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amm1812
3 years ago
9

94.

Mathematics
1 answer:
attashe74 [19]3 years ago
5 0

Answer:

are you cheating again?

Step-by-step explanation:

cuz I wanna know the answer too

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Answer:

  • arc BC = 60°
  • m∠ADC = 60°
  • m∠AEB = 105°
  • m∠ADP = 45°
  • m∠P = 60°

Step-by-step explanation:

The sum of arcs of a circle is 360°. The given conditions tell us arc BC ≅ arc AB, so the four arcs of the circle have ratios ...

  CB : BA : AD : DC = 2 : 2 : 3 : 5

The sum of ratio units is 2+2+3+5 = 12, so each one stands for 360°/12 = 30°. Then the arc lengths are ...

  arc BC = arc BA = 60° . . . . 2 ratio units each

  arc AD = 90° . . . . . . . . . . . . 3 ratio units

  arc DC = 150° . . . . . . . . . . . .5 ratio units

The inscribed angles are half the measure of the intercepted arcs:

  ∠ADC = (1/2) arc AC = 1/2(120°) = 60°

  ∠ADP = 1/2 arc AD = 1/2(90°) = 45°

The angles at E are half the sum of the measures of the intercepted arcs.

  ∠AEB = (arc AB + arc CD)/2 = (60° +150°)/2 = 105°

Angle P is half the difference of the intercepted arcs.

  ∠P = (arc BD -arc AD)/2 = (210° -90°)/2 = 120°/2 = 60°

__

In summary, ...

  arc BC = 60°

  m∠ADC = 60°

  m∠AEB = 105°

  m∠ADP = 45°

  m∠P = 60°

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Step-by-step explanation:

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Option 1. (-2)(5x) + (-2)(-\frac{3}{4}) and option 4.-10x + \frac{3}{2} are equivalent to -2(5x-\frac{3}{4} ).

Step-by-step explanation:

Step 1:

The given expression is expanded as follows.

The -2 is multiplied with the 5x and then the -2 is multiplied with the -\frac{3}{4}.

So the expression becomes as follows;

-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}).

This is the first option given so the first expression is equivalent.

Step 2:

-2(5x-\frac{3}{4} ) = (-2)(5x) + (-2)(-\frac{3}{4}) = -10x + \frac{6}{4} = -10x + \frac{3}{2} .

Of the other four options, only the fourth expression has the fraction \frac{3}{2} so the fourth expression is also equivalent.

Expressions 1 and 4 are equivalent to the given expression.

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