Which ordered pair is the solution to the system of equations?

2x-5y=-5
x+2y=11

The value of u is -144

Solution:

Given that,

We have to solve for "u"

From given,

Convert the division problem into multiplication, by changing the division sign to multiplication sign. Then invert the number to right of division sign

Thus we get,

Isolate for u

Thus the value of u is -144

The surface area of the composite shape is 1560 square inches

Step-by-step explanation:

The surface area of the top cardboard is,

SA = 5 x area of each side

Because one side is attached with another cardboard box . So while finding the area only 5 sides are calculated.

SA = 5 ( 10 x 10)

  = 500 square inches

The surface area of the rectangular prism cardboard,

Given that,

l = 20 in

w =15 in

h = 8 in

A = 2(lw + wh + hl) - 100

We are subtracting 100 because it is the area of one side of the square cardboard box on top of the rectangular prism box .

A = 2(300 + 120 + 160) - 100

= 2(580) - 100

= 1160-100

= 1060 square inches

Total surface area = SA + A

= 500 + 1060

= 1560 square inches

The surface area of composite shape is 1760 square inches, if two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in and the bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.

Step-by-step explanation:

The given is,

                The top box is a cube with sides of 10 in

                The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.

Step:1

      Surface area of composite figure = Surface area of cube +

                                                                  Surface area of rectangular prism

Step:2

        Formula for surface area of cube,

        ( Only 5 sides area considered )

        Where, a - Side of cube

       From given, a = 10 inches

       From the surface area equation,

                                             = (5)(100)

                                             = 500

         Surface area of cube = 500 square inches

Step:3

          Formula surface area of rectangular prism,

         Where, w - Width

                      l - Length

                      h - Height

         From the given values.

                     w = 15 inches

                       l = 20 inches

                      h = 8 inches

         Surface area equation becomes,

                                                 = 2 ( 300 + 160 + 120 )-100

                                                 = 2 (580)-100

         Surface area of rectangular prism = 1060 square inches

         From the step 1,

              Surface area of composite shape = 500+1060

                                                                        = 1560 square inches

Result:

        The surface area of composite shape is 1560 square inches.

Answer:

66.67 ml of 5% solution and 133.33 ml of 6.5% solution are mixed.

Step-by-step explanation:

Let 200 ml of 6% solution is formed by mixing x ml of 5% solution and y ml of 6.5% solution.

We can write the equation x + y = 200 ........ (1)

Now, x ml of 5% solution will contain ml of acid  

Again, y ml of 6.5% solution will contain ml of acid.

So, mixing them together will give (0.05x + 0.065y) ml of acid in 200 ml of solution.

So, from the condition given we can write  

⇒ 0.05x + 0.065y = 12  

⇒ x + 1.3 y = 240 ........... (2) {Dividing both sides by 0.05}

Now, solving equations (1) and (2), we get

0.3y = (240 - 200) = 40

⇒ y = 133.33 ml  

From equation (1) we get, x = 200 - 133.33 = 66.67 ml

Therefore, 66.67 ml of 5% solution and 133.33 ml of 6.5% solution are mixed. (Answer)