Question

What is the zero of the function d=70-2.4t

Answer 1

Answer:  The "zero" is:  " 2 $\frac{11}{12}$ " ;  or, write as:  " 2.92 " .

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              →    " t = 2 $\frac{11}{12}$ " ;  or, write as:  " t = 2.92 " .

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Step-by-step explanation:

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Letting assume that this given function is supposed to be written as:

 "distance as a function of time" ;  that is:

           d(t) = 70 - (2.4)t ;

  →  since distance, "d" is the dependent variable (cannot be "manipulated or controlled") and as such, belongs on the "y-axis"—as the "dependent variable" ;  whereas as time, "t" ; can be somewhat controlled (with respect to distance, at list as a starting point); and as such belongs on the "x-axis" as the "independent variable" .

Since no "specific units" are given to us in the problem for Either "distance" or "time" ; we shall use the term "units" to describe their values.

We have:

 d(t) = 70 - (2.4)t ;

Let us rearrange this:

70 - (2.4)t  ;   ↔

  =  70  +  (- 2.4)t  ;  ↔

  =  (-2.4)t  +  70 ;

And rewrite the function:

          →   d(t) = (-2.4)t + 70 ;

To find the "zero" ; or "zeros" ; of this function; set "d(t)" equal to "zero" ; that is; "0" ; and solve for  the value(s) for "t" when "d(t)" = 0 :

          →  0 = -2.4(t) + 70 ;  ↔

   Rewrite as:

          →  -2.4(t) + 70 = 0 ;  

For simplicity;  let us multiply Each side of the equation by "10" ;

to get rid of the decimal value:

    10*[ (-2.4)t) + 70 ] = 10 * [0] ;

From the left-hand side of the question:

Note the "distributive property" of multiplication:

    a(b + c) = ab + ac ;

As such:

   10* [-2.4(t) + 70 ] =

    [10* -2.4(t)] + [10 * 70] =

      -24t + 70 ;

From the "right-hand side" of the equation:

    10 * 0 = 0 .

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So; we rewrite the equation as:

  -24t + 70 = 0 ;

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Solve for " t " ;  

 -24t + 70 = 0 ;

Subtract "70" from Each Side of the equation;

  -24t + 70 - 70 = 0 - 70 ;  

to get:

  -24t = -70 ;

Now, let's multiply each side of the equation by "-1" ;

       to get rid of the "negative values" ;

  -1* (-24t) = -1(-70) ;

to get:

   24t = 70 ;

Now, let's divide Each Side of the equation by "24" ;

to isolate:  "t" ;  on one side of the equation; & to solve for "t" ;

   24t / 24 = 70/24 ;

to get:  

         t = 70/24 ;

To simplify:  either:  

1)  use calculator:  70 ÷ 24 = 2.916666666 ;

                             →  round to:  2.92 ;

                             →  t ≈ 2.92 ;

 or:  " $\frac{70}{24} =\frac{(70/2)}{(24/2)}=\frac{35}{12}$ ;

→  write as simplified improper fraction:  " t = $\frac{35}{12}$ "

→  or:  write as mixed number:

           →  " $\frac{35}{12}$ = 35 ÷ 12 =

                              2 R 11

                     12 ⟌35

                          - 24  

                             1 1

         

           →  write as:  " 2$\frac{11}{12}$ " ;

                                                               →  " t = 2 $\frac{11}{12}$ " .

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Hope this is helpful to you.

        Wishing you the best!

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