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Diano4ka-milaya [45]
3 years ago
6

Solve the system of equations. 14x+5y=31 2x−3y=−29 ​

Mathematics
1 answer:
Nastasia [14]3 years ago
8 0

Answer:

  (x, y) = (-1, 9)

Step-by-step explanation:

A graphical solution can be quick and easy. It shows the solution to be ...

  (x, y) = (-1, 9)

__

Another suitable method is Cramer's rule. It makes use of a particular pattern of sum of products of coefficients and constants. The denominator in each case is the same sum of products.

  x = (5(-29)-(-3)(31))/(5(2)-(-3)(14)) = -52/52 = -1

  y = (31(2)-(-29)(14))/52 = 468/52 = 9

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y=10x

Step-by-step explanation:

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A cylindrical container has a radius of 3 centimeters and a height of 12 centimeters. The container is filled with water up to t
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Answer:

volume of empty space = 141.3 cm³

Step-by-step explanation:

volume of empty space = volume of the cylinder - volume of water

First, we need to calculate the volume of the container

volume of a cylinder = πr²h

 where r = radius of the container   and   h is the height of the container

r = 3cm  and h = 12 cm    π is a constant which is ≈ 3.14

volume of a cylinder = πr²h

                                  =3.14 × 3²×12

                                   =3.14×9×12

                                    =339.12 cm³

We will proceed to find the volume of water

since liquid will take the shape of its container,

then volume of water =  πr²h

r is the radius of the container   and    h is the height of the water

r = 3cm    and   h = 7cm      

volume of water =  πr²h

                             = 3.14 ×3²×7

                              =3.14×9×7

                              =197.82 cm³

volume of empty space = volume of the cylinder - volume of water

                                          =339.12 cm³    -    197.82 cm³

                                          = 141.3 cm³

OR

WE CAN SOLVE DIRECTLY

height of empty space = height of container - height of water

                                       = 12 - 7

                                        =5 cm

volume of empty space = πr²h

                                        =3.14×3²×5

                                        =3.14×9×5

                                         =141.3 cm³

volume of empty space = 141.3 cm³

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