What does the unknown number z represent in 118 / 13 equals 59 / z

z= 13/2= 6.500

Step-by-step explanation:

Step  1  :

           59

Simplify   ——

           z

Equation at the end of step  1  :

 118    59

 ——— -  ——  = 0

 13     z

Step  2  :

           118

Simplify   ———

           13

Equation at the end of step  2  :

 118    59

 ——— -  ——  = 0

 13     z

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       13

     The right denominator is :       z

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

13101

Product of all

Prime Factors  13113

                 Number of times each Algebraic Factor

           appears in the factorization of:

   Algebraic    

   Factor      Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

z  011

     Least Common Multiple:

     13z

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = z

  Right_M = L.C.M / R_Deno = 13

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      118 • z

  ——————————————————  =   ———————

        L.C.M               13z  

  R. Mult. • R. Num.      59 • 13

  ——————————————————  =   ———————

        L.C.M               13z  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

118 • z - (59 • 13)     118z - 767

———————————————————  =  ——————————

        13z                13z    

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  118z - 767  =   59 • (2z - 13)

Equation at the end of step  4  :

 59 • (2z - 13)

 ——————————————  = 0

      13z      

Step  5  :

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 59•(2z-13)

 —————————— • 13z = 0 • 13z

    13z    

Now, on the left hand side, the  13z  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  59  •  (2z-13)  = 0

Equations which are never true :

5.2      Solve :    59   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

5.3      Solve  :    2z-13 = 0

Add  13  to both sides of the equation :

                     2z = 13

Divide both sides of the equation by 2:

                    z = 13/2 = 6.500

One solution was found :

                  z = 13/2 = 6.500

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

answer is 12345678900987654321234567890987654321

step-by-step explanation: