Chapter 1: Fundamentals

The speed of light is about 186,000 mi/s. Use the information in Exercise 88(a) to find how long it takes for a light ray from the sun to reach the earth.

The imaginary number i has the property that $i^2=\_\_\_$.

Explain in your own words what it means for an equation to model a real-world situation, and give an example.

We find the “steepness.” Or slope, of a line passing through two points by dividing the difference in the coordinates of these points by the difference in the coordinates . So the line passes through the points (0,1) and (2,5) slope.

Question: 1. Give an example of each of the following:

1. A natural number
2. An integer that is not a natural number
3. A rational number that is not an integer
4. An irrational number

The point that is 3 units to the right of the y-axis and 5 units below the x-axis has coordinates$\left(\text{\_\_\_\_,\_\_\_}\right)$.

(a) If $x<5,$ then $x-3\_\_\_\_\_\_\_\_\_\_2$.

(b) If $x\le 5,$ then $3x\_\_\_\_\_\_\_\_\_\_15$.

(c) If $x\ge 2,$ then $-3x\_\_\_\_\_\_\_\_\_\_-6$

(d)If $x<-2,$ then $-x\_\_\_\_\_\_\_\_\_\_2$.

a. Using exponential notation, we can write the product$5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5$as ______ .

b, In the expression$3^4$the number 3 is called the ______ , and the number 4 is called the _____ .

Give an example of each of the following:

a. A natural number

b. An integer that is not a natural number

c. A rational number that is not an integer

d. An irrational number

The solutions of the equation $x^2-2x-3=0$ are the _____-intercepts of the graph of$y=x^2-2x-3$.