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I think this is how you would do this:

(n-2)(180)  = 1578  +  (n-2)(180) /n

180 n - 360  - 1578  = ( n-2)(180) / n

180n^2 - 1938n = 180 n - 360

180n^2 - 2118 n + 360 = 0               Quadratic formula shows n = 11.59      could be 11 sides or 12 sides

try n = 12         180 (n-2) = 1800     1800 - 1578 = 222  for remaining side     (too big....must be less than 180)

try n = 11         180 ( n-2) = 1620    1620 - 1578 =  42 degrees    OK

Sum of 11 sided poly= (2n-4)x90 deg = 18x90= 1620deg leaves (1620-1578) = 42 deg for last angle

Sum of dodecagon = 1800, leaves 122 for the last angle 

Sum of 13 sided poly = 1980, leaves 302 deg for the last angle, BUT since poly is convex, this is impossible.

Hence polygon has 11 or 12 sides, with the last angle being either 42 or 122

(A,B,C,D,E) = (1,-3,1,-2,1)

(A,B,C) = (2,0,-1)

(A,B,C,D) = (3,-1,2,-2).

The measure of the remaining interior angle is 27 degrees.

cos(-1)=.28

cos=73.740deg

sin73.740=0.96

c+d=304

d+18=2/3(c/4)

d=28, c=276

c-d=248

c+d=304

d+18=2/3(c/4)

d=28 c=276

sqrt96

The first term can be either 2, 3, or 5.

If the first term is 2, there are 5! = 5 x 4 x 3 x 2 x 1 = 120 ways to permutate the other terms.

Similarly, there are 120 ways if the first term is a 3 and there are 120 ways if the first term is a 5.

Therefore there is a total of 360 possible permutations for the denominator of the probability.

If the third term is a 2 and the first term is a 3, there are 4 x 3 x 2 x 1 = 24 ways.

Similarly, if the third term is a 2 and the first term is a 5, there are 24 ways.

Adding, we get 48 ways for the numerator of the probability.

The probability will be  24 / 360.

The sum of two numbers a and b  is 20. Write an expression for the sum of their squares, in terms of a.  

Okay, so we want a² + b² but we want it in terms of a only.  We can do that. 

Since a + b = 20, that means that b = 20 – a.         So, we'll just substitute it in.  

a² + b²  =                        a² + (20 – a)²                  Next, multiply out that second term.  

a² + (20 – a)²  =              a² + (400 – 40a + a²)      Then, combine like terms.  

a² + (400 – 40a + a²)  =  2a² – 40a + 400              The 2 will come out of that  

2a² – 40a + 400  =           2 • (a² – 20a + 200)         I think that's about as far as it will reduce. 

_.

What is the measure of x?

Hello Guest!

x = 45°

  !

What is the range?

Hello Guest!

The range is [0,infinity).

  !

Seven

Not sure I understand the question...but here is a try

  Inflation DE-values the investment by 4.6 % per year :    i = -.046

  Find the investment rate that results in 55000 in 24 years if   i =  x/ 2    compounded semi

   55000 = 24500 ( 1 + x/2)⁴⁸   ( 1 - .046)²⁴

x = 8.244%    nominal interest rate    ( the interst rate if inflation is taken into account)

       3.34  real interst rate            effective rate = 3.43 %    (these are the values if there is no inflation)      

Ja, ich verstehe     

Given That

Amount of tape used by Justin = 1/5 of tape

Cost of a new tape = $1.63

To find

The amount will have to pay by Justin to his

father.

Since Justin used 1/5^th of tape. Hence,

The cost of 1/5 Part of tape

                    = $1.63/5 = $0.326

∴ The amount will have to pay by Justin = $0.326

According to the question we know in Album A: local : foreign = 3:2

So it's could be: 3/5 : 2/5 = 9/15 : 6/15

in Album B: local foreign = 4/15 : 15-4/15 = 4/15 : 11/15 So we can get : local : 9/15 + 4/15 = 13/15

foreign : 6/15 + 11/15 = 17/15

So the answer is 13/15:17/15=13:17

So we should choose B) 13:17

BC = sqrt(5).

https://web2.0calc.com/questions/algebra_2480

the degree of g(x) is 8

999^(-1) mod 1000 ==999

x = number of 2's

12-x  = number of 7's

[2 *x   +   7 (12-x)] / 12     = 3.25

 2x -7x    + 84 = 39

-5x = -45

x = 9   

52 cards total

12 cards are a   J  Q  or  K    plus   10 more red cards

22/52   ==   11/26