The second angle in a triangle is one third as the first. The third angle is two thirds as large as the first angle. Plz find the angle measures (plz show work). Thanks for your help.

Answer:

10.77

Step-by-step explanation:

Answer:

(k4+3+3k3)+(-5k3+6k3+8k5)

Final result :

 8k5 + k4 + 4k3 + 3

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((k4)+3)+(3•(k3)))+(((0-(5•(k3)))+(6•(k3)))+23k5)

Step  2  :

Equation at the end of step  2  :

 (((k4)+3)+(3•(k3)))+(((0-(5•(k3)))+(2•3k3))+23k5)

Step  3  :

Equation at the end of step  3  :

 (((k4)+3)+(3•(k3)))+(((0-5k3)+(2•3k3))+23k5)

Step  4  :

Equation at the end of step  4  :

 (((k4) +  3) +  3k3) +  (8k5 + k3)

Step  5  :

Checking for a perfect cube :

5.1    8k5+k4+4k3+3  is not a perfect cube

Trying to factor by pulling out :

5.2      Factoring:  8k5+k4+4k3+3

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  k4+3

Group 2:  8k5+4k3

Pull out from each group separately :

Group 1:   (k4+3) • (1)

Group 2:   (2k2+1) • (4k3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.3    Find roots (zeroes) of :       F(k) = 8k5+k4+4k3+3

Polynomial Roots Calculator is a set of methods aimed at finding values of  k  for which   F(k)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  k  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  8  and the Trailing Constant is  3.

The factor(s) are:

of the Leading Coefficient :  1,2 ,4 ,8

of the Trailing Constant :  1 ,3

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -8.00    

     -1       2        -0.50        2.31    

     -1       4        -0.25        2.93    

     -1       8        -0.13        2.99    

     -3       1        -3.00       -1968.00    

     -3       2        -1.50        -66.19    

     -3       4        -0.75        -0.27    

     -3       8        -0.38        2.75    

     1       1        1.00        16.00    

     1       2        0.50        3.81    

     1       4        0.25        3.07    

     1       8        0.13        3.01    

     3       1        3.00        2136.00    

     3       2        1.50        82.31    

     3       4        0.75        6.90    

     3       8        0.38        3.29    

Polynomial Roots Calculator found no rational roots

Final result :

 8k5 + k4 + 4k3 + 3

Step-by-step explanation:

Answer:

A: The x-intercept is x = -5 and the graph approaches a vertical asymptote at x = -6

Step-by-step explanation:

The diagram shows translated to the left graph of the logarithmic function.

This graph intersects the x-axis at point x = -5, hence the x-intercept is at x = -5.

This graph approaches to the vertical line. The line passes through the point (-6,0), so the equation of this vertical line is x = -6.

Therefore, correct option is A: The x-intercept is x = -5 and the graph approaches a vertical asymptote at x = -6

To justify the yearly membership, you want to pay at least the same amount as a no-membership purchase, otherwise you would be losing money by purchasing a yearly membership.  So set the no-membership cost equal to the yearly membership cost and solve.

no-membership costs $2 per day for swimming and $5 per day for aerobic, in other words, $7 per day.  So if we let d = number of days, our cost can be calculated by "7d"

a yearly membership costs $200 plus $3 per day, or in other words, "200 + 3d"

Set them equal to each other and solve:

7d = 200 + 3d

4d = 200

d = 50

So you would need to attend the classes for at least 50 days to justify a yearly membership.  I hope that helps!