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marusya05 [52]
1 year ago
14

Two figures are shown. EFJL is dialation of ABIK AB has a length of 12 and EF has a length of 3

Mathematics
1 answer:
Dimas [21]1 year ago
4 0

The scale factor of dilation from AB to EF is 0.25

<h3>How to determine the scale factor of dilation?</h3>

The given parameters are:

  • EFJL is dilation of ABIK
  • AB has a length of 12
  • EF has a length of 3

From the above parameters, side lengths AB and EF are corresponding sides

This means that:

The scale factor of dilation (k) is

k = AB/EF

So, we have

k = 3/12

Evaluate

k = 0.25

Hence, the scale factor of dilation from AB to EF is 0.25

Read more about scale factors at:

brainly.com/question/15891755

#SPJ1

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ELEN [110]

Answer:

<h3>Hence required integers are 11 and 13</h3>

Let x an odd positive integer

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x^2 +(x+2)^2=290

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Step-by-step explanation:

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7 0
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Please help! Thank you!
KIM [24]
The correct answer is:  [B]:  " (2, 5) ".
__________________________________________
Given:
__________________________________________
  -5x + y = -5 ;
  -4x + 2y = 2 .
___________________________________________
  Consider the first equation:
___________________________
-5x + y = -5 ;  ↔ y + (-5x) = -5 ;

↔ y - 5x = -5 ;  Add "5x" to each side of the equation; to isolate "y" on one side of the equation; and to solve in terms of "y".
_____________________________________________
   y - 5x + 5x = -5 + 5x  

   y = -5 + 5x ;  ↔ y = 5x - 5 ;
____________________________________________
 Now, take our second equation:
______________________________
     -4x + 2y = 2 ; and plug in "(5x - 5)" for "y" ;  and solve for "x" :
_____________________________________________________
         -4x + 2(5x - 5) = 2 ; 
______________________________________________________
Note, 2(5x - 5) = 2(5x) - 2(5)  = 10x - 10 ;
__________________________________________
So:   -4x + 10x - 10 = 2 ;

On the left-hand side of the equation, combine the "like terms" ;

-4x +10x = 6x ;  and rewrite:

6x - 10 = 2  ;

Now, add "10" to each side of the equation:

6x - 10 + 10 = 2 + 10 ;

to get:

           6x = 12 ;  Now, divide EACH side of the equation by "6" ; to isolate "x" on one side of the equation; and to solve for "x" ; 

           6x/6 = 12 / 6 ;
 
                 x = 2 ;
_________________________________
Now, take our first given equation; and plug our solved value for "x" ; which is "2" ; and solve for "y" ;
_____________________________________
-5x + y = -5  ;

-5(2) + y = -5 ;

-10 + y = -5 ;  ↔
                              y - 10 = -5  ;

Add "10" to each side of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;
     
         y - 10 + 10 = -5 + 10 ;

                   y = 5 .
_____________________________
So, we have, x = 2 ; and y = 5 .
____________________________
Now, let us check our work by plugging in "2" for "x" and "5" for "y" in BOTH the original first and second equations:
______________________________
first equation: 

-5x + y = -5 ;

-5(2) + 5 =? -5?

-10 + 5 =? -5 ? YES!
______________________
second equation:

-4x + 2y = 2 ;

-4(2) + 2(5) =? 2 ?

-8 + 10 =? 2 ?  Yes!
_______________________________________________________
So, the answer is: 
___________________________________________________________
          x = 2 , y = 5 ; or, "(2, 5)" ;  which is: "Answer choice: [B] " .
___________________________________________________________



3 0
3 years ago
Given that the series kcoskt kº +2 k=1 converges, suppose that the 3rd partial sum of the series is used to estimate the sum of
3241004551 [841]

Answer:

c

Step-by-step explanation:

Given that:

\sum \limits ^{\infty}_{k=1} \dfrac{kcos (k\pi)}{k^3+2}

since cos (kπ) = -1^k

Then, the  series can be expressed as:

\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^kk)}{k^3+2}

In the sum of an alternating series, the best bound on the remainder for the approximation is related to its (n+1)^{th term.

∴

\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^{(3+1)}(3+1))}{(3+1)^3+2}

\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^{(4)}(4))}{(4)^3+2}

= \dfrac{4}{64+2}

=\dfrac{2}{33}

5 0
2 years ago
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