3 Rewrite the number without using the absolute value symbol

3. Rewrite the number without using the absolute value symbol, and simplify the result.(a)

(2)|5 9|

(b)   5/|3|

(c) |3| + |2|

4.-The given numbers are coordinates of points A, B, and C, respectively, on a coordinate line.

1, 8, 7

(a) Find the distance d(A, B).
d(A, B) =

(b) Find the distance d(B, C).
d(B, C) =

(c) Find the distance d(C, B).
d(C, B) =

(d) Find the distance d(A, C).
d(A, C) =

5.-Rewrite the expression without using the absolute value symbol, and simplify the result.

|9 + x| if x < 9

6.-Replace the symbol ? with either = or to make the resulting statement true for all real numbers a, b and c, whenever the expressions are defined.

7.-Approximate the real-number expression to four decimal places.(a)

3.5²

  


(b)   

8.-Express the number in scientific form.(a)     449,000

× 10

(b)     0.000 000 055

× 10

(c)     730,000,000

× 10

9.-In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in six light years. (Round your answer to three significant figures.)

× 10

mi

10.-The population dynamics of many fish are characterized by extremely high fertility rates among adults and very low survival rates among the young. A mature specimen of a particular fish may lay as many as 3.5 million eggs, but only 0.00015% of the offspring survive to the age of 3 years. Use scientific form to approximate the number of offspring that live to age 3. (Round your answer to the nearest whole number.)

offspring

Solution

3

a)

|5 9|= |-4| = 4

(b)   5/|3| = 5/3

(c) |3| + |2| = 3 +2 = 6

4.

The given numbers are coordinates of points A, B, and C, respectively, on a coordinate line.

1, 8, 7

Lets assume the coordinate line is x axis:

(a) Find the distance d(A, B).
d(A, B) = sqrt(8-1)^2 = 7

(b) Find the distance d(B, C).
d(B, C) = sqrt( -7 -8)^2 = 15

(c) Find the distance d(C, B).
d(C, B) = sqrt( 8 - -7)^2 = sqrt(15)^2 = 15

(d) Find the distance d(A, C).
d(A, C) = sqrt(-7 -1)^2 = 8

8.-Express the number in scientific form.(a)     449,000 = 4.49 x 10^5

(b)     0.000 000 055 = 5.5 x 10^-8

(c)     730,000,000 = 7.3 x 10^8