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Delicious77 [7]
3 years ago
9

An open box is to be made from a flat piece of material 19 inches long and 3 inches wide by cutting equal squares of length xxfr

om the corners and folding up the sides. Write the volume VVof the box as a function of xx. Leave it as a product of factors, do not multiply out the factors.
Mathematics
1 answer:
Whitepunk [10]3 years ago
6 0

Answer:

V=x(19-2x)(3-2x)

Step-by-step explanation:

The flat piece of material is 19Inches Long and 3 Inches Wide.

If we cut a square if length x from each corner:

Length if the Box=19-x-x=19-2x

Width if the Box=3-x-x=3-2x

The flap that will be folded up will be the height.

Therefore, Height of the Box= x inches.

Volume of a cuboid=lwh

Therefore the volume of the box will be:

V=x(19-2x)(3-2x)

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Solve the equation.<br><br> x+4=−14<br><br> what does x equal
lisabon 2012 [21]
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2 years ago
Four darts are thrown at this dartboard. If all four darts hit the board, how many different point totals are possible. (Dartboa
jonny [76]

Answer:

Different point total are possible = 497

Step-by-step explanation:

Given - Four darts are thrown at this dartboard. Dartboard regions are  

             1, 4, 7, 10 points

To find - If all four darts hit the board, how many different point totals are

              possible.

Proof -

Are given there are 4 regions -

1st region - 1 point

2nd region - 4 points

3rd region - 7 points

4th region - 10 points

Case I :

If all the darts hit the different region -

Total points possible are - 1 + 4 + 7 + 10 = 22 points

Case II :

If all the darts hit the same region -

It means either they hit 1 region or 2nd region or 3rd region or 4th region

If they all 4 hit first region , points are - 1+1+1+1 = 4

If they all 4 hit second region , points are - 4+4+4+4= 16

If they all 4 hit third region , points are - 7+7+7+7 = 28

If they all 4 hit fourth region , points are - 10+10+10+10 = 40

So,

the Total points possible are - 4 + 16 + 28 + 40 = 88

Case III :

If 3 darts hit the same region -

Sub-case 1 :

If 1 dart hit 1st region, other 3 dart hit 2nd region

Points are - 1 + 4 + 4+ 4 = 13

Sub-case 2 :

If 1 dart hit 1st region , other 3 dart hit 3rd region

Points are - 1 + 7 + 7 + 7 = 22

Sub-case 3 :

If 1 dart hit 1st region , other 3 dart hit 4th region

Points are - 1 + 10 + 10 + 10 = 31

Sub-case 4 :

If 1 dart hit 2nd region , other 3 dart hit 1st region

Points are - 4 + 1 + 1 + 1 = 7

Sub-case 5 :

If 1 dart hit 2nd region , other 3 dart hit 3rd region

Points are - 4 + 7 + 7 + 7 = 25

Sub-case 6 :

If 1 dart hit 2nd region , other 3 dart hit 4th region

Points are - 4 + 10 + 10 + 10 = 34

Sub-case 7 :

If 1 dart hit 3rd region , other 3 dart hit 1st region

Points are - 7 + 1 + 1 + 1 = 10

Sub-case 8 :

If 1 dart hit 3rd region , other 3 dart hit 2nd region

Points are - 7 + 4 + 4 + 4 = 19

Sub-case 9 :

If 1 dart hit 3rd region , other 3 dart hit 4th region

Points are - 7 + 10 + 10 + 10 = 37

Sub-case 10 :

If 1 dart hit 4th region , other 3 dart hit 1st region

Points are - 10 + 1 + 1 + 1 = 13

Sub-case 11 :

If 1 dart hit 4th region , other 3 dart hit 2nd region

Points are - 10 + 4 + 4 + 4 = 22

Sub-case 12 :

If 1 dart hit 4th region , other 3 dart hit 3rd region

Points are - 10 + 7 + 7 + 7 = 31

So,

Total points possible are - 13+22+21+7+25+34+10+19+37+13+22+31 = 254

Case IV :

If 2 darts hit the same region -

Sub-case 1:

If 2 darts hits 1st region , other 2 darts hit 2nd region

Points are - 1 + 1 + 4 + 4 = 10

Sub-case 2:

If 2 darts hits 1st region , other 2 darts hit 3rd region

Points are - 1 + 1 + 7 + 7 = 16

Sub-case 3:

If 2 darts hits 1st region , other 2 darts hit 4th region

Points are - 1 + 1 + 10 + 10 = 23

Sub-case 4:

If 2 darts hits 2nd region , other 2 darts hit 3rd region

Points are - 4 + 4 + 7 + 7 = 22

Sub-case 5:

If 2 darts hits 2nd region , other 2 darts hit 4th region

Points are - 4 + 4 + 10 + 10 = 28

Sub-case 6:

If 2 darts hits 3rd region , other 2 darts hit 4th region

Points are - 7 + 7 + 10 + 10 = 34

So,

Total points possible are - 10 + 16 + 23 + 22 + 28 + 34 = 133

Case V :

If 1 darts hit the same region -

This case is include in the Case III.

∴ we get

Different point total are possible = Points in Case I +  II +  III +  IV

                                                       = 22 + 88 + 254 + 133

                                                       = 497

⇒Different point total are possible = 497

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2 years ago
Find the slope-intercept form of the equation that passes through the points (3, -4) and (1, 2)
quester [9]

Answer:

y = -3x + 5

Step-by-step explanation:

(y2-y1)/(x2-x1)

Plug coordinates into that

Then plug one of the coordinates into y = -3x+b to get b

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2 years ago
Paloma ran 3 3/4 miles around the school track. If each lap is 1/2 mile, how many laps did she run?
Ratling [72]

Answer:

9

Step-by-step explanation:

It is 9 because 1/2 goes into 3, 6 times, and then 3/4 divided by 1/2 is 1 1/2 so 1/2 goes into 3/4 1/12 times, so then figure out how mnay 1/2 is in 1 1/2 and youll get 3 so 6 plus 3 equals 9 :)

7 0
2 years ago
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