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zhannawk [14.2K]
3 years ago
15

Match the following reasons with the statements in the given proof. Prove that if two angles are complementary to the same angle

then they are equal in measure. 1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.
a) Substitution
2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90
b) Definition of complementary
3. m∠1 + m∠2 = m∠3 + m∠2
c) Subtraction property of equality
4. m∠1 = m∠3
d) Given
Mathematics
2 answers:
yulyashka [42]3 years ago
4 0

1. --> d

2. --> b

3. --> a

4. --> c

1 is d because that is the only piece of information that sounds like a given.

2 is b because we know that from the given, m∠1 is complementary to m∠2 and in the first problem, m∠1 + m∠2 = 90, they are added together. The definition of complementary angles is "Two angles with measures that, when added together, equal 90 degrees". Same thing with m∠3 and m∠2.

3 is a because since both of the problems equal 90 degrees, you can just take away the 90 and put an equal sign in between the two problems because they equal the same thing.

4 is c because you are subtracting m∠2 from the problems and ending up with just m∠1 = m∠3.

Hope this helps! :)

Elza [17]3 years ago
4 0

Answer:

1.   ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.-->Given(A)

2.   m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90-->Definition of complementary(D)

3.   m∠1 + m∠2 = m∠3 + m∠2-->Substitution(C)

4.   m∠1 = m∠3-->Subtraction property of equality(B)

Step-by-step explanation:


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80.027

Step-by-step explanation:

    139.65-59.623 = 80.027

                 

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Find the distance between the two points in simplest radical form.
Jlenok [28]

Answer:

d=\sqrt{58}\approx7.6

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

d=\sqrt{(-2-1)^2+(8-1)^2

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Square:

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Add:

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This cannot be simplified.

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Use the formula for the probability of two dependent events P(A and B) to derive the conditional probability formula for P(B | A
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The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).

<h3>What is said to be dependent events?</h3>

When the outcome from one event influences the outcome of the other, two events are referred to as dependent.

  • Dependent events in probability are generally real-life events that depend on another event to occur.
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The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).

This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.

Step 1: Write the multiplication rule down:

           P(A and B) = P(A)*P(B|A)

Step 2: P(A) divides both sides of the equation:

           P(A and B) / P(A) = P(A)*P(B|A) / / P(A)

Step 3: On the right side of the equation, cancel P(A):

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Step 4: Rewrite the equation as follows:

           P(B|A) = P(A and B) / P(A)

Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).

To know more about the conditional probability, here

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