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meriva
3 years ago
14

Rewrite 48 + 60 using the distributive property

Mathematics
1 answer:
Flauer [41]3 years ago
3 0

Answer:

12* ( 4+5)

Step-by-step explanation:

48 = 12 * 4

60 = 12 * 5

48 + 60 = 12*4 + 12*5

             = 12*( 4 + 5)

            = 12* 9

            = 108

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You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f
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Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m   (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m   and   W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L       is  L - 2*x               l =  4 - 2*x

For the side W      is  W - 2*x             w=  2 - 2*x

The height              is  x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x    ⇒  V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x     V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0       8  - 24x + 12x² = 0     reordering    12x² - 24x + 8  = 0

or    3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂  = ( 6 ± √36 - 24 ) /6

x₁,₂  = ( 6 ± 3.46) /6

x₁  =  6 + 3,46 /6     x₁  = 1.58  we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂  =( 6 - 3,46 ) / 6

x₂  = 0,42 m

Dimensions of the open box

l  = 4 - 2*x     l  = 4 - 0,85      l  =  3,15 m

w = 2 -2*x    w  = 2 - 0,85     w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

8 0
2 years ago
3. Simplify: 13.6 - 4.1 - 3.8 + 6.7
Art [367]

Answer:

12.4 is the answer

=13.6+6.7-4.1-3.8

=20.3-7.9

=12.4

5 0
2 years ago
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okay so I don't really understand how to change a decimal to a fraction and the teacher never really explained it to us and she
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A rental car service charges $25 to rent a car, plus $2 per mile. If x represents the number of miles driven, then the expressio
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2 years ago
a chess player won 72 of the games he played . if his ratio of wins to loses was 9:4, how many games did he play in total
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Answer: He played a total of 104 chess games.

Step-by-step explanation:

9:4

72:x

9:4 = 72:x

72 * 4 = 288

288/9 = 32

x = 32

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