Write a complete two-column proof for the following information. hint: use the angle addition theorem and the fact that a line is made up of two opposite rays.

given: m∠1 = 62° and lines t and l intersect

prove: m∠4 = 62°

Given

m∠1 = 62°

lines t and l intersect

Prove: m∠4 = 62°

To proof

Angle addition property

Two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.

As shown in the diagram

m ∠1 + m∠ 2 = 180 °

( by linear pair property )

Given:

m∠1 = 62°

Put in the above equation

we get

m∠ 2 = 180° -62°

m ∠2= 118°

Also

m∠ 2 + m∠4 = 180°

( By linear pair property )

m∠4 = 180° - 118°

m ∠4 = 62°

Hence proved

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

2/5

step-by-step explanation: