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Algebra and Trigonometry Quiz

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Questions and Answers

What is the graph representation of the inequality $2x + 3y ≤ 6$?

It is a shaded region below the line $2x + 3y = 6$ in the Cartesian plane.

Given the graph that shows $y > 2x + 1$, what does this indicate about the relationship between y and the line?

It indicates that y is greater than the value provided by the line $y = 2x + 1$ for any x.

What is the solution for the quadratic inequality $x² - 2x - 3 ≤ 0$?

The solution is $-1 ≤ x ≤ 3$.

What are the intervals where the inequality $-x² + x + 12 < 0$ holds true?

The intervals are $x < -3$ and $x > 4$. Signup and view all the answers

If $cos θ = -0.6753$, what are the possible values of θ in degrees?

The possible values are $132.5°$ and $227.5°$. Signup and view all the answers

Using the given angles and side AB, how would you determine the length of side b in the triangle?

By applying the Law of Sines, we can find side b using the ratio of the sides to the sine of their opposite angles. Signup and view all the answers

How do you verify the measure of angle R in the triangle with the given side lengths and angle P?

You can check angle R using the triangle sum theorem which states that the sum of angles in a triangle is 180°. Signup and view all the answers

What formula would you use to calculate the height of a television screen given its diagonal and width?

The Pythagorean theorem, $d^2 = w^2 + h^2$, can be used where $d$ is the diagonal, $w$ is the width, and $h$ is the height. Signup and view all the answers

What method would you use to calculate the time it takes for two friends to complete a paper route together?

The harmonic mean of their individual times can be used to determine the combined time for both completing the task. Signup and view all the answers

How would you determine the average speed for the dog race given the total distance and time, considering the speed change on the return trip?

You would first find the speed for the outbound trip, then calculate average speed by dividing the total distance by the total time. Signup and view all the answers

Study Notes

PC 11 Feedback

Topic: Graphing inequalities
Example: 2x + 3y ≤ 6
Example solution: ex.1 p.466

Inequalities from Graph

Topic: Writing inequalities from graphs
Example: y > 2x + 1
Example solution: ex.3 p.469

Solving by Graphing

Topic: Solving quadratic inequalities graphically
Example: x² - 2x - 3 ≤ 0
Example solution: ex.1 p.478

Solving Inequalities

Topic: Solving quadratic inequalities using intervals
Example: -x² -x + 12 ≥ 0
Example solution: ex.2 p.480

Trigonometry

Topic: Finding trigonometric values given specific conditions
Example: θ is an angle in standard position with terminal arm in quadrant III, and cos θ = -3/4
Find sin θ
Exact value = -√7/4
θ = 132.5°, 227.5° (example solution)
Example solution: ex.3 p.92
Example solution: ex.6 p.95

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Description

Test your understanding of graphing inequalities, writing inequalities from graphs, and solving quadratic inequalities. Additionally, explore trigonometric values related to specific conditions. Challenge yourself with practical examples and solutions provided.