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Hunter-Best [27]
3 years ago
8

Point slope form. (-5,-1) and (6,-5)

Mathematics
1 answer:
TEA [102]3 years ago
6 0

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

<em>m</em><em> - slope</em>

<em>(x₁, y₁)</em><em> - point on a line</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have two points (-5, -1) and (6, -5). Substitute:

m=\dfrac{-5-(-1)}{6-(-5)}=\dfrac{-5+1}{6+5}=-\dfrac{4}{11}

Put the value of a slope and coordinates of a point to the equation of a line:

(-5,\ -1),\ m=-\dfrac{4}{11}\\\\y-(-1)=-\dfrac{4}{11}(x-(-5))\\\\y+1=-\dfrac{4}{11}(x+5)

(6,\ -5),\ m=-\dfrac{4}{11}\\\\y-(-5)=-\dfrac{4}{11}(x-6)\\\\y+5=-\dfrac{4}{11}(x-6)

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Step-by-step explanation:

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3 years ago
What is 0.8 and 5/8 and 0.01 in a percentage
vovikov84 [41]

The correct answers are:

__________________________

   1)      " 0.8  =  80 % "  .

__________________________

   2)      " \frac{5}{8}  =  62. 5 % " .

__________________________

   3)     " 0.01  =  1 % " .

__________________________

Explanation:

To solve:

__________________________

Write the numbers:  " 0.8 " ;   " 5/8 " ;  <u><em>and</em></u>:  " 0.01 " ;  as "percentages" .

To write a "number" as a "percentage" :

  • You take the "number" ;
  • Multiply that "number"  by "100"  ;   <em><u>AND</u></em>:
  • add a  "percent symbol";

                 →   that is:  " % " ;

                 → to denote the "percentage" ;  or, "parts per hundred" .

__________________________

Let us start with the number:  " 0.8 " .

→  " 0.8 "  *  100  =  ?

→   Take the decimal point, and move it 2 decimal spaces to the right; since we are "multiplying" by "100" (which has "2 zeros")  ;

→    0.8  * 100 = ?  ;   If we move the decimal space "one space" forward, we have:  "8" .  If we move the decimal space yet "one more space forward" ;

      →  "8."  to:   " 80 " .

→ Then we add the "percent symbol":

     →  " 80 "  ;   to:  " 80 % "

Answer:  " 0.8  =  80 % " .

_________________________

Other method:

_________________________

→ Note that "percentage" means:  "parts per hundred" :

→ Given:  " 0.8 " ;  Convert to a "percentage" :

→  " 0.8  = \frac{8}{10} " ;

        →  " \frac{8}{10}  = \frac{?}{100} " ;

        →   Find the "?" value.

        →  To do so; look at the "denominators" :

                 →  " 10 * (what) = 100 " ?

                 →  Divide each side by "10" ;

                 → " [10 * what ] / 10  = 100 / 10 " ;

                 →  to get:  

                 →  " [what] " =  "10" .        

                 →    So;   " \frac{8}{10}  = \frac{?}{100} " ;

                 →    If  "{10 * 10 = 100}" ;  then, "{8 * 10 = 80}" .

                 →    So;  " {?} " =  " 80 " .

                 →    So;    " \frac{8}{10}  = \frac{80}{100} " ;

                 →    As such:   " 0.8 "    =  " (\frac{80}{100}) " ;

                                                       =   " 80 "   parts per hundred  ;

                                                       =   " 80  % " .

Answer: " 0.8 "   =   80 %  "  .                                    

__________________________

Now, let convert:  "(\frac{5}{8})" ; into a percentage.

→  Multiply by "100" ;

→  "(\frac{5}{8})"   *   100  ;

→     "(\frac{5}{8})    *   (\frac{100}{1})"  ;

→     "(\frac{(5*100)}{(8*1)})"   ;

→   "(\frac{500}{8})"  ;

   =    " { 500 ÷ 8 } "  ;

  =   " 62. 5 "  ;

→  Now, add the "percent symbol" ;

    →    "  62. 5 "   ;    →  62. 5 % " .

Answer:  " \frac{5}{8}  =  62. 5 % " .

__________________________

Now, let us finish with our last "given value":

Convert:  " 0.01 " ;  to a "percentage" :

→  " 0.01 "  *  100  =  ?

→   Take the decimal point, and move it 2 decimal spaces to the right; since we are "multiplying" by "100" (which has "2 zeros")  ;

→    0.01  * 100 = ?  ;   If we move the decimal space "2 spaces forward" , we have:  " 1 " .  

As such:

      →  " 0.01 "  to:   " 1 " .

→ Then we add the "percent symbol":

     →  " 1 "  ;   to:  " 1 % "  .

Answer:   " 0.01  =  1 % " .

__________________________

Hope this answer is of help to you.

Best wishes!

__________________________

5 0
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weqwewe [10]
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