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astraxan [27]
1 year ago
11

So,some please help me with this question !

Mathematics
2 answers:
Tamiku [17]1 year ago
4 0

\qquad \qquad  \bf \huge\star \:  \:  \large{  \underline{Answer} }  \huge \:  \: \star

\qquad❖ \:  \sf   \: \angle C  = 63 \degree

\textsf{  \underline{\underline{Steps to solve the problem} }:}

\qquad❖ \:  \sf \:x + 4x  + 12 + x=180°

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

\qquad❖ \:  \sf \:6x + 12 = 180

\qquad❖ \:  \sf \:6x = 180 - 12

\qquad❖ \:  \sf \:6x = 168

\qquad❖ \:  \sf \:x = 28 \degree

Next,

\qquad❖ \:  \sf   \: \angle C + \angle D + x = 180°

\qquad❖ \:  \sf   \: \angle C +3x + 5  + x = 180°

\qquad❖ \:  \sf   \: \angle C +4x  = 180 - 5

\qquad❖ \:  \sf   \: \angle C +4(28)  = 175

( x = 28° )

\qquad❖ \:  \sf   \: \angle C +112  = 175

\qquad❖ \:  \sf   \: \angle C  = 175 - 112

\qquad❖ \:  \sf   \: \angle C  = 63 \degree

\qquad \large \sf {Conclusion}  :

\qquad❖ \:  \sf   \: \angle C  = 63 \degree

neonofarm [45]1 year ago
4 0
<h3>Answer:  63 degrees  (choice A)</h3>

=============================================================

Explanation:

Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.

Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.

So,

(angleEBA) + (angleEBD) + (angleDBC) = 180

( x ) + (4x+12) + (x) = 180

(x+4x+x) + 12 = 180

6x+12 = 180

6x = 180-12

6x = 168

x = 168/6

x = 28

Angles EBA and DBC are 28 degrees each.

This means angle D = 3x+5 = 3*28+5 = 89

-----------

Then we have one last set of steps to finish things off.

Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.

D+B+C = 180

89 + 28 + C = 180

117+C = 180

C = 180 - 117

C = 63 degrees

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3 years ago
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patriot [66]

Part A

x = amount of money she starts with

(4/9)x = cost of the dress

(5/9)x = amount of money leftover after buying the dress

note that 4/9 and 5/9 add to 1 to represent 100% of her money

(3/4)*(5/9)x = (15/36)x = (5/12)x = amount spent on shoes

We see that she spent 5/12 of her original amount of money on shoes.

-----------------------

We can look at a more concrete example if the previous section does not make sense.

Let's multiply the denominators 9 and 4 to get 9*4 = 36. Doing this trick will mean that the later steps won't involve decimal values.

Let's say she starts off with $36

Multiply that with 4/9 to get (4/9)*36 = 16. So in this hypothetical situation, the dress costs $16 and she's left with 36-16 = 20 dollars.

Multiply that 20 by 3/4 to get (3/4)*20 = 15

In this situation, the shoes cost $15

We'll then divide the cost of the shoes (15) over the original amount of money she started with (36)

15/36 = (3*5)/(3*12) = 5/12

-----------------------

<h3>Answer:  5/12</h3>

=======================================================

Part B

From the first section in part A, we found that:

  • (4/9)x = amount of money spent on the dress
  • (5/12)x = amount of money spent on shoes

Add those two expressions

(4/9)x + (5/12)x = (16/36)x + (15/36)x = (31/36)x

This indicates that buying the dress and shoes will cost (31/36)x dollars, where x is the original amount of money Jing has to start with.

The amount left over is (5/36)x because 5/36 adds with 31/36 to get 1.

Take 1/3 of this to get:

(1/3)*(5/36)x = (5/108)x

Then set this equal to 18 and solve for x

(5/108)x = 18

5x = 18*108

5x = 1944

x = 1944/5

x = 388.80

--------------------

Let's check the answer

If she starts with 388.80 dollars, then the dress costs (4/9)*388.80 = 172.80

She's left with 388.80 - 172.80 = 216 dollars after buying the dress.

She then spends the remaining 3/4 of that on shoes. So (3/4)*216 = 162 dollars is spent on the shoes.

Jing now has 216 - 162 = 54 dollars left over.

1/3 of which is spent on the shoe bag, meaning it costs (1/3)*54 = 18 dollars

This confirms our answer.

--------------------

<h3>Answer:  $388.80</h3>
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Step-by-step explanation:

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