If only two points are needed to determine a​ line, why are three ordered pair solutions or points found for a linear​ equation?

Answer:

The accurate statements are 2 and 3.

Step-by-step explanation:

Consequently, point S maps to point V, point R corresponds with point U, and point Q corresponds with point T.

Based on this information, let's review the statements:

1) SQ corresponds to VU. False as SQ corresponds to VT

2) ∠R corresponds to ∠U. True

3) UV corresponds to RS. True

4) ∠S corresponds to ∠T.  False since ∠S corresponds to ∠V

5) QS corresponds to RS. False since QS corresponds to TV

Therefore, the true statements are 2 and 3.

2) ∠R corresponds to ∠U

3) UV corresponds to RS.

Answer:

1. Conduct four flips of a fair coin; heads will stand for teenagers who like to watch films in theaters, while tails represent those who prefer otherwise.

2. Draw four cards from a standard deck, where red suits indicate those who enjoy going to theaters for movies, and black suits indicate the opposite.

4. Roll a six-sided die four times; even numbers will denote teenagers who favor theater viewings, while odd numbers will denote those who do not.

Step-by-step explanation:

The procedure involves repeating an action four times, each time presenting a 50/50 probability.

To elaborate on point 1, the flipping of the coin occurs four times, with a fair coin presenting each outcome with equal chances.

For point 2, drawing four cards allows for a balanced chance of pulling either a red or black card from the deck.

Point 3 inaccurately states performing the action three times, so it is incorrect.

In point 4, rolling the die four times also adheres to a 50/50 ratio for even versus odd outcomes.

Point 5 is incorrect because the range of 0-5 consists of six figures, while 6-9 includes only four, failing to create a balanced 50/50 scenario.

Answer: 0.5507

Step-by-step explanation:

Given: The time between sightings of speeders by a radar system is represented by the continuous random variable X, which follows a cumulative distribution function

If we convert 12 minutes into hours, it equals hours or 0.2 hours.

To find the probability of waiting less than 12 minutes:

Thus, the probability we are looking for is: 0.5507

Answer:

6.79 miles

Step-by-step explanation:

Consider triangle ABC where A marks the starting point and C indicates the end point.

|AB|=5.2 miles

|BC|=3.0 miles

∠ABC = 90 + 75 = 165°

We're given two side lengths and an angle that is not opposite to either side.

The approach to resolve this scenario is known as the Cosine Rule.

Each side opposite an angle is designated by the corresponding lowercase letter.

The Cosine Rule asserts that:

b² = a² + c² - 2acCosB

|AC|²=3² + 5.2² - (2 × 5.2 × Cos 165°)

|AC|²=9 + 27.04 + 10.05

|AC|²=46.09

|AC|=√46.09=6.79 miles

Thus, the straight-line distance from A to C measures 6.79 miles