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Gennadij [26K]
3 years ago
13

The figure is a parallelogram.

Mathematics
2 answers:
slavikrds [6]3 years ago
6 0
Answer:  " m∠ACD = 40° " .
______________________________________________________
Explanation:
______________________________________________________
We are asked to find:  "m∠ACD" ; 
______________________________________
Note:  m∠ACD  =  m∠ABD ; 
______________________________________________________
So, given: 

m∠ACD  =  (4x + 4)° ;

m∠ABD =   <span>(6x - 14)° ;
_______________________________________________________
  4x + 4 = 6x - 14 ;

Solve for "x" ; then solve for:  "m</span>∠ACD"  ;
_______________________________________________________
 Add "14" to each side of the equation; and subtract "4x" from each side of the equation ; 

  4x + 4 + 14 - 4x  = 6x - 14 + 14 - 4x  ;

to get:

18 = 2x ;

↔  2x = 18 ;

Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" ;
__________________________________________________________
     2x / 2 = 18/2 ;

      x = 9 .
_________________________________________________________
Now, to solve for:  " m<span>∠ACD "  :
</span>_________________________________________________________
      m∠ACD =  <span>(4x + 4)°  ;

Substitute "9" for "x" ; 
</span>
      m∠ACD = (4*9) + 4 = 36 + 4 = 40° .
_____________________________________________
Answer:  " m∠ACD = 40° " .
_____________________________________________
Let us check our answer:
_____________________________________________
m∠ACD = 40 ; and m<span>∠ABD = (6x - 14) ;

</span>m∠ACD = ∠ABD ; 
<span>
Since </span>m∠ABD = (6x - 14) ;  

If x = 9;  if we plug in "9" into the expression for "m∠ABD" ; will the value obtained be "40" ??

m∠ABD = (6x - 14) ;  Let us plug in "9" for "x" ; to see if the value obtained is "40"

6x - 14 = ? (6*9) - 14 ??
 
6x - 14 = ?  54 - 14 ??

6x - 14 = ? 40 ?? Yes!
______________________________________________
Softa [21]3 years ago
5 0

Answer:

c:40

Step-by-step explanation:

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Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1
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The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1  <u><em>Expresion A</em></u>

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

  • If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
  • If p> 0 and q <0, the parabola shifts p units to the right and q units down.
  • If p <0 and q> 0, the parabola shifts p units to the left and q units up.
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In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, <u><em>the parabola is translated down 2 units.</em></u>

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