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il63 [147K]
3 years ago
12

Proving Vertical Angles Are Congruent

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
4 0

Answer:

Statements:                                                 Reasons:

1) ∠2 and ∠4 are vertical angles               given

2) limes <em>m </em>and <em>n </em>intersect at <em>P                    </em>definition of vertical angles

3) ∠3 and ∠4 are linear pair                       definition of linear pair

4) ∠2 and ∠3 are linear pair                       definition of linear pair

5) m∠3 + m∠4 =180                                     angle addition postulate

6) m∠2 + m∠3 =180                                     angle addition postulate

7) m∠2 + m∠3 = m∠3 + m∠4                   substitution property

8) m∠2 = m∠4                                             subtraction property

9) ∠2 ≅ ∠4                                                 definition of congruent(≅) angles

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Answer:

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Step-by-step explanation:

Given that

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The population mean, x-bar is calculated by saying

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One factor of the function f(x) = x3 − 8x2 + 17x − 10 is (x − 5). Describe how to find the x-intercepts and the y-intercept of t
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Answer:

see explanation

Step-by-step explanation:

given (x - 5) is a factor of f(x) then x = 5 is a zero

dividing f(x) by (x - 5) using synthetic division

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    ↓    5   - 15    10

    ----------------------

     1   - 3    2       0 ← remainder = 0 indicates (x - 5) is a factor

quotient = x² - 3x + 2 = (x - 1)(x - 2)

then

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to find the x- intercepts let f(x) = 0 , that is

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equate each factor to zero and solve for x

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the x- intercepts are x = 1, x = 2, x = 5

to find the y- intercept let x = 0 , then

f(0) = (0 - 5)(0 - 1)(0 - 2) = (- 5)(- 1)(- 2) = 5 × - 2 = - 10

the y- intercept is y = - 10

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