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bazaltina [42]
3 years ago
5

Find the number of rectangles in 8×8 chessboard. (not just the 1x1 squares)

Mathematics
1 answer:
Gekata [30.6K]3 years ago
8 0

Answer:

288

Step-by-step explanation:

<em>                                             Number of rectangles</em>

<em>____________________________________________________________</em>

1 × 1 squares 9-1 = 1 = 8*8 = 64

1 × 2 squares 9-2 = 7 = 8*7 = 56

1 × 3 squares 9-3 = 6 = 8*6 = 48

1 × 4 squares 9-4 = 5 = 8*5 = 40

1 × 5 squares 9-5 = 4 = 8*4 =32

1 × 6 squares 9-6 = 3 = 8*3 = 24

1 × 7 squares 9-7 = 2 = 8*2 = 16

1 × 8 squares 9-8 = 1 = 8*1 = 8

64 + 56 + 48 + 40 + 32 + 24 + 16 + 8 = 288

<em>Thus,</em>

<em>the number of squares on a chessboard is 228.</em>

<em />

<em>Hope this helps :)</em>

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The sum of a number and its reciprocal is 5/2 Find the number and its reciprocal.
sergiy2304 [10]

Answer:

Step-by-step explanation:

Let the number be 'x'

Reciprocal = \frac{1}{x}

x+\frac{1}{x}=\frac{5}{2}\\\\\frac{x*x}{1*x}+\frac{1}{x}=\frac{5}{2}\\\\\frac{x^{2}+1}{x}=\frac{5}{2}

Cross multiply

(x² + 1) *2 = 5*x

2x² + 2 = 5x

2x² - 5x + 2 =0

Factorize the equation,

Sum = -5

Product = 4

Factors = -1 , -4

2x² - x - 4x + 2 = 0

x(2x - 1) - 2(2x - 1) = 0

(2x -1 )(x - 2) = 0

2x - 1 = 0               ; x -2 = 0

    2x =1                ; x = 2

       x = 1/2

Number = 2 , and its reciprocal = 1/2

6 0
3 years ago
150% of 150 is what number? (15 points I think?)
zysi [14]

225 percent

Step-by-step explanation:

150 is the whole and 150 divided by 150 is 1.

1 whole is 100 percent

6 0
3 years ago
Read 2 more answers
Alana ate breakfast at a restaurant. The bill came to $79.75. If she left 20% tip, how much was the tip?
Lana71 [14]
$79.75*0.2= 15.95
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3 0
3 years ago
Please i need help :( <br> What is the Y- intercept of the graph of the linear function ?
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Answer:

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Step-by-step explanation:

4 0
2 years ago
Solve for x <br><br> Please help
Elodia [21]

Answer:

The answer to your question is below

Step-by-step explanation:

1) Alternate interior angles measure the same

       10x - 10° = 100°

       10x = 100° + 10°

        10x = 110°

           x = 110° / 10°

           x = 11°

2) Alternate exterior angles measure the same

       x + 99° = 90°

       x = 90° - 99°

       x = -9°

3) Supplementary angles measure 180°

       (6x + 12) + (14x + 8) = 180°

        6x + 12 + 14x + 8 = 180°

        20x + 20 = 180

        20x = 180 - 20

        20x = 160

            x = 160 / 20

            x = 8

4)  Alternate exterior angles measure the same

           26x + 1 = 131°

            26x = 131° - 1°

            26x = 130°

            x = 130° / 26°

            x = 5

5) Consecutive interior angles measure 180°

             x + 100 + 85° = 180°

             x + 185 = 180

            x = 180 - 185

              x = -5

             

6) Corresponding angles measure the same

            7x - 7 = 70

            7x = 70 + 7

            7x = 77

              x = 77 / 7

              x = 11

7) Supplementary angles measure 180°

            (12x + 8) + (100°) = 180°

              12x + 8 + 100 = 180

              12x + 108 = 180

              12x = 180 - 108

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                  x = 72 / 12

                  x = 6

8) Consecutive interior angles measure 180°

              18x + 8x - 2 = 180°

              26x = 180 + 2

               26x = 182

                   x = 182 / 26

                   x = 7

9) Corresponding angles measure the same

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10) Consecutive interior angles measure 180°

              (x + 107) + (x + 87) = 180

               x + 107 + x + 87 =  180

               2x + 194 = 180

               2x = 180 - 194

               2x = -14

                 x = -14 / 2

                 x = -7

   

         

       

5 0
3 years ago
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