Intermediate Algebra (11th edition)

To solve use the quadratic formula with and

Substitute.

Solve for t.

The solutions are and NOW TRY

OBJECTIVE 2 Solve applied problems using the

Pythagorean theorem.The Pythagorean theorem, repre-

sented by the equation

is illustrated in FIGURE 2and was introduced in Section 8.3.

It is used to solve applications involving right triangles.

Using the Pythagorean Theorem

Two cars left an intersection at the same time, one heading due north, the other due

west. Some time later, they were exactly 100 mi apart. The car headed north had gone

20 mi farther than the car headed west. How far had each car traveled?

Step 1 Readthe problem carefully.

Step 2 Assign a variable.

Let the distance traveled by the car

headed west.

Then the distance traveled by the car

headed north.

See FIGURE 3. The cars are 100 mi apart, so the

hypotenuse of the right triangle equals 100.

Step 3 Write an equation.Use the Pythagorean theorem.

Step 4 Solve. Square the binomial.

Standard form Divide by 2. Factor.

or Zero-factor property

or Solve for x.

Step 5 State the answer.Since distance cannot be negative, discard the negative

solution. The required distances are 60 mi and mi.

Step 6 Check.Since 602 + 802 = 1002 ,the answer is correct. NOW TRY

60 + 20 = 80

x=- 80 x= 60

x+ 80 = 0 x - 60 = 0

1 x+ 8021 x- 602 = 0

x^2 + 20 x- 4800 = 0

2 x^2 + 40 x- 9600 = 0

x^2 + x^2 + 40 x+ 400 = 10,000

x^2 + 1 x+ 2022 = 1002

a^2 +b^2 = c^2

x+ 20 =

x=

EXAMPLE 3

a^2 b^2 c^2 ,

t=

- k- 2 k^2 + 8 s

4

t=.

- k+ 2 k^2 + 8 s

4

t=

- k 2 k^2 + 8 s

4

t=

- k 2 k^2 - 41221 - s 2

2122

c=-s.

2 t^2 +kt- s=0, a=2, b=k,

524 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

North

Intersection

West

100

x

x + 20

90 °

FIGURE 3

1 x+y 22 =x^2 + 2 xy+y^2

NOW TRY
EXERCISE 3
Matt Porter is building a new
barn, with length 10 ft more
than width. While determin-
ing the footprint of the barn,
he measured the diagonal as
50 ft. What will be the dimen-
sions of the barn?

NOW TRY
EXERCISE 2
Solve for r.

r^2 + 9 r=-c

NOW TRY ANSWERS

30 ft by 40 ft

r=

9 281 - 4 c
2