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vodomira [7]
2 years ago
12

A ballroom has a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increase

d by one foot, would its area be a rational number? explain
Mathematics
2 answers:
Vikentia [17]2 years ago
7 0
Yes, in the sense that the new area could be written as (x+1)^2  /   1.
Usually we would not bother with the "1" as divisor.

Let's actually do the work:  what is the area of the square if we increase the side length of the existing square by 1 ft?

(x+1)^2 = x^2 + 2x + 1        (This is not a fraction, and thus not the ratio of
                                            two integers, which, in turn, is the definition of
                                            "rational number."
lidiya [134]2 years ago
7 0

Answer:

The area is a rational number.

Step-by-step explanation:

Consider the provided information.

A ballroom has a square dance floor. The area of the floor is 400 square feet.

Area of square = (side)²

Substitute the respective value in above formula.

400 = (side)²

√400 = side

20 feet = side

Ignore the negative value as side cannot be a negative number.

Now it is given that the length of each side of the square increased by one foot,

Thus, the new side is 20 + 1 = 21 feet

Now find the area of new square = (side)²

A = 21²

A = 21×21

A = 441 square feet

The number 441 is a rational number.

Hence, the area is a rational number.

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posledela

Answer:

3:1

Step-by-step explanation:

24:8 can both be divided by 8, 24/8 = 3, 8/8 = 1, making the ratio

3:1 ,

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Step-by-step explanation:

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What’s the opposite of negative two
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Answer: The answer is two

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a pet shop sells a 6 can multipack of dog food for £3.18 and a 15 can multipack for £7.80. which multipack is the best value for
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Lake Michigan's volume is approximately 1,180 cubic miles and its surface area is approximately 14,332,090 acres. The 2015 water
galben [10]

Answer:

a.)   depth of the lake = (volume of the lake) / area of lake

            = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet

b.) 11 inches  = 0.9167 feet

    Water gained in cubic feet gained by the lake

         = 624,305,840,400 \times  0.9167  

         = 572,282,434,719.5 cubic feet

c.) the percentage change in the lake volume over that year

      = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet

      =  0.0033

      = 0.33%

Step-by-step explanation:

i) acres to square feet :    1 acre = 43560 square feet

  therefore 14,332,090 acres  = 624,305,840,400 square feet

ii) 1 mile  = 5280 feet

   1 cubic mile  = 5280 \times 5280 \times 5280 = 147,197,952,000 cubic feet

therefore 1180 cubic miles  = 173,693,585,360,000 cubic feet

a.)   depth of the lake = (volume of the lake) / area of lake

            = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet

b.) 11 inches  = 0.9167 feet

    Water gained in cubic feet gained by the lake

    = 624,305,840,400 \times  0.9167   = 572,282,434,719.5 cubic feet

c.) the percentage change in the lake volume over that year

  = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet

   =  0.0033

  = 0.33%

7 0
3 years ago
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