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Use distance formula

(x-4)^2 + (21-7)^2 = (10 sqrt3)^2

 (x-4)^2 + 196 = 300

(x-4)^2    = 104

x^2 - 8x -88 = 0         Quadratic Formula shows x = 4 + 2 sqrt(26)    and    4 - 2 sqrt (26)    Add them together = 8

https://web2.0calc.com/questions/help-algebra_61906    <======= very similar method to solve

|4-7|= 3

then     |2-3| = 1

x^4   *  2 x^4  = 2 x⁴⁺⁴  =  2x⁸      degree 8

5 * x    +   1 * 4x   = 45

9x =45

x = five dollar bills = 5      then ones = twenty

The domain includes all real 'x' except the values that cause the denominator to equal zero

   so x cannot be 3  or - 2.5      

        You can take it from here ?

The sum of the coefficients is f(1) - f(0) = 32 - 47 = -15.

This questions was answered here:

https://web2.0calc.com/questions/congruence_4

graph it on desmos.com/calculator (if ur allowed to) then find the number of lattice points (integer). 

The smallest possible value of x + y is 27 + 54 = 81.

1 triangle 2 = 2 + 2^1 = 4

4 triangle 3 = 2 + 3^4 = 83.

x^2 + 10x + 25 = 18.     re-arrange

x^2 + 10x + 7 = 0      Use Quadratic Formula to find the x values    ....then choose the smaller of the two

   a = 1    b = 10   c = 7

\(x = {-10 \pm \sqrt{10^2-4(1)(7)} \over 2(1)}\)            Calculate to finish.....

Multiplying a polynomial by a constant does not change the roots....so

  multiply  x^2 + 8x + 4 = 0     by 2    to get    2x^2 + 16x + 8 = 0      <=====mow you can see A and B to finish !

By Lagrange Interpolation Formula, f(4) = -7.

correct...you couldve done it 8 + 7 + 6 + 5 + ... + 1 ... 

78910 , 78920 , 78921 , 78930 , 78931 , 78932 , 78940 , 78941 , 78942 , 78943 , 78950 , 78951 , 78952 , 78953 , 78954 , 78960 , 78961 , 78962 , 78963 , 78964 , 78965 , 78970 , 78971 , 78972 , 78973 , 78974 , 78975 , 78976 , 78980 , 78981 , 78982 , 78983 , 78984 , 78985 , 78986 , 78987 , Total =  36 such numbers

ty ep!

s = #student         revenue =  4s

a = # adults = (165 - s)    revenue =    7 ( 165-s)                summed, the two revenues = 795

4s +    7(165-s)     =   795                  solve for 's'

letters = 26

numbers = 10 C 2 =  10!/(8!2!) = 45 choices    BUT they can be in three different positions

26 * 45 * 3 = __________ combos

-y^2 + 4y - 4 - 2y + 7

-y^2 + 2y + 3  is a sideways parabola opening to the left     shold have but 1 x -axis intercept   and  two y-axis intercepts

x-3      when x = 3 is subbed into the equation Remainder = 0 `

  so   k = 29

         ________3x^2 -11x_-4___________

  x-3|   3x^3 - 20x^2+29x+12

            3x^3   -9x^2

                      -11x^2 + 29 x +12

                      -11x^2  +33x

                                  - 4x  + 12

                                  -4x   +12                   

                                                    R = 0

Now factor   3x^2 - 11x -4          (3x+1)(x-4)      then don't forget the RED factor above:

                                p(x) =   (x-3)(3x+1)(x-4)  

(not sure of this)

when   divided by (x-1)   r = 5      sub in x = 1

a (1^3) -6(1^2)+ b(1) - 5 = 5

a + b = 16      or   b = 16- a

when divided by (x-2)   r = - 53    sub in x = 2

8a -24 +2b-5 = - 53

8a + 2b = - 24                   sub in red equation for 'b'

8a + 2 ( 16-a) = - 24

6a = - 56

a = -9.333     then b = 16-a = 25.333      

Here is a graph I used to verify:

https://www.desmos.com/calculator/e2svzjdotb

as  |x| goes to infinity the fxn approaches zero

  as |x| approaches zero the fxn heads towards infinity

(0,+inf)