The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?

Answers

Answer 1

Answer:
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 first 20 consecutive odd numbers.

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).

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Does the equation represent a direct variation? If so, find the constant of variation.4x -5y = 0

a. yes; k = -5 b. no c. yes; k = 4/5 d. yes; k = - 4

Answers

Answer:

4/5

Step-by-step explanation:

4x-5y=0

subtract 4x on both the sides

4x-4x-5y = 0-4x

-5y = -4x

divide by -5 on both the sides

-5y/-5 = -4x/-5

y =( 4/5 )x

Miguel completed the division problem below. What is Miguel’s error?A.He included a 5 in the quotient, which does not belong.
B.He multiplied the divisor by 10 and the dividend by 100.
C.He subtracted 208 from 234 incorrectly.
D.He multiplied the divisor by 100 and the dividend by 10.
down there is a jpg

Answers

Answer:

he need to add one more zero to 7540

Step-by-step explanation:

He needs to add another zero at the end of 7540

When x = 3 and y = 5, by how much does the value of 3x^2 – 2y exceed the value of 2x^2 – 3y ?F. 4
G. 14
H. 16
J. 20
K. 50

Answers

$3\cdot3^2-2\cdot5-(2\cdot3^2-3\cdot5)=27-10-(18-15)=17-3=14$

A video game is on sale for 30% off the regular price of $50.

Answers

30% is equal to 0.30.
You do:
0.3 * 50= $15
The price is now $15

How to do HCF and LCM

Answers

To find the GCF, list the prime factors of each number, then multiply the factors that both number have in common. To find the LCD, find the smallest possible integer divisible by both numbers.

Answer:For HCF you can list the factors of the numbers and see which is the highest factor that they have in common. For LCM you list put the multiples and find the lowest one they have in common

For which of the following inequalities is x greater than or equal to 4 a solution?A) x + 3 is greater than or equal to 1
B) 3x is greater than or equal to 1
C) x - 3 is greater than or equal to 1

Answers

Either a or b. Depends on what X equals.For example, question a.-X+3, it has to be at least 1.Answer b-3X, has to be a little over 2. So I guess the most correct answer has to be A.

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