1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
14 bugs are crawling on the steps. Some of the bugs are black, and 4 are
docker41 [41]

Answer:

b  = 14-4

Step-by-step explanation:

Let the number of black bugs be b

Let the number of green bugs be g

If 14 bugs are crawling on the step, then;

b + g = 14 ....1

If there are 4 green bugs, then g = 4

Substitute g = 4 into the equation

b + g = 14

b + 4 = 14

b = 14 - 4

Hence the sentence that can be required to find the number of black bugs is b  = 14-4

8 0
3 years ago
M - 37 = 56<br> jack has 56 marbles Kyle has 37 fewer than jack
Goshia [24]

Do we have to solve for M if so, the answer is

m-37  = 56

m =56 + 37

m = 93

hope it's helpful

8 0
3 years ago
Carolyn swim 35 laps in 1/2 hour. How far will she swim in 4 hours? Please help.
NARA [144]
70 laps in 40 hours


1/2+1/2=4

35+35=70
I think
3 0
2 years ago
Read 2 more answers
Sue's average score for three bowling games was 162. In the second game, Sue scored 10 less than in the first game. In the third
natali 33 [55]

Answer:

Her score in the first game was 173.

Step-by-step explanation:

Sue's total score for the 3 games = 3*162 = 486 points.

Let her score in the first game be x points. Then in the second game she scored (x - 10)  and in the third, ( x - 10 - 13) points:

x + (x - 10) + (x - 23) = 486

3x - 33 = 486

3x = 519

x = 173 (answer).


7 0
2 years ago
Read 2 more answers
Laree is buying a car that costs 4,155. she has 1,575 and will borrow the rest from her parents. will payments of 225 per month
Natasha_Volkova [10]
The car cost $4,155 and she has $1,575 so $4,155-$1,575=$2,580as the balanced owed if she borrows the rest from her parents and has a one year to pay it off it will be paid off because her payments are $225 a month for one year  at 225x12=$2,700 its a little over but it will be paid off
5 0
2 years ago
Other questions:
  • How do you write the expressions part
    11·1 answer
  • A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 88 wood and 1111 graphite are defective an
    14·1 answer
  • Triangle ABC is shown below: Triangle ABC is shown. A is at 2, 1. B is at negative 1, 4. C is at 3, 7. If triangle ABC is reflec
    6·2 answers
  • models the cost, in dollars, of a rug with width x feet. What is the cost of a rug that is 9 feet wide?
    5·2 answers
  • Name the properties of a rectangle
    7·1 answer
  • What is the total amount paid for a bill of $64.00 with a tip of 15%? (Round to the nearest cent.)
    10·1 answer
  • Frank has a compass but no straightedge. Which of the following can Frank construct with just the compass?
    15·2 answers
  • If y equals -18 when x is 6 find x when y is 6
    14·1 answer
  • Plz help me fast plz
    5·2 answers
  • Given each bottle, match the Height vs. Volume graph that will be created as the bottle is consistently filled with a liquid.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!