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Paraphin [41]
2 years ago
5

Simplify the expression 6h +(-7.7d) – 16 + 5d - 2.6h.

Mathematics
1 answer:
blagie [28]2 years ago
8 0

Answer:

3.4h-2.7d-16

Step-by-step explanation:

Before we even start, we can already simplify some things

For example, in this equation it says +(-7.7d)

We can simplify this to 6h-7.7d-16+5d-2.6h

Now we have to get all of the common variables together

So the d’s and h’s have to be combined together in this equation

This makes a new equation of 3.4h-2.7d-16

That is our answer!

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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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