ALGEBRA Solve

Write the equation.

Take the square root of each side.

The equation has two solutions,Answer:

Notice that

Answer:

ALGEBRA Solve

Ch. 3-4

The Pythagorean Theorem

Vocabulary

Pythagorean Theorem: describes the

relationship between the lengths of the legs

and the hypotenuse for any right triangle

C² = a² + b²

a c

b

Hypotenuse: the side opposite the right angle. It is the longest

side of the triangle.

LegsLegs

KITES Find the length of the kite string.

The kite string forms the hypotenuse of a right triangle. The vertical and horizontal distances form the legs.

Pythagorean Theorem

c = 13Answer: The string of the kite is 13 ft.

KITES Find the length of the kite string.

Answer: 26 ft

The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg.

Pythagorean Theorem

Replace c with 33 and b with 28.

Subtract 784 from each side.

Simplify.

Take the square root of each side.

Answer: The length of the other leg is about 17.5 cm.

The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. Find the length of the other leg.

Answer: about 19.7 cm

MULTIPLE–CHOICE TEST ITEM A 10–foot ramp is extended from the back of a truck to the ground to help movers load furniture onto the truck. If the ramp touches the ground at a point 9 feet behind the truck, how high off the ground is the top of the ramp?

A about 1 foot

B about 4.4 feet

C about 13.5 feet

D about 19 feet

Read the Test Item You know the length of the ramp and the distance from the truck to the bottom of the ramp. Make a drawing of the situation including the right triangle.

Answer: BThe top of the ramp is about 4.4 feet off the ground.

Pythagorean Theorem

Replace c with 10 and b with 9.

Subtract 81 from each side.

Simplify.

Take the square root of each side.

Simplify.

Evaluate

Solve the Test Item

MULTIPLE–CHOICE TEST ITEM The base of a 12–foot ladder is 5 feet from the wall. How high can the ladder reach?

A about 7 feet

B about 10.9 feet

C about 11.8 feet

D about 13 feet

Answer: B

The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle.

Answer: The triangle is a right triangle.

Pythagorean Theorem

Simplify.

Replace a with 7, b with 24, and c with 25.Evaluate

The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle.

Answer: yes

Ch.3-5

Distance on the Coordinate Plane

Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points.

Let the distance between the two points, ,

a

b c

c² = a² + b²

c² = 5² + 5²

c² = 25 + 25

c² = 50

c = √50 ≈ 7.07Answer: The points are about 7.1 units apart.

Graph the ordered pairs (0, –3) and (2, –6). Then find the distance between the points.

Answer: about 3.6 units

TRAVEL Melissa lives in Chicago. A unit on the grid of her map shown below is 0.08 mile. Find the distance between McCormickville at (–2, –1) and Lake Shore Park at (2, 2).

Let the distance between McCormickville and Lake Shore Park. Then a = 3 and b = 4.

Pythagorean Theorem

Answer: Since each unit equals 0.08 mile, the distance is 0.08 5 = 0.4 mile.

The distance between McCormickville and Lake Shore Park is 5 units on the map.

Replace a with 3 and b with 4.

Take the square root of each side.

TRAVEL Sato lives in Chicago. A unit on the grid of his map shown below is 0.08 mile. Find the distance between Shantytown at (2, –1) and the intersection of N. Wabash Ave. and E. Superior St. at (–1, 1).

Answer: 0.4 mile

Ch. 3-3

The Real Number System

Integers: …,-2,-1,0, 1,2,…

Whole numbers: 0,1,2,3,…

Natural Numbers: 1,2,3,…

Rational numbers: has terminated decimal or repeating decimal. E.g. 1/6 =0.1666… or 1/8 = 0.125

Irrational numbers: no terminated decimal or repeating

decimal. E.g. √2 = 1.4142135…

Real numbers: rational numbers + irrational numbers. So, all numbers are real numbers.

Name all sets of numbers to which belongs.

Answer: Since it is a whole number, an integer, and a rational number.

Answer: whole, integer, rational

Name all sets of numbers to which belongs.

Answer: Since the decimal does not repeat or terminate, it is an irrational number.

Name all sets of numbers to which belongs.

…

Answer: irrational

Name all sets of numbers to which belongs.

Name all sets of numbers to which 0.090909… belongs.

The decimal ends in a repeating pattern.

Answer: It is a rational number because it is

equivalent to

Name all sets of numbers to which 0.1010101010… belongs.

Answer: rational

5-Minute Check

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