out the ones with exponent from the root

3x\sqrt{3.2} \\= 3x\sqrt{6}

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14 and 15 please thank you
Elanso [62]

Problem 14

<h3>Answer: They bought <u>too much</u> sand</h3>

-----------------------

Explanation:

Because the sandbox is a rectangular prism, aka a block, we multiply the length width and height to get the volume.

Volume = length*width*height = 6*5*1.2 = 36

The volume of the sandbox is 36 cubic feet.

The customer bought 40 cubic feet of sand, which exceeds the volume we computed earlier. The customer bought <u>too much</u> sand.

If it was a choice of buying too much or too little, I think it's better to go overboard just so you don't have to return to the store. The extra amount of sand (40-36 = 4 cubic feet) can possibly sold or donated at a later time.

==========================================================

Problem 15

<h3>Answers:</h3>
  • The equation could be 306.52 = 19.4h or  19.4h = 306.52
  • Either equation mentioned solves to h = 15.8; so the height of the prism is 15.8 meters

-----------------------

Explanation:

The rectangular prism formula to calculate the volume is

Volume = length*width*height

Note that the portion "length*width" can be replaced with "base area", because the base area is a rectangle.

So we can have this alternative formula

Volume = (base area)*height

If we know the area of the floor, and multiply by the height of the wall, then we can calculate the volume of a room like this. In this case, the floor is 19.4 square meters in area. The overall room is 306.52 cubic meters. We'll let h be the height of the wall. Use algebra to solve for h

Volume = (base area)*height

306.52 = 19.4h .... is one equation to set up

19.4h = 306.52

h = 306.52/19.4

h = 15.8

We divide both sides by 19.4 to undo the multiplication going on.

The height of the prism is 15.8 meters.

6 0
3 years ago
Can someone plz help, multiple choice
Diano4ka-milaya [45]
Where are the questions?
3 0
3 years ago
for the State Fair next month 132 people volunteer to plan the fairs activities the volunteers form 12 equal groups how many vol
MA_775_DIABLO [31]

Answer:

11

132/12

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Let the random variable X be the outcome of rolling a 6-sided die. Assuming the die is fair, the probability distribution is as
gayaneshka [121]
The answer would be 1.  

1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6.  
Divide by 6 and you have 1 for the answer.  
6 0
3 years ago
Read 2 more answers
. An amusement park bought some arcade games that cost $2,000 each and photo booths that cost $3,200 each. A total of 22 of both
geniusboy [140]

Answer:

14 arcade games and 8 photobooths were purchased

Step-by-step explanation:

x will represent the number of arcade games

y will represent the number of photobooths

We know that 22 total machines were bought which means that x+y=22

We also know that the total was 53600 which means that 2000x+3200y=53600

We can use substitution to solve this

x+y=22

x-22= -y

-x+22=y

Then plug this in for y in the next equation

2000x+3200(-x+22)=53600

Solve this and get x=14

Then plug in x=14 into any equation (I will choose the x+y one because that's easiest to solve)

14+y=22

this means y=8

This means that 14 arcade games and 8 photobooths were purchased

I double checked the math on desmos and it is correct

6 0
2 years ago
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