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Irina18 [472]
3 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]3 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]3 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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8 0
3 years ago
Solve |5x+30|=10x ......
Orlov [11]

Answer:

Option A

Step-by-step explanation:

We need to solve out ,

\implies |5x + 30| = 10x

We can write it as ,

\implies 5x + 30 = \pm 10x

On simplyfing further,

\implies 5x + 30 =  10x \quad or \quad 5x +30=-10x

On solving the above equation , we will get ,

\implies \boxed{ x = 6,-2}

Now we know that the value of modulus is never negative so when we will put x is equal to 2 on the RHS we will get -20 which is not possible . Therefore , the extraneous root is -2 .

<u>Option</u><u> </u><u>A </u><u>is </u><u>correct</u><u> </u><u>.</u>

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3 years ago
What is (43/7÷ x+32/9) ÷25/6=4/3
Fittoniya [83]

The value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

<h3>How to solve for x in the equation?</h3>

The equation is given as:

(43/7 ÷ x + 32/9) ÷ 25/6 = 4/3

Rewrite as a product

(43/7 ÷ x + 32/9) x 6/25 = 4/3

Multiply both sides of the equation by 25/6

(43/7 ÷ x + 32/9)= 4/3 x 25/6

Evaluate the product

(43/7 ÷ x + 32/9)= 50/9

Rewrite the equation as:

43/7x + 32/9= 50/9

Subtract 32/9 from both sides

43/7x = 2

Multiply both sides by 7x

14x = 43

Divide by 14

x =43/14

Hence, the value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

Read more about equations at:

brainly.com/question/2972832

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3 0
2 years ago
In how many ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other?
balandron [24]
The 5 people can seat in a row in 5! ways
But we need to exclude the ways <span>that ann and bob are seated next to each other which is = 4! * 2!
</span>
So, the number of <span>ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other = 5! - 4! * 2! = 72
</span>
<span>=====================================================
</span>
<span>Another solution:
</span>
<span>If ann seated in one of the ends, the number of ways = 3*2
</span>
<span>If ann didn't seat in one of the ends , the number of ways = 2*3
</span>
So, the total number of <span>ways that can <span>ann, bob be seated = 3*2 + 2*3 = 12
</span></span>
The remaining persons can seat with a number of ways = 3! = 6
So, the total ways that the five persons can seat = 12*6 = 72
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Step-by-step explanation:

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6 0
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