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ivolga24 [154]
2 years ago
10

Pleasseeee help I'll give you brainlest answer

Mathematics
1 answer:
Greeley [361]2 years ago
5 0

Answer:

The value of x is 10

Step-by-step explanation:

<em>The measure of the </em><em>exterior angle at one vertex</em><em> of a triangle equals </em><em>the sum of the measures of the two opposite interior angles </em><em>to this vertex.</em>

In ΔNOP

∵ ∠OPQ is an exterior angle of the triangle at vertex P

∵ ∠PNO and ∠NOP are the opposite interior angles of vertex P

→ By using the rule above

∴ m∠OPQ = m∠PNO + m∠NOP

∵ m∠OPQ = (6x - 15)°

∵ m∠PNO = (2x + 18)°

∵ m∠NOP = (2x - 13)°

→ Substitute them in the equation above

∴ 6x - 15 = 2x + 18 + 2x - 13

→ Add the like terms in the right side

∵ 6x - 15 = (2x + 2x) + (18 - 13)

∴ 6x - 15 = 4x + 5

→ Subtract 4x from both sides

∵ 6x - 4x - 15 = 4x - 4x + 5

∴ 2x - 15 = 5

→ Add 15 to both sides

∵ 2x - 15 + 15 = 5 + 15

∴ 2x = 20

→ Divide both sides by 2 to find x

∴ x = 10

∴ The value of x is 10

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The fruity snack company is packaging fruit loop cereal in small snack bags each snack is to weigh 30 grams with a tolerance of
katrin [286]

9514 1404 393

Answer:

  1. |w -30| > 1.6
  2. (-∞, 28.4) U (31.6, ∞)

Step-by-step explanation:

1. The snack bags will be rejected if their weight differs from 30 grams by more than 1.6 grams:

  |w -30| > 1.6

__

2. This inequality resolves to two inequalities.

  w -30 > 1.6

  w > 31.6 . . . . . add 30

and

  -(w -30) > 1.6

  w -30 < -1.6 . . . multiply by -1

  w < 28.4 . . . . . add 30

The solution in interval notation is the union of the two disjoint intervals:

  (-∞, 28.4) U (31.6, ∞)

4 0
3 years ago
Write a polynomial equation with roots 5 and -9i. X^3-?x^2+?X-?=0
jek_recluse [69]

Answer:

x³ - 5x² + 81x - 405 = 0

Step-by-step explanation:

Complex roots occur in conjugate pairs.

Thus given x = - 9i is a root then x = 9i is also a root

The factors are then (x - 5), (x - 9i) and (x + 9i)

The polynomial is the the product of the roots, that is

f(x) = (x - 5)(x - 9i)(x + 9i) ← expand the complex factors

    = (x - 5)(x² - 81i²) → note i² = - 1

    = (x - 5)(x² + 81) ← distribute

    = x³ + 81x - 5x² - 405, thus

x³ - 5x² + 81x - 405 = 0 ← is the polynomial equation

6 0
3 years ago
Solve the system of equations y= 3/2 - 1, -x+ y =-3
kaheart [24]

Answer:

(x, y) = ( 1/2, -3 )

Step-by-step explanation:

y = -3

3/2 - 1 - x + y = - 3

3/2 - 1 - x - 3 = - 3

x = 1/2

solution : (x , y ) = ( 1/2, -3)  

here we are gonna see why is that answer :

-3 = 3/2 -1 - 1/2 - 3 = -3

-3 = -3 = -3

i hope this helps

5 0
2 years ago
Thomas went to the store to buy video games for $13.50 each and controllers that cost $55 each and controllers. the total amount
Goshia [24]

Answer:6 games

Step-by-step explanation:

Thomas spent a total of 136 dollars so you subtract 55 from 136 and divide by 13.50 to get 6.

3 0
3 years ago
Select the symbol that accurately replaces the ? 1.01 ? 1.0009
Elena L [17]
<span> 1.01 > 1.0009 ????????</span>
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3 years ago
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