This problem will prepare you forthe Concept Connection on page 102. a. For how many

Vocabulary Explain why a conjecture may be true or false.

Find the next item in each pattern. March, May, July,

Find the next item in each pattern. 1 3 , _ 2 4 , _ 3 5 ,

Find the next item in each pattern. 4

Complete each conjecture The product of two even numbers is ? .

Complete each conjecture A rule in terms of n for the sum of the first n odd positive integers is ? .

Biology A laboratory culture contains 150 bacteria. After twenty minutes, the culture contains 300 bacteria. After one hour, the culture contains 1200 bacteria. Make a conjecture about the rate at which the bacteria increases.

Show that each conjecture is false by finding a counterexample. Kennedy is the youngest U.S. president to be inaugurated.

Show that each conjecture is false by finding a counterexample. Three points on a plane always form a triangle.

Show that each conjecture is false by finding a counterexample. For any real number x, if x 2 1, then x 1.

Find the next item in each pattern. 8 A.M., 11 A.M., 2 P.M.,

Find the next item in each pattern. 75, 64, 53,

Find the next item in each pattern. 13

Complete each conjecture. A rule in terms of n for the sum of the first n even positive integers is ? .

Complete each conjecture. The number of nonoverlapping segments formed by n collinear points is ? .

Industrial Arts About 5% of the students at Lincoln High School usually participate in the robotics competition. There are 526 students in the school this year. Make a conjecture about the number of students who will participate in the robotics competition this year.

Show that each conjecture is false by finding a counterexample. If 1 - y > 0, then 0 < y < 1.

Show that each conjecture is false by finding a counterexample. For any real number x, x 3 x 2

Show that each conjecture is false by finding a counterexample. Every pair of supplementary angles includes one obtuse angle.

Make a conjecture about each pattern. Write the next two items. 2, 4, 16,

Make a conjecture about each pattern. Write the next two items. 1 2 , _ 1 4 , _ 1 8 ,

Make a conjecture about each pattern. Write the next two items. 3, 6, 9, 12,

Draw a square of dots. Make a conjecture about the number of dots needed to increase the size of the square from n n to (n + 1) (n + 1) .

Determine if each conjecture is true. If not, write or draw a counterexample. Points X, Y, and Z are coplanar.

Determine if each conjecture is true. If not, write or draw a counterexample. If n is an integer, then n is positive.

Determine if each conjecture is true. If not, write or draw a counterexample. In a triangle with one right angle, two of the sides are congruent.

Determine if each conjecture is true. If not, write or draw a counterexample. If BD

bisects ABC, then mABD = mCBD.

Estimation The Westside High School band is selling coupon books to raise money for a trip. The table shows the amount of money raised for the first four days of the sale. If the pattern continues, estimate the amount of money raised during the sixth day.

Write each fraction in the pattern _1 11 , _2 11 , _3 11 , as a repeating decimal. Then write a description of the fraction pattern and the resulting decimal pattern.

Math History Remember that a prime number is a whole number greater than 1 that has exactly two factors, itself and 1. Goldbachs conjecture states that every even number greater than 2 can be written as the sum of two primes. For example, 4 = 2 + 2. Write the next five even numbers as the sum of two primes.

The pattern 1, 1, 2, 3, 5, 8, 13, 21, is known as the Fibonacci sequence. Find the next three terms in the sequence and write a conjecture for the pattern.

Look at a monthly calendar and pick any three squares in a rowacross, down, or diagonal. Make a conjecture about the number in the middle.

Make a conjecture about the value of 2n - 1 when n is an integer.

Critical Thinking The turnaround date for migrating gray whales occurs when the number of northbound whales exceeds the number of southbound whales. Make a conjecture about the turnaround date, based on the table below. What factors might affect the validity of your conjecture in the future?

Write About It Explain why a true conjecture about even numbers does not necessarily hold for all numbers. Give an example to support your answer.

This problem will prepare you for the Concept Connection on page 102. a. For how many hours did the Mock Turtle do lessons on the third day? b. On what day did the Mock Turtle do 1 hour of lessons?

Which of the following conjectures is false? If x is odd, then x + 1 is even. The sum of two odd numbers is even. The difference of two even numbers is positive. If x is positive, then x is negative.

A student conjectures that if x is a prime number, then x + 1 is not prime. Which of the following is a counterexample? x = 11 x = 6 x = 3 x = 2

The class of 2004 holds a reunion each year. In 2005, 87.5% of the 120 graduates attended. In 2006, 90 students went, and in 2007, 75 students went. About how many students do you predict will go to the reunion in 2010? 12 15 24 30

Multi-Step Make a table of values for the rule x 2 + x + 11 when x is an integer from 1 to 8. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample?

Political Science Presidential elections are held every four years. U.S. senators are elected to 6-year terms, but only __1 3 of the Senate is up for election every two years. If __1 3 of the Senate is elected during a presidential election year, how many years must pass before these same senate seats are up for election during another presidential election year?

Physical Fitness Rob is training for the Presidents Challenge physical fitness program. During his first week of training, Rob does 15 sit-ups each day. He will add 20 sit-ups to his daily routine each week. His goal is to reach 150 sit-ups per day. a. Make a table of the number of sit-ups Rob does each week from week 1 through week 10. b. During which week will Rob reach his goal? c. Write a conjecture for the number of sit-ups Rob does during week n.

Construction Draw AB . Then construct point C so that it is not on AB and is the same distance from A and B. Construct AC and BC . Compare mCAB and mCBA and compare AC and CB. Make a conjecture.

Determine if the given point is a solution to y = 3x - 5. (Previous course) (1, 8)

Determine if the given point is a solution to y = 3x - 5. (Previous course) (-2, -11)

Determine if the given point is a solution to y = 3x - 5. (Previous course) (3, 4)

Determine if the given point is a solution to y = 3x - 5. (Previous course) (-3.5, 0.5)

Find the perimeter or circumference of each of the following. Leave answers in terms of x. (Lesson 1-5) a square whose area is x 2

Find the perimeter or circumference of each of the following. Leave answers in terms of x. (Lesson 1-5) a rectangle with dimensions x and 4x - 3

Find the perimeter or circumference of each of the following. Leave answers in terms of x. (Lesson 1-5) a triangle with side lengths of x + 2

Find the perimeter or circumference of each of the following. Leave answers in terms of x. (Lesson 1-5) a circle whose area is 9 x 2

A triangle has vertices (-1, -1) , (0, 1) , and (4, 0) . Find the coordinates for the vertices of the image of the triangle after each transformation. (Lesson 1-7) (x, y) (x, y + 2)

A triangle has vertices (-1, -1) , (0, 1) , and (4, 0) . Find the coordinates for the vertices of the image of the triangle after each transformation. (Lesson 1-7) (x, y) (x + 4, y - 1)