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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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Annie needs $30 to buy a coat she has saved $12 and plans to work as a baby siter to earn $6 per hour which inequality shows the
tekilochka [14]

Answer:

The answer would be B. 12 + 6n is greater than or equal to 30, so n is less than or equal to 3.

explanation:

I'm bad with explaining things, but I'll try my best to explain why this is the right answer.

12 + 6n ≥ 30, so n ≤ 3

let's start with the 12 at the beginning of the inequality, Annie already has $12, so the 12 in the inequality shows the amount of money she already has being added to the $6 per hour of babysitting she needs to do (n).

Now for the + 6n, the plus is there to show that the $12 Annie already has is being added to the 6n. The 6n then represents the $6 Annie makes each hour and the n represents how many hours she needs to babysit in order to get $30. The 6 is being multiplied by the amount of hours she needs to babysit to show how much money Annie would make. Then you add on the $12 she already has.

Annie then needs at least $30, but if she makes more than $30 then she will simply have more money than needed, therefore you use the greater than or equal to sign to show that she can have more money than just $30 after working.

I hope this helps, and sorry if my explanation is hard to understand lol.

6 0
2 years ago
What is the length of DE in the right triangle below ?
olganol [36]
B.25
sorry if my writing is not clear 

3 0
3 years ago
Read 2 more answers
if you deposit $500 at an interest rate of 3% for four years, how much will you receive when you withdraw it from the bank?
Ray Of Light [21]
 1st year 500* 0.03 = 15+500=515
 2nd year 515*0.03=  15.45 + 515 = 530.45
 3rd year 530.45*0.03= 15.9135 + 530.45 = 546.3635
 4th year 546.3635 * 0.03 = 16.390905 + 546.3635 = 562.754405
562.754405
8 0
3 years ago
If ΔABC is an equilateral triangle with, AB = 2x + 17, BC = 6x - 19, AC = 4x-1, find x and the measure of each side
Soloha48 [4]

Answer:

x=9, AB=BC=AC=35

Step-by-step explanation:

Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that AB=BC=AC. We are given the lengths of all 3 sides in terms of x, but we only need to set two of them equal to each other to solve for x. Let's use AB and BC to solve for x. We know that AB=BC, AB=2x+17, and BC=6x-19. Therefore, we can write the following equation to solve for

AB=BC\\2x+17=6x-19 (Substitute given values into equation)

Solving for x, we get:

2x+17=6x-19\\2x+17-17=6x-19-17 (Subtract 17 from both sides of the equation to isolate constants)

2x=6x-36 (Simplify)

2x-6x=6x-36-6x (Subtract 6x from both sides of the equation to isolate x)

-4x=-36 (Simplify)

\frac{-4x}{-4}=\frac{-36}{-4} (Divide both sides of the equation by -4 to get rid of x's coefficient)

x=9 (Simplify)

Therefore, AB=2x+17=2*9+17=18+17=35, and AB=BC=AC=35. Hope this helps!  

3 0
2 years ago
Pleaseee Solve x? - 8x = 20 by completing the square. Which is the solution set of the equation?
gavmur [86]
The correct answer is A. -22,14
3 0
3 years ago
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