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-42

2/3

Simplify the following:
-5 (-4) n m^3 m^2 n^4

-5 n m^3 (-4) m^2 n^4 = -5 n^(1+4) m^(3+2) (-4):
-5 (-4) n^(1+4) m^(3+2)

3+2 = 5:
-5 (-4) n^(1+4) m^5

1+4 = 5:
-5 (-4) n^5 m^5

-5 (-4) = 20:
Answer: |20 n^5 m^5

Expand the following:
(x-3) (x+1)

(x-3) (x+1) = (x) (x) + (x) (1) + (-3) (x) + (-3) (1):
x x+x-3 x-3

x x = x^2:
x^2+x-3 x-3

x-3 x = -2 x:
Answer: |x^2 - 2x - 3

Since the 7th term=26

And the 3rd term =10

7 - 3 =4 the difference between the 2 terms

26 - 10 =16 the difference between their values, therefore:

16 / 4 = 4 common difference

5th term=3rd + (2 x 4)

             =10 + 8

             = 18

FV =$23,000 x e^(.06*4)

FV=$23,000 x 1.27124....

FV=$29,238.73

If the mean of five numbers is 6.7, then the total of the five numbers is 5 x 6.7  =  33.5

If the mean of four of those numbers is 7.2, then the total of those four numbers is 4 x 7.2  =  28.8

Therefore the missing number must have value:  33.5 - 28.8  =  4.7

Is the problem 1/2(12x8)? The answer would be 6x4, which is 24.

If it doesn't have perenthesis , and the problem is 1/2 x 12 x 8, the answer would be 6x8, which is 48.

If it's an arithmetic sequence:                (d  is the common difference)

     a₃  =  10

     a₄  =  a₃ + d  =  10 + d

     a₅  =  a₄ + d  =  (10 + d) + d  =  10 + 2d

     a₆  =  a₅ + d  =  (10 + 2d) + d  =  10 + 3d

     a₇  =  a₆ + d  =  (10 + 3d) + d  =  10 + 4d

Since  a₇  =  26   --->   26  =  10 + 4d

                                       16  =  4d

                                         4  =  d

Since  a₅  =  10 + 2d   --->   a₅  =  10 + 2(4)  =  10 + 8  =  18

GI  bisects  angle(DGH)     angle(DGI)  =  x - 3      angle(IGH)  =  2x - 13

Since the angle is bisected:  angle(DGI  =  angle(IGH)

                                                            x - 3  =  2x - 13

Subtract x from both sides:                  -3  =  x - 13

Add 13 to both sides:                           10  =  x

(x+2)^2+y^2

The center would be (-2, 0)

Unfortunately, we need an equation to determine the radius  [ i.e., an equal sign and a number appended to what you have]

(1)   floor [  (2 - 3x) / ( x + 5) ]

Note     f(1) = -1    and f(1000)   = -3

f(1) = -1  

f(2) = -1

f(3)  = -1

f(4)  = - 2

Now, we need to find out where the function  =  exactly  -2

Solving this

[  (2 - 3x) / ( x + 5) ]  = -2, we have   x = 12

So.....from f(4) to f(12), the function takes  on a  floor value of -2  for each successive integer value of x

And from f(13) to f(1000)  the function takes on a floor value of -3  for each successive integer value of x

So

f(1) + f(2) + f(3) + ... + f(999) + f(1000)   =

3(-1) + 9(-2) + 988(-3)  = 

-2985

2x-3+3x-2=90  combine like terms on the left

5x - 5  = 90      add 5 to each sides

5x  = 95          divide both sides by 5

x = 19

To determine the number of rows, we have :

Length of the seating area / length of each row  = 

[35 + 3/4] / [3 + 1/4 ] =

[143/4] / [ 13/4]  =

143 / 13 =  

11 rows

Since [ 3 + 2 ] = 5 students sit in each row........the number of children that the bus can carry =  11 * 5  =  55 students

oh okay - derp moment there

just put \(\frac{5}{95}\)instead of \(\frac{3}{95}\)

which cancels to \(\frac{1}{19}\)

You need to choose 4 out of 8 females and 16 out of 22 males.

Since order is not important, this is a combinations problem:

 ₈C₄ · ₂₂C₁₆   =  5 222 910  ways

\((-1)2x+(-1)x\) right?

times out the brackets

\((-2x)+(-x)\)

minus + minus is a minus :D

\(-2x-x\)

collect terms

\(-3x\)

ta dah!

not a very clear question...

i guess \(\frac{-9}{1}\)

or maybe \(\frac{-1}{\frac{1}{9}}\)

maybe just \(x(8+19){(x(4-1))}^{-1}\)

i dont even...

LEt me try to answer question #3:

(x + 7) / (x² - x - 2)  =  A / (x - 2) + B / (x + 1)

Since  x² - x - 2  =  (x - 2)(x + 1)

--->   (x + 7) / (x² - x - 2)  =  (x + 7) / [ (x - 2)(x + 1) ]  =

(x + 7) / [ (x - 2)(x + 1) ]  =  A / (x - 2) + B / (x + 1)

Writing with the common denominator of  (x - 2)(x + 1)

(x + 7) / [ (x - 2)(x + 1) ]  =  [ A(x + 1) ] / [ (x - 2)(x + 1) ] + [B(x - 2) ] / [ (x - 2)(x + 1) ]

Since the denominators are equal, they can be ignored:

x + 7  =  A(x + 1) + B(x - 2)

x + 7  =  Ax + A + Bx - 2B

x + 7  =  Ax + Bx + A - 2B

Set the x-term on the left side equal to the x-terms on the right side:  x  =  Ax + Bx

   --->   x  =  (A + B)x   --->   1x  =  (A + B)x   --->   1  =  A + B

Set the number term on the left side equal to the number terms on the right side:  7  =  A - 2B

Solving:  A +   B  =  1   --->   x -1   --->   -A -  B  =  -1

                A - 2B  =  7                      --->    A - 2B  =  7

Adding down the columns:                         -3B  =  6

                                                                           B  =  -2

Since  B = -2:   A + B  =  1   --->   A + -2  =  1   --->   A  =  3

\(2x-3+3x=90\)

add 3 to both sides

\(2x+3x=90+3\)

collect terms

\(5x=93\)

divide by 5

\(x=\frac{93}{5}\)

ta dah!