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Find the cardinal number for the following sets 

A = {106, 107, 108, 109,...,142}

B= {106, 108, 110, . . ., 256}

Set A = { 106, 107, 108, 109,...,142 }
subtract from each element 105, we have 1, 2, 3, ... , 37
n(A) = 142 -105 = 37

Set B = { 106, 108, 110, . . ., 256 }
subtract from each element 104 we have 2, 4, 6, ... , 152
152= 2n

so

n(B) = 152/2 = 76

either type a non-negative number then press the ± button, or type a - (minus) sign before the number.

help trying to figure out what to substract/add

64 students in a classical music lecture class were  polled

with the results that

37 like Wolfgang Amadeus  Mozart,

36 like Ludwig von  Beethoven,

30 like Franz Joseph  Haydn,

14 like Mozart and  Beethoven,

21 like Mozart and  Haydn,

14 like Beethoven and  Haydn, and

8 like all three composers

Thank you so much 

For this equation, you will need to complete the square.

x^2 + 8x +5 = 0.

Add (b/2)^2 to get...  (Because you added 16 to the left side of the equation, you have to add 16 to the right side of the equation as well. And in this case, (b/2)^2 is 16.

(x^2 +8x + 16) + 5 = 16

Factor to get...

(x+4)^2 +5 = 16.

Subtract both sides by 16 to get...

(x+4)^2  -11 = 0.

Does anyone know how to write exponents in Windows 10?

9-5=0*2 + 0.5*a*2^2

9-5=0 + 0.5*a*4

9-5 = 2*a

4 = 2*a

Divide both sides by 2 to get... 2 = a.

a = 2.

Of course you can post it Juriemagic  :D

\(|x-5|<-1 \)

If you are talking real numbers that is impossible.

The absolute value of anything has to be greater or equal to 0.

It can not be less than a negative number!

Thanx Gh0sty 15..I'll do that..

https://www.youtube.com/watch?v=i6lfVUp5RW8

And some examples from Khan Academy.

3 can be 4 if you add 1 to it. 

But 3 itself is...3.

As long as it is somewhat related to math, I think it's okay. (I don't know exactly...try messaging one of the moderators) 

Find the cardinal number for the following sets

A = {114, 115, 116, 117, ...173}

B = {114, 116, 118, ... 414} 

Set A = { 114, 115, 116, 117, ...173 }
subtract from each element 113 we have 1, 2, 3, ... , 60
n(A) = 173-113 = 60

Set B = { 114, 116, 118, ... 414 }
subtract from each element 112 we have 2, 4, 6, ... , 302
302 = 2n

so

n(B) = 302/2 = 151

Find the cardinal number for the following sets.

A  = {104 , 105, 106 , 107 ,..., 141}

B  = {104 , 106 , 108 , ..., 304 }

Set A = {  104 , 105, 106 , 107 ,..., 141 }
subtract from each element 101 we have 1, 2, 3, ... , 40
n(A) = 141-101 = 40

Set B = {  104 , 106 , 108 , ..., 304  }
subtract from each element 102 we have 2, 4, 6, ... , 202
202 = 2n

so

n(B) = 202/2 = 101

Note that 

r = 3/a  

And the sum of the series can be represented as

S = 4 / [ 1 - 3/a ]  =  4a / [ a - 3]

Note that if a = 4, then the sum  is   4 (4) / [ 4 - 3]  =  16/ 1  =  16   which is a perfect square 

Thanks CPhill

The sum of the series  can be represented by :

a / ( 1 - r)  = 12

a = 12 ( 1- r )    (1)

So....note that the sum of the  terms  with odd powers of r  can be represented by :

ar  + ar^3  + ar^5 + ar^7 +  ..... + ar^(2n - 1)  =  5   (2)

And note that the sum of the  terms  with even powers of r  can be represented by :

a  +  ar^2  + ar^4 + ar^6 + ar^8 +  ..... + ar^(2n)  =  7   (3)

Multiply (2)  by r on both sides

ar^2  + ar^4  + ar^6 + ar^8 +  ..... + ar^(2n )  =  5r     (4)

Subtract   (4)  from (3)

a  = 7 - 5r    (5)

Sub (5)  into (1)

7 - 5r  = 12(1 - r)

7 - 5r  =  12 - 12r

7r = 5     →   r  =  5/7

Check

a = 7 - 5(5/7)  =  24/7

a / ( 1 - r)  =

(24/7) / ( 1- 5/7)  =

(24/7) / ( 2/7)  =

24 / 2   =

12 

We need to find the slope of 9x+12y=15

In this form,   Ax + By  =  C....the slope is given by   -A / B  =  -9 / 12  =  -3 / 4

And a line perpendicular to this will have a negative reciprocal slope = 4 / 3

So.....the equation of a line with this slope passing through (10, 16)  is given by :

y = (4/3) ( x - 10) + 16     simplify

y =  (4/3)x - 40/3 + 16

y = (4/3)x - 40/3 + 48/3

y = (4/3)x + 8/3    and this is in slope-intercept form

Here you go :  

http://www.purplemath.com/modules/exponent3.htm

Since the molar mass of Fe = 55.845 g/mol = 6.022 x 10^23 atoms. It, therefore, follows that:

787g contain = (787 / 55.845) x (6.022 x 10^23) = 8.487  x  10^24 atoms.

Thank you so much!

2x + 5 > 3     subtract  5  from both sides

2x > -2          divide both sides by 2

x > -1

A bus went 318 km farther than a car. The car went one-third as far as the bus. How far did each vehicle travel? Choices for the car's distance 

Let  the distance that the car travels  = D

Let the distance that the bus ravels = 3D

So...we have that

3D - D  =  318     simplify

2D  = 318       divide both sides by 2

D  =   159   km  = distance that the car traveled

The height of the flagpole is three-fourths the height of the school. The difference in their heights is 4.5 m. What is the height of the school? Choices for the school height are 18, 20, 24

Let the hight of the school  =  H

So....the height of the flagpole  =  (3/4) H

And we know that

H - (3/4)H  = 4.5   simplify

(1/4)H =  4.5        multiply both sides by 4

H  =  4 * 4.5   =   18 m  =   height of school

Since 12π/5 =2π +2π/5 and 2π is one complete rotation, therefore the coterminal angle between 0 and 2π  is 2π/5

To prove this

2π≈ 6.2831853071795865 and

2π/5≈ 1.2566370614359173

0<1.2566370614359173<6.2831853071795865

y=2x-2

For the x-intercept set y=0 and solve for x.

0=2x-2

+2    +2

2/2=2x/2

1=x

x-intercept occurs at the coordinate (1,0)

For the y-intercept set x=0 and solve for y.

y=2(0)-2

y=0-2

y=-2

The y-intercept occurs at the coordinate (0,-2)