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ollegr [7]
3 years ago
15

The sum of three consecutive even integers is -78, what are the integers ?

Mathematics
1 answer:
Digiron [165]3 years ago
5 0
First, you need to analize and understand the problem, then you must choose and strategy. There is a wide variety of strategies to solve a mathematical problem, in this case, you can use the following, which is based on the information given above:
 1. You have that t<span>he sum of three consecutive even integers is </span>-78<span>, therefore, you can given the variable </span>x&#10;<span> to the first integer, the second even integer is </span>x+2<span> and the third one is </span>x+4&#10;<span>.
 2. Calculate x:
 </span>x+(x+2)+(x+4)=-78<span>
 </span>3x+6=-78
<span> </span>x=-28&#10;<span>
 </span>x+2=-28+2=-26&#10;<span>
 </span>x+4=-28+4=-24&#10;<span>
 Therefore, the answer is:</span>-28,-26,-24&#10;
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Tell me what each angle is in the following triangle: angle 1 is 8x, angle 2 is 2x+3, angle 3: 30 degrees. give me the two answe
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Answer:  117.6° ;  32.4° .
_________________________
Explanation:
_______________________________________________________
Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.   
_____________________
We are given the following:
_______________________
We have a triangle.

Angle 1:  m∡1 = (8x) ;

Angle 2:  m∡2 = (2x + 3) ;

Angle 3:  m∡3 = 30.
______________________________________
We are asked to find:  "m∡1"  and " m∡2" .
______________________________________
Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
________________________________________
   So, " m∡1 + m∡2 + m∡3 = 180 " . 
________________________________________
Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation;  then solve for "x" ;  then substitute that solved value for "x" into the given expressions for BOTH  "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ; 
___________________________________________
 
                m∡1 + m∡2 + m∡3 = 180  ; 
___________________________________________
             8x + (2x + 3) + 30 = 180 ;
___________________________________________
             8x + 2x + 3 + 30 = 180 ;
___________________________________________
  Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
____________________________________________________________
            +8x + 2x = +10x ;
___________________________________________
              +3 + 30 = +33 ; 
___________________________________________
  Rewrite the entire equation, as:
___________________________________________
         10x + 33 = 180 ; 
___________________________________________
 Now, subtract "33" from EACH SIDE of the equation:
___________________________________________
         10x + 33 − 33 = 180 −<span> 33 ;
___________________________________________
 to get:
___________________________________________
         10x    =   147 ;  
____________________________________________
   Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" : 
____________________________________________
         10x / 10 = 147 / 10 ; 
____________________________________________
   to get: 
____________________________________________
              x = 14.7 ;
___________________________________________
    Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2";  as follows:
________________________________________________

Angle 1:  "(8x)" = 8*(14.7) =  117.6° ; 
________________________________________________
Angle 2:  "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
________________________________________________
These are the two answers; that is the 2 (TWO) values asked for in the question:   117.6° ;  32.4° .
<span>____________________________________</span><span>
 Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
___________________________________________
Let us check:
_______________________________
   m∡1  +  m∡2  +  m∡3 = 180 ; 
_______________________________
Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
______________________________________________
   → 117.6 + 32.4 + 30 = ? 180 ??
______________________________________________
   → 117.6 + 32.4 = 150  ;   → 150 + 30 =? 180 ?  Yes!
______________________________________________
4 0
4 years ago
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