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Elenna [48]
3 years ago
8

The length of a rectangle is 6 feet longer than its width. If the perimeter of the rectangle is 56 feet, find its length and wid

th.
Mathematics
1 answer:
alexira [117]3 years ago
6 0
2(6+x) + 2x=56
12+4x=56
-12       -12
4x=44
÷4   ÷4
x=11

The measure of the width is 11ft
and the measure of the length is:
11+6=17ft
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The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?
Amanda [17]

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

         1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm.  That's interesting.  64 happens to be the square of 8 . 
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3                                   Items = 2, Sum = 4
1, 3, 5, 7                           Items = 4, Sum = 16
1, 3, 5, 7, 9, 11                 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing !  The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.

I slogged through it on my calculator, and it's true.

I never knew this before.  It seems to be something valuable
to keep in my tool-box (and cherish always).


3 0
3 years ago
The scale on a map indicates that 1 inch corresponds to an actual distance of 95 miles. two cities are 4.5 inches apart on the m
arlik [135]
The two cities are actually 427.5 miles apart.
3 0
3 years ago
Lonny is serving soup for charity. Each bowl holds 2.15 cups of soup. How many bowls will Lonny use if he serves a total of 94.6
azamat

Answer: 44 bowls

Step-by-step explanation:

94.6 divided by 2.15 = 44 bowls of soup

***If you found my answer helpful, please give me the brainliest. :) ***

7 0
3 years ago
What is the value of the expression? Negative 16 + 12
Vera_Pavlovna [14]

Answer:

B) Negative 4

4 0
3 years ago
For what value of x does 3^4 x = 27^x - 3? a.–9 b.–3 c.3 d.9
Inessa05 [86]

Answer:

A

Step-by-step explanation:

3 0
3 years ago
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