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maw [93]
3 years ago
15

Explain why it is possible to draw more than two different rectangles with an area of 100 square units, but it is not possible t

o draw more than two different rectangles with an area of 55 square units. The sides of the rectangles are whole numbers.
Mathematics
1 answer:
earnstyle [38]3 years ago
7 0

Answer:

100 has more divisors than 55.

Step-by-step explanation:

The prime factorization of 100 is ...

... 100 = 2²×5²

The number of divisors of 100 is the product of the exponents of these factors, after each has been increased by 1: (2+1)(2+1) = 9. Those divisors are ...

... 1, 2, 4, 5, 10, 20, 25, 50, 100

A rectangle can be formed with each divisor as the length of a side. If we count 1×100 and 100×1 as the same rectangle, then 5 different rectangles are possible:

... 1×100, 2×50, 4×25, 5×20, 10×10

_____

On the other hand, the prime factorization of 55 is ...

... 55 = 5¹×11¹

This means the number of divisors is (1+1)(1+1) = 4. Those divisors are ...

... 1, 5, 11, 55

The number of rectangles that can be formed from these is 2:

... 1×55, 5×11

100 has more divisors, so there are more ways that rectangles can be formed from them.

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Gia is running for school president. Her best friend designed a rectangular button that measures 2.5 inches by 2 inches. Gina li
vaieri [72.5K]

Answer:

B. 1 inch to 2 feet

Step-by-step explanation:

from 2.5 inches by 2 inches to 5 feet by 4 feet

hence.

the scale factor is "<u>2 inche</u>s to <u>4 feet</u>" which is 1 inch to 2 feet

8 0
3 years ago
The sum of the digits in a two-digit whole number is 9. The number in the
Arte-miy333 [17]

Answer:

63

Step-by-step explanation:

x = # in ones place

y = # in tens place

x + y = 9

y = x - 3

substitute:

x + x-3 = 9

2x - 3 = 9

2x = 12

x = 6

y = 3

8 0
2 years ago
At midnight, the temperature was 30 degrees Fahrenheit. By 6:00 am, IT had dropped 5 degrees Fahrenheit and by noon, it had incr
Allisa [31]
At noon, the temperature was 36 degrees. At midnight, the temperature was 30 degrees. By 6:00 am it drooped 5 degrees. Since it dropped 5 degrees, you subtract 5 from 30, which equals 25. It then increased by 11 degrees. Since the temperature increased, you add 11 to 25, which equals 36. At noon, the temperature was 36 degrees.
4 0
2 years ago
The value of a house that was purchased 20 years ago has been appreciating by 1.2% each year since it was purchased. If the hous
Kamila [148]

I believe it would have been $347,316.95 at the time of purchase.

1.2% of 456996 is 5483.952

5483.952 \times 20 = 109679.04

So:

456996 - 109679.04 = 347316.95

7 0
3 years ago
The rule is "Multiply by 8." Which statement is true? Number of Packages 3 5 6 8 Number of Juice Boxes 24 40 48 ? A. The number
riadik2000 [5.3K]

The statement (C) the number of juice boxes must be an even number is correct.

<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a rule is “Multiply by 8"

Number of Packages:         3    5   6    8

Number of Juice Boxes:     24  40  48

The statements are:

  • A. The number of juice boxes will always be greater than 24.
  • B. The number of packages will always be greater than the number of juice boxes.
  • C. The number of juice boxes must be an even number.
  • D. The number of juice boxes will always be 21 more than the number of packages.

Number of package starts from 3

Applying the rule: "Multiply by 8.

Number of Juice Boxes = 3×8 = 24

The statement should be the number of juice boxes will always be greater than and equal to 24.

When we multiply even with odd we get an even number.

8 is an even number.

Thus, the statement (C) the number of juice boxes must be an even number is correct.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ1

6 0
2 years ago
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