Provide reasons for the proof.

Given:<2 ≅ <4

and <2 and <3 is supplementary

Prove: <1 ≅ <3

Statement Reason
1. < 2 ≅ <4 1. Given

2. m<2 = m<4 2. Angle congruence postulate

3. <2 and <3 are supplementary 3. Given

4. m<2 + m<3 = 180° 4. Definition of supplementary angles

5. <1 and <4 are supplementary 5.

6. m<1 + m<4 = 180° 6. Definition of supplementary angles

7. m<1 + m<4 = m<2 + m<3 7.

8. m<1 + m<4 = m<4 + m<3 8.

9. m<1 = m<3 9.

10. <1 ≅ <3 10.

Atemperature of 1.64◦f corresponds to answer in units of ◦c.

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)