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grandymaker [24]
3 years ago
9

The two figures are similar

Mathematics
1 answer:
anyanavicka [17]3 years ago
6 0

Answer:

Part a) \frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}

Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure.(the scale factor is greater than 1)

Part c) The scale factor is 3

Step-by-step explanation:

Part a) Write the similarity statement

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}

substitute the values

\frac{9}{27}=\frac{12}{36} =\frac{15}{45}

\frac{1}{3}=\frac{1}{3} =\frac{1}{3} ----> is true

therefore

the figures are similar

Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure. (the scale factor is greater than 1)

Part c) we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z------> the scale factor

x-----> corresponding side of the image

y------> corresponding side of the original figure

so

z=\frac{x}{y}

we have

x=A'B'=27\ units

y=AB=9\ units

substitute

z=\frac{27}{9}=3

The scale factor is greater than 1

therefore

Is an enlargement

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Answer:

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Step-by-step explanation:

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3 years ago
LN bisects KLM into two congruent angles measuring (3x-4) and (4x-27). Find klm
Vanyuwa [196]
Answer:  The m ∡KLM is:  130° .
___________________________________________________________
Explanation:
__________________________________________________________
(3x − 4) = (4x − 27) ;  (Since these are "bisected, congruent angles", they are equal).

⇒ 3x − 4 = 4x − 27 ;

⇒ Subtract "4x" from  EACH SIDE of the equation; and add "4" to EACH SIDE of the equation;

⇒    3x − 4 − 4x + 4 = 4x − 27 − 4x + 4 ;

to get:

⇒  - 1x = -23 ;

⇒  Divide EACH SIDE of the equation by "-1" ; to isolate "x" on one side of the equation; and to solve for "x" ;

⇒  -1x / -1 = -23 / -1 ;  to get:

⇒  x = 23;
___________________________________
To find m ∡KLM :

m ∡ KLM = (3x − 4) + (4x − 27) ;

{Note:  Remember:  (3x − 4) = (4x − 27) } ;

So, plug in our solved value for "x" ; which is: "x = 23" into one of the expressions for one of the congruent angles.

Let us start with: "(3x − 4)" . 

(3x − 4) = 3x − 4 = 3(23) − 4 = 69 − 4 = 65 .

By plugging in our solve value for "x" ; which is: "x = 23" ; into the expression for the other congruent angle, we should get: "65" ;

Let us try:

(4x − 27) = 4x − 27 = 4(23) − 27 = 92 − 27 = 65.  Yes!
________________________________________________
So to find m ∡KLM:

(3x − 4) + (4x − 27) = 65 + 65 = 130° .
_______________________________________________
Alternate method:
_______________________________________________
At the point which we have:
_______________________________________________
To find m ∡KLM :

m ∡ KLM = (3x − 4) + (4x − 27) ; and at which we have our solved value for "x" ; which is:  "x = 23" ;
_______________________________________________

We can simply plug in our known value for "x" ; which is:  "23" ; into the following:
m ∡ KLM = (3x − 4) + (4x − 27) = [(3*23) − 4] + [(4*23) − 27] ;
                                                   = (69 − 4) + (92 − 7) = 65 + 65 = 130° .
_____________________________________________________________
{Note:  Using this method, we determine that each angle is equal; that is, "65° ".}.
______________________________________________________________
4 0
3 years ago
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Answer:

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Step-by-step explanation:

The area of the base is ...

  A = πr²

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The height is 10.5 cm.

5 0
4 years ago
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