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sum_(n=1)^100(n + 43) = 9,350

This should work: 

I redacted my solution.

Oops!

Your final answer is correct, but 180-76 is not 140  

( x + 5 )² + 5² = ( x + 6 )²   

Im sorry, but what do you mean? Thanks!

:)

140 ???

Since we know that there were 12 boys, and their mean score was 5, we can say that they scored a total of 60 points.

We can also say that the girls scored a total of 8N points. We can form this equation:

60 + 8N = 180

8N = 120

N = 15

Therefore, there were 15 girls.

:)

We see that since BDC is an iscosoles triangle, so therefore angle BDC = angle BCD = x.

28 + 2x = 180

2x = 152

x = 76

From here, we see that angle EDB = 180 - 76 = 104

Since we are talking about a parallelogram, angle EDB = angle EAB = 104

:)

If: The signs are different.

This is because it can't remain constant. One will be addition, while the other subtraction, or they are both subtraction, but from different values.

Let's test it out. 
 

Positive: 

a = 2

b = 3

|2 - 3| = 1

|2| - |3| = 1

Negative:
a = -2

b = -3

|-2 + 3| = 1

|-2| - |-3| = 1

One positive, one negative:

a = 2

b = -3

|2 + 3| = 5

|2| - |-3| = -1

(same vice versa)

:)

Let angle(AOB) be x. Based on the information we have, we can conclude that angle(COD) is 3x. Now, we can form an equation:

4x + 110 = 180    <------ angle of straight line

4x = 70

x = 17.5

:)

Thank you!!!!!!!!! Can you please help with the problem I just posted??

To calculate this, we first need to "find" the area of both shapes: the big rectangle and the small rectangle.

BIG RECTANGLE: 

4x * (x + 2) = 4x^2 + 8x

SMALL RECTANGLE:

x * (3x + 5) = 3x^2 + 5x

[ shaded area ] = [ big rectangle area ] - [ small rectangle area ]

This is 4x^2 + 8x - (3x^2 + 5x) = 4x^2 + 8x - 3x^2 - 5x = x^2 + 3x

:)

The width is 40.

Incorrect :(

Hint:  4 is also a common factor of the two terms within parentheses in the denominator.

To do this, we need to find how many bolts they make each in 1 hour. 
 

Machine A: 25 bolts per hour        <----- divide by 5

Machine B: 33 1/3 (we can round to 33) bolts per hour        <----- divide by 3

Now, we add them together: 25 + 33 = 58

Or, if they want the exact amount, it is 25 + 33 1/3 = 58 1/3

:)

To find the surface area, we need to find the area of each piece.
 

Bottom: 

6 * 15 = 60 + 30 = 90

Triangles (both) :

6 * 10 = 60

Top (both) :

Pythagorean ----> sqrt(109) * 15 * 2 = 30sqrt(109)

Now, add it all together:

90 + 60 + 30sqrt(109) = 150 + 30sqrt(109)

:)

What would you like? A factored form? I'm guessing factor, since that is what you can do:

Sorry, but I am a bit confused on why the reciprocal is needed....could you explain? Thanks! (I think OP meant a repeating decimal, not division?)

:)

                                             ----

I am assuming you mean 0.054   (Sorry, latex not working...)

Since this is a repeating decimal, we put it over [ the amount of spaces after the decimal * 9 ] (not multiplied, just that amount of 9's: ex if there was 7 spaces after the decimal, it would be 9999999)

This is 3 * 9 = 999

Now, we put 54 in the numerator:

 54       6

----- = -----

999    111

                                          --------

Therefore, the answer is  | 6/111 |  (yikes, this is much uglier than the /boxed{} command)

                                          --------

:)

Take the reciprocal of it and you get 1 / 18.5

18.5 can be written as: 18 1/2 = 37 / 2

You want the reciprocal of 37 / 2, then all you do is flip it and it becomes:

2 / 37 - That is it.

Remember, it's not asking for how many gallons of 42%, but 50%!

:)