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Thepotemich [5.8K]
3 years ago
14

Solve for x. −4≤11−3x Enter your answer as an inequality in the box.

Mathematics
1 answer:
Mamont248 [21]3 years ago
6 0

Answer:

x\leq 5

Step-by-step explanation:

  • the given expression is : −4≤11−3x
  • we use following operations to solve the inequality:
  • by adding 4 on both sides, the inequality will become :

-4+4 ≤ 11-3x +4

0 ≤ 15 -3x

  • adding 3x on both sides, the inequality will become:

3x ≤ 15

  • dividing both the sides of the inequality by 3, the inequality will become:

3x/3 ≤ 15/3

x ≤ 5                  ( since, 15/3 = 5)

  • therefore the solution for x as an inequality will be x ≤ 5
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Irina18 [472]

Answer:

<u>TO FIND :-</u>

  • Length of all missing sides.

<u>FORMULAES TO KNOW BEFORE SOLVING :-</u>

  • \sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}
  • \cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}
  • \tan \theta = \frac{Side \: opposite \: to \: \theta}{Side \: adjacent \: to \: \theta}

<u>SOLUTION :-</u>

1) θ = 16°

Length of side opposite to θ = 7

Hypotenuse = x

=> \sin 16 = \frac{7}{x}

=> \frac{7}{x} = 0.27563......

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2) θ = 29°

Length of side opposite to θ = 6

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Length of side opposite to θ = x

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=> \sin 30 = \frac{x}{11}

=> \frac{x}{11} = 0.5

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4) θ = 43°

Length of side adjacent to θ = x

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=> \frac{x}{12} = 0.73135......

=> x = 12 \times 0.73135.... = 8.77624.... ≈ 8.8

5) θ = 55°

Length of side adjacent to θ = x

Hypotenuse = 6

=> \cos 55 = \frac{x}{6}

=> \frac{x}{6} = 0.57357......

=> x = 6 \times 0.57357.... = 3.44145.... ≈ 3.4

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Length of side adjacent to θ = 8

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=> \frac{8}{x} = 0.29237......

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7) θ = 69°

Length of side opposite to θ = 12

Length of side adjacent to θ = x

=> \tan 69 = \frac{12}{x}

=> \frac{12}{x} = 2.60508......

=> x = \frac{12}{2.60508....}  = 4.60636.... ≈ 4.6

8) θ = 20°

Length of side opposite to θ = 11

Length of side adjacent to θ = x

=> \tan 20 = \frac{11}{x}

=> \frac{11}{x} = 0.36397......

=> x = \frac{11}{0.36397....}  =30.22225.... ≈ 30.2

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