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stepladder [879]
3 years ago
9

Given △ABC, AB=15, BD=9, AD ⊥ BC , m∠C=30° Find: The perimeter of △ABC.

Mathematics
1 answer:
Ann [662]3 years ago
7 0

Answer:

48 + 12√3 units

Step-by-step explanation:

ALL LENGTHS MUST BE POSITIVE (I did this to avoid writing ± and showing that only + works)

1. Find AD (you'll find why later): 15² = 9² + AD² --> AD² = 144 --> AD =  12

2. 30-60-90: 12-DC-AC --> AC = 24, DC = 12√3 (side opposite of 90 is double side opposite of 30, side opposite of 60 is √3 times the opposite of 30)

P = AB + BD + DC + AC = 15 + 9 + 12√3 + 24 = 48 + 12√3 units

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I need help please I don’t understand
defon

9514 1404 393

Answer:

  1. ∠EDF = 104°

  2. arc FG = 201°

  3. ∠T = 60°

Step-by-step explanation:

There are a couple of angle relationships that are applicable to these problems.

  • the angle where chords meet is half the sum of the measures of the intercepted arcs
  • the angle where secants meet is half the difference of the measures of the intercepted arcs

The first of these applies to the first two problems.

1. ∠EDF = 1/2(arc EF + arc UG)

  ∠EDF = 1/2(147° +61°) = 1/2(208°)

  ∠EDF = 104°

__

2. ∠FHG = 1/2(arc FG + arc ES)

  128° = 1/2(arc FG +55°) . . . substitute given information

  256° = arc FG +55° . . . . . . multiply by 2

  201° = arc FG . . . . . . . . . subtract 55°

__

3. For the purpose of this problem, a tangent is a special case of a secant in which both intersection points with the circle are the same point. The relation for secants still applies.

  ∠T = 1/2(arc FS -arc US)

  ∠T = 1/2(170° -50°) = 1/2(120°)

  ∠T = 60°

3 0
3 years ago
(115) the product of integers x, y, and z is even. is z even?
djyliett [7]
1. X/Y = Z

if x = 6, y = 2, then z = 3, not even

if x = 6, y = 3, then z = 2, even

<span>2. Z=XY </span>

so (z)^2 = 2*k (because x*y*z = 2k, where k is an integer)

<span>Sufficient, as if square of an integer is even ,then the integer is even</span>
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4 years ago
The mean weight of four trucks were 3,700 pounds.The first truck was 3,250 pounds.The second truck was 3,890 pounds.Tue lady tru
9966 [12]

Answer:

4,020

Step-by-step explanation:

mean = average

  • Ideally, in order for us to have a 3,700 pound average, each of the four trucks would be 3,700 pounds. Added up, we would have a total of: 14,800 pounds (3,700×4)
  • Let's see how much pounds we already have:
  • 3,250 + 3,890 + 3,640 = 10,780

Now we need to find how much pounds we are missing: 14,800 - 10,780 =

<h2>4,020 for the fourth truck</h2>
  • Let's check: 3,250 + 3,890 + 3,640 + 4,020 = 14,800
  • 14,800/4 = 3,700 pounds
<h3>Good job! I hope this helps</h3>
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