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

 The "zero" is:  " 2 " ;  or, write as:  " 2.92 " .

_____________________________________

              →    " t = 2 " ;  or, write as:  " t = 2.92 " .

_____________________________________

Step-by-step explanation:

_____________________________________

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 .

__________________________________

So; we rewrite the equation as:

  -24t + 70 = 0 ;

__________________________________

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:  " ;

→  write as simplified improper fraction:  " t = "

→  or:  write as mixed number:

           →  " = 35 ÷ 12 =

                              2 R 11

                     12 ⟌35

                          - 24  

                             1 1

           →  write as:  " 2 " ;

                                                               →  " t = 2 " .

_____________________________________

Hope this is helpful to you.

        Wishing you the best!

_____________________________________

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it