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Irina18 [472]
2 years ago
6

11) MZHGF = 16x + 4, m EGF = 110°, and MZHGE = 3x + 11. Find x. G H F E

Mathematics
2 answers:
Darya [45]2 years ago
6 0
<h3>Answer:  x = 9</h3>

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

Explanation:

The smaller angles HGE and EGF combine to form the largest angle HGF.

This is an example of the angle addition postulate.

(angle HGE) + (angle EGF) = angle HGF

(3x+11) + (110) = 16x+4

3x+121 = 16x+4

121-4 = 16x-3x

117 = 13x

13x = 117

x = 117/13

x = 9 which is the final answer

We can stop here.

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

Extra info (optional section)

Use this x value to find each angle shown below

  • angle HGE = 3x+11 = 3*9+11 = 27+11 = 38 degrees
  • angle HGF = 16x+4 = 16*9+4 = 144+4 = 148 degrees

Then notice how,

(angle HGE)+(angle EGF) = 38+110 = 148

which is exactly the measure of angle HGF

This confirms that the equation

(angle HGE) + (angle EGF) = angle HGF

is true for that x value of x = 9. Therefore, the answer is confirmed.

PIT_PIT [208]2 years ago
3 0

9514 1404 393

Answer:

  11) x = 9°

  13) x = -12°

Step-by-step explanation:

11) ∠HGE +∠EGF = ∠HGF

  (3x +11) +(110°) = (16x +4)

  117° = 13x . . . . . . . . . . . . . . . subtract 3x+4, collect terms

  9° = x . . . . . . . . . . . . divide by 13

__

13) ∠BCF +∠FCD = ∠BCD

  (x +78) +(x +41) = 95°

  2x = -24°

  x = -12°

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7 0
2 years ago
A ladder leans against a 22-feet-tall apple tree. The base of the ladder forms a 42° angle with the ground. Approximately how ta
igomit [66]

(D) 33 feet

<u>Explanation:</u>

Given:

Height of the tree, h = 22 feet

angle, θ = 42°

Length of the ladder, l = ?

We know:

sin θ = Perpendicular / hypotenuse

So,

Sin θ = height of the tree / length of the ladder

sin 42^0 = \frac{22}{l} \\\\0.67 = \frac{22}{l} \\\\l = 32.84 feet

l = 32.84 feet ≈ 33 feet

Therefore, the length of the ladder be to reach the top of the apple tree is 33 feet.

6 0
3 years ago
A teacher asked each of his students how many books were read during the summer. Which histogram accurately displays this data?
devlian [24]

Answer:

The frequency distribution is given below:

Class                      Frequency

0 - 9                               9

10 - 19                             6

20 - 29                           3

30 - 39                           3

40 - 49                           3

From the given 4 options, the histogram in option A accurately displays this data. Hence the option A is correct.



6 0
3 years ago
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Divide. Write your answer as a decimal.<br><br> 0.459 divided by 0.17 =
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Answer:

0.459 divided by 0.17 equals 2.7

Step-by-step explanation:

4 0
3 years ago
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How do you find X for this problem? <br> Plz help me!
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Step-by-step explanation:

it's been a while but I think it's 84°

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