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You pay for a $500 purchase using a credit card. The credit card company charges a 24% interest rate, compounded monthly, on the unpaid balance. How much will you owe after 3 months? (Assume you don't make any payments during this time.)

FV = PV x [1 + R]^N

FV = 500 x [1 + 0.24/12]^3

FV = 500 x [1.02]^3

FV = 500 x  1.061208

FV = $530.60 - amount that you will owe on the credit card after 3 months, principal + interest.

If you can map one figure onto another using similarity transformations, then the figures are similar. 

1) Translate the center of the circle with radius q to the center of the circle with radius t.

Translations are considered to be an isometry, a specific type of transformation where the size and shape remain unaffected.

2) Dilate the circle with radius q about C by a factor of t/q

In general: \((\frac{m}{n})=\frac{m!}{n!(m-n)!}\)

so:    

  \((\frac{4}{0})=1\\ (\frac{5}{1})=5\\ (\frac{6}{2})=15 \\ (\frac{7}{3})=35\)

I’ll leave you to add up the numbers!

(Note that 0! = 1)

f(3)  =  1

f(6)  = f(2 * 3) = 2f(3)  = 2 * 1  = 2

f(12)  = f(2 * 6)  = 2f(6)  = 2 * 2  = 4

f(24)  = f(2 * 12) = 2f(12) = 2 * 4 = 8

f(48) = f(2 * 24)= 2f(24) = 2 * 8   = 16

f(96) = f(2 *48) = 2f(48) = 2 * 16 = 32

f(192) = f(2 * 96) = 2f(96) = 2 * 32  = 64

So

f(192)  =  64       which implies that

f^-1(64)  =  192

C) a_n = a_{n − 1} − 5.6, where a₁ = −2.7

Note that we are subtracting  5.6  from a previous term to get the successive term

So

Second term  =  -2.7 - 5.6  =  -8.3

Third term  =  -8.3  - 5.6  = -13.9      ....etc.    

C (223, 221)  =

    223!                             223 * 222         223 * 111  = 24753

_______________  =      ________  =

(223 - 221)! * 221!                2! 

Adding two polynomials of different degrees will result in a polynomial  that has the same degree as the highest degree polynomial in the sum

So....p(x) + g(x)  will result in a degree 11  polynomial

what would c=(223,221) be?

C (n, m)  is defined as

       n!

__________

(n - m)! * m!

So

C(14,6)  =

      14!                       14!             14*13*12*11*10*9

___________  =     ______  =    _______________  =

  (14 - 6)! * 6!           8! * 6!                   6!

2162160

_______    =     3003

   720

This is a floor function graph

For any x, floor (x)  is defined as the greatest integer less than or equal to x

For  example, let x  = 3  ....so....

floor (3)  = 3

So

floor(3)  - 3  =  0

And   let x  = 2.5     .....so....

floor (2.5)  = 2 

So

floor (2.5) -  3  =  2  - 3  =  -1

The last graph is correct

but can you explain why (14,6) = 3003 im really confused on why that equals 3003

Don't know the second one.....but for the first

We want to choose  any 6 people from 14....so

C(14,6)   = 3003  ways 

I think the second function should be

lxl + 1  if      -1 ≤ x ≤ 1

If so.....the second graph is correct

Here's as good as I could do :

https://www.desmos.com/calculator/bitllr7apo

1. The graph shifts 7 units left and 2 units up.

2. f(x)  =  x^2 + 3x - 28             (x + 7) ( x - 4)             x  -  4

              ___________    =      ____________  =  

                 X + 7                          x +  7

The " hole"  occurs at   x  =  -7   and  y  = (-7) - 4  =  -11

So ⇒   (-7, -11)

(1)  I think this is might be :

f(x)={(x-2)^2 if x<-1, |x|+1 if  [-1 1 ]

Here's the graph : https://www.desmos.com/calculator/gil1qev4k5

(2)   Here's the graph  : https://www.desmos.com/calculator/ujnjjgqrww

(3) Here's the graph  : https://www.desmos.com/calculator/mq3qju8rxb

Vertical asymptote  :  x  = 7

Horizontal asymptote :  y  = 2

(4)  No choices shown

b)

a=9    and   n=8

a =18 and   n=5

I discussed this question a day or two ago!!

I'm so sorry. I forgot 2a.     Here is the correction. Thanks Alan.

x₁=\(\frac{3}{2}\)

x₂=-\(\frac{5}{3}\)

Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1)
in terms of a and n.

We can write  the above sum as

n*a  +  ( 1 + 2 + 3 + ....+ n - 1 )  =

n*a   +   (n - 1) (n)/2  =

n [ a +  ( n - 1) / 2 ]   =

n [ 2a + n - 1] / 2  =

(n/2)  [ 2a + n - 1 ]

Heureka's result looks right to me:

.

im not sure thats correct

Amazing solution, CPhill! Thanks so much!

Here's a pic of the feasible region :

The vertices  of the quadrilateral are shown

The longest side =

√ [ 3^2 + 3^2 ]   =

√18 =

3√2   units