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3 years ago

In this figure, mBDA=_ and mBCA=_.

Mathematics

2 answers:

Serhud [2]3 years ago

5 0

∠BDA is inscribed angle
inscribed angle = 1/2 × central angle
the central angle is small ∠BOA, use ∠BOA that face the same direction as ∠BDA

Find the central angle ∠BOA
central angle = 360° - large ∠BOA
central angle = 360° - 250°
central angle = 110°

Find ∠BDA
inscribed angle = 1/2 × central angle
∠BDA = 1/2 × small ∠BOA
∠BDA = 1/2 × 110°
∠BDA = 55°

To find ∠BCA, use tetragon BOAC to solve the problem
The sum of interior angles in tetragon is 360°. Because CA and CB is tangent of the circle, the angles which is formed by the tangent is 90°. So ∠CAO and ∠CBO are both equal to 90°
∠BCA + ∠CAO + ∠CBO + small ∠BOA = 360°
∠BCA + 90° + 90° + 110° = 360°
∠BCA + 290° = 360°
∠BCA = 360° - 290°
∠BCA = 70°

THE ANSWER
m∠BDA = 55°
m∠BCA = 70°

san4es73 [151]3 years ago

4 0

MBDA= ADB and mBCA= ACB

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The following figure shows A ABC with side lengths to the nearest tenth.

xz_007 [3.2K]

Answer:

17.7

Step-by-step explanation:

angle B = 180 - 81 - 65 = 34 degrees

as the sum of all angles in any triangle is always 180 degrees.

a/sin(A) = b/sin(B) = c/sin(C)

the sides are always on the opposite side of the angle.

so,

10/sin(34) = AB/sin(81)

AB = 10×sin(81) / sin(34) = 17.7

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2 years ago

1. Prove or give a counterexample for the following statements: a) If ff: AA → BB is an injective function and bb ∈ BB, then |ff

Fantom [35]

Answer:

a) False. A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1

b) True

c) True

d) B = {1}, A = N, f: N ⇒ {1}, f(x) = 1

Step-by-step explanation:

a) lets use A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1. Here f is injective but 2 is an element of b and |f−¹({b})| = 0., not 1. This statement is False.

b) This is True. If A were finite, then it can only be bijective with another finite set with equal cardinal, therefore, B should be finite (and with equal cardinal). If A were not finite but countable, then there should exist a bijection g: N ⇒ A, where N is the set of natural numbers. Note that f o g : N ⇒ B is a bijection because it is composition of bijections. This, B should be countable. This statement is True.

c) This is true, if f were surjective, then for every element of B there should exist an element a in A such that f(a) = b. This means that f−¹({b}) has positive cardinal for each element b from B. since f⁻¹(b) ∩ f⁻¹(b') = ∅ for different elements b and b' (because an element of A cant return two different values with f). Therefore, each element of B can be assigned to a subset of A (f⁻¹(b)), with cardinal at least 1, this means that |B| ≤ |A|, and as a consequence, B is finite.

b) This is false, B = {1} is finite, A = N is infinite, however if f: N ⇒ {1}, f(x) = 1 for any natural number x, then f is surjective despite A not being finite.

4 0

3 years ago

There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 peop

Delvig [45]

Answer:

$\frac{11}{87}$

Step-by-step explanation:

Total number of people = 130

Number of people who use the gym = 73

Number of people who use the pool = 62

Number of people who use the track = 58

Number of people who use the gym and the pool = 22

Number of people who use the pool and the track = 29

Number of people who use the gym and the track = 25

Number of people who use all three facilities = 11

Total number of people who use at least two facilities = 22 + 29 + 25 + 11 = 87

The probability that the randomly selected person uses all three facilities = number of those who use all three facilities ÷ total number of people who use at least two facilities.

==> 11 ÷ 87

==> $\frac{11}{87}$

3 0

2 years ago

7.003 x 10 to the power of 4

pishuonlain [190]

In scientific notation, just move the decimal point over however many numbers are in the power.

In 7.003 • 10^4, move the decimal point over 4 places to the right, (or left if it's negative) making it 70,030

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3 years ago

Read 2 more answers

HELP PLEASE<br><br> Combine like terms to create an equivalent expression.

k0ka [10]

SOLUTION:

= ( 7 / 8 )m + 9 / 10 - 2m - 3 / 5

= - ( 9 / 8 )m + 3 / 10

6 0

3 years ago

In this figure, mBDA=___ and mBCA=___.

In this figure, mBDA=_ and mBCA=_.