Transcript 2.8 - TeacherWeb

Warm-Up Exercises
1. Write an equation for “3 more than twice a is 24.”
ANSWER
2a + 3 = 24
2. A square has a side length of 8 feet. Find the area of
the square using the formula A = s2.
ANSWER
64 ft2
Warm-Up Exercises
3. A rectangular serving tray is 26 inches long and
18 inches wide. What is the tray’s serving area?
ANSWER
468 in.2
EXAMPLE
Warm-Up1Exercises
Solve a literal equation
Solve ax + b = c for x. Then use the solution to solve
2x + 5 = 11.
SOLUTION
STEP 1 Solve ax + b = c for x.
ax + b = c
ax = c – b
c–b
x=
a
Write original equation.
Subtract b from each side.
Assume a  0. Divide each side by a.
EXAMPLE
Warm-Up1Exercises
Solve a literal equation
STEP 2 Use the solution to solve 2x + 5 = 11.
c–b
x = a
11 – 5
= 2
=3
ANSWER
Solution of literal equation.
Substitute 2 for a, 5 for b, and 11 for c.
Simplify.
The solution of 2x + 5 = 11 is 3.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
Solve the literal equation for x. Then use the
solution to solve the specific equation
1. a – bx = c; 12 – 5x = –3
ANSWER
a–c
x = b ;3
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
Solve the literal equation for x. Then use the
solution to solve the specific equation
2. ax = bx + c; 11x = 6x + 20
ANSWER
c
x=
;4
a–b
Warm-Up2Exercises
EXAMPLE
Rewrite an equation
Write 3x + 2y = 8 so that y is a function of x.
3x + 2y = 8
2y = 8 – 3x
y = 4 – 3x
2
Write original equation.
Subtract 3x from each side.
Divide each side by 2.
Warm-Up3Exercises
EXAMPLE
Solve and use a geometric formula
1
The area A of a triangle is given by the formula A = bh
2
where b is the base and h is the height.
a.
Solve the formula for the height h.
b.
Use the rewritten formula to find the
height of the triangle shown, which
has an area of 64.4 square meters.
SOLUTION
a.
1
A = 2 bh
2A = bh
Write original formula.
Multiply each side by 2.
Warm-Up3Exercises
EXAMPLE
Solve and use a geometric formula
2A
=h
b
b.
Divide each side by b.
Substitute 64.4 for A and 14 for b in the rewritten
formula.
2A
h= b
=
Write rewritten formula.
2(64.4)
14
= 9.2
ANSWER
Substitute 64.4 for A and 14 for b.
Simplify.
The height of the triangle is 9.2 meters.
Warm-Up
Exercises
GUIDED
PRACTICE
3.
for Examples 2 and 3
Write 5x + 4y = 20 so that y is a function of x.
ANSWER
y = 5 – 5x
4
Warm-Up Exercises
Warm-up: Continue working on benchmark test
from yesterday.
Homework: Page 129 #11-31 all
Warm-Up Exercises
1.
Write the equation 15 = 5y – 4x so that y is a
function of x.
ANSWER
2.
Solve C = 2pr for r.
ANSWER
3.
y= 4 x+3
5
r=
C
p
2
Solve V = 1 Bh for B.
3
ANSWER
B = 3V
h
Warm-Up
Exercises
GUIDED
PRACTICE
4.
for Examples 2 and 3
The perimeter P of a rectangle is given by the
formula P = 2l + 2w where l is the length and w is the
width.
a. Solve the formula for the width w.
ANSWER
w=
P – 2l
2
or w =
P
–l
2
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
b . Use the rewritten formula to find
the width of the rectangle shown.
ANSWER
2.4
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
Temperature
You are visiting Toronto, Canada, over the weekend.
A website gives the forecast shown. Find the low
temperatures for Saturday and Sunday in degrees
5
Fahrenheit. Use the formula C = (F – 32) where C is
9
the temperature in degrees Celsius and F is the
temperature in degrees Fahrenheit.
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
SOLUTION
STEP 1 Rewrite the formula. In the problem, degrees
Celsius are given and degrees Fahrenheit
need to be calculated. The calculations will be
easier if the formula is written so that F is a
function of C.
5
C = 9 (F – 32)
Write original formula.
9 5
9
C = · (F – 32)
5 9
5
9
C = F – 32
5
9
C + 32 = F
5
9
Multiply each side by , the
5
reciprocal of 5 .
9
Simplify.
Add 32 to each side.
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
ANSWER
9
The rewritten formula is F = C + 32.
5
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
STEP 2
Find the low temperatures for Saturday
and Sunday in degrees Fahrenheit.
Saturday (low of 14°C)
9
F = C + 32
5
9
= 5 (14)+ 32
Sunday (low of 10°C)
9
F = C + 32
5
9
= 5 (10)+ 32
= 25.2 + 32
= 18 + 32
= 57.2
= 50
ANSWER
ANSWER
The low for Saturday
is 57.2°F.
The low for Sunday is 50°F.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
5. Use the information in Example 4 to find the
high temperatures for Saturday and Sunday
in degrees Fahrenheit.
ANSWER
71.6°F, 60.8°F
Daily
Homework
Quiz
Warm-Up
Exercises
4. On a round-trip bicycle trip from Santa
Barbara to Canada, Phil rode 2850 miles in
63 days. Find his average miles per day for
the trip. Use the formula d = rt where d is
distance, r is rate, and t is time. Solve for r
to find the rate in miles per day to the
nearest mile.
ANSWER
about 45 miles per day