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lisov135 [29]
3 years ago
15

Antoinette solves the linear equation 3(x-3)+2x+9 = 2X+ 2(x-1) using the steps shown below.

Mathematics
2 answers:
ArbitrLikvidat [17]3 years ago
7 0

Answer:

A

Step-by-step explanation:

taurus [48]3 years ago
5 0

Answer:

Antoinette's error

Option A) She distributed incorrectly.

Step-by-step explanation:

We are given the following information in the question:

Antoinette solves the linear equation

3(x-3)+2x+9 = 2x+ 2(x-1)

Antoinette made mistake in step 1 that is she did not distributed correctly.

If she would have distributed correctly, then she would have got the following solution:

3(x-3)+2x+9 = 2x+ 2(x-1)\\\text{Step 1: }3x-9+2x+9 = 2x + 2x-2\\\text{Step 2: }5x = 4x -1\\\text{Step 3: }5x-4x = -1\\\text{Step 4: }x = -1

Substituting x = -1 in the given equation, we gwt:

3(-1-3)+2(-1)+9 = 2(-1)+ 2(-1-1)\\-12-2+9 = -2-4\\-6=-6\\\text{which is true}

Antoinette's error

Option A) She distributed incorrectly.

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A bike rental stand at the beach charges $5 to rent a bike in targit charges to every half hour it is rented if someone pays $17
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They would have the bike for 1.7 hours

Step-by-step explanation:

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Solve the right triangle​ ABC, with Cequals90degrees. Aequals58.3degrees​, cequals24.8 ft
horsena [70]

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Step-by-step explanation:

If ABC is a right triangle, where the right angle is B, then

  • The hypotenuse of the triangle is b and a , c are its legs
  • sin(A) = \frac{a}{b}
  • sin(C) = \frac{c}{b}
  • b=\sqrt{a^{2}+c^{2}}
  • The sum of the measures of the two acute angles A and C is 90°

∵ ABC is a right triangle

∵ m∠C = 90°

∴ c is the hypotenuse and a , b are its legs

∵ m∠A = 58.3°

- The sum of the two acute angles in the right triangle = 90°

∴ m∠A + m∠B = 90°

- Substitute the measure of angle A

∴ 58.3 + m∠B = 90

- Subtract 58.3 from both sides

∴ m∠B = 31.7°

∵ sin(A) = \frac{a}{c}

∵ c = 24.8 feet

∴ sin(58.3) = \frac{a}{24.8}

- By using cross multiplication

∴ a = (24.8) × sin(58.3)

∴ a = 21.1 ft

∵ sin(B) = \frac{b}{c}

∵ c = 24.8 feet

∴ sin(31.7) = \frac{b}{24.8}

- By using cross multiplication

∴ b = (24.8) × sin(31.7)

∴ b = 13.0 ft

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Learn more:

You can learn more about solving the triangle in brainly.com/question/12985572

#LearnwithBrainly

5 0
3 years ago
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