Download no.4 ch.3 and 4 presentation slides

(0, -2)
(1, 2)
Opener #1
Graph: y < 4x - 2
Notes
#4
(3.1, 3.2, 3.5)
Applications
3
[
0
1
[
)
2
6
[
)
Opener #2
Graph: y= 1 x
3
9
)
Work on the Opener
problems with your group.
You may use notes, book,
homework.
The runner is the person
with the oldest living
grandparent.
Turn in Notes / HW #3 with
your group.
(1, 2, 1)
Solve:
-2x + 5y + 3z = 11
-4x - 3y - 8z = -18
6x + 8y - 5z = 17
Opener #3
The students will be able
to solve application
problems using 2 or more
variables in 2 or more
equations.
Target Goal:
p. 171; 1, 3, 5, 9-19 odd
Questions on HW #3???
Let
x = 1st #
y = 2nd #
z = 3rd #
Define the Variable
See board for work.
x + y + z = 83
y = x + 10
2x + 5 = z
Set up a system of eqns/solve
Answer the problem
#1
The sum of three numbers is 83. The second
number is ten more than the first number.
Twice the first number, increased by five
equals the third number. Find the three
numbers.
Solve the system of eqns.
Answer the problem.
for 2 vbls . . .)
Define the variables.
Set up equations using the
variables (2 eqns for 2 vbls, 3 eqns
Applications:
Set up a system of eqns/solve
Answer the problem
Let
x = 1st #
y = 2nd #
z = 3rd #
Define the Variable
x + y + z = 83
y = x + 10
2x + 5 = z
Set up a system of eqns/solve
(17, 27, 39)
Answer the problem
#1
The sum of three numbers is 83. The second
number is ten more than the first number.
Twice the first number, increased by five
equals the third number. Find the three
numbers.
Let
x = 1st #
y = 2nd #
z = 3rd #
Define the Variable
#1
The sum of three numbers is 83. The second
number is ten more than the first number.
Twice the first number, increased by five
equals the third number. Find the three
numbers.
Set up a system of eqns/solve
Answer the problem
Let
x = bottom seats
y = middle seats
z = upper seats
Set up a system of eqns/solve
Answer the problem
Answer the problem
See board for work.
x + y + z = 49000
35x+30y+25z=1,419,500
x+y=z
Set up a system of eqns/solve
Let
x = bottom seats
y = middle seats
z = upper seats
Define the Variable
There are 49,000 seats in a sports stadium. Tickets for the
seats in the upper level sell for $25, the ones in the middle
level cost $30 and the ones in the bottom level are $35 each.
The number of seats in the middle and bottom levels
together equals the number of seats in the upper level.
When all of the seats are sold for an event, the total revenue
is $1,419,500. How many seats are there in each level?
Define the Variable
#3
(20, 40, 50)
Answer the problem
There are 49,000 seats in a sports stadium. Tickets for the
seats in the upper level sell for $25, the ones in the middle
level cost $30 and the ones in the bottom level are $35 each.
The number of seats in the middle and bottom levels
together equals the number of seats in the upper level.
When all of the seats are sold for an event, the total revenue
is $1,419,500. How many seats are there in each level?
1x
2
x + y + z = 110
y = 2x
Let
x = 1st #
y = 2nd #
z = 3rd #
z = 3x -
Set up a system of eqns/solve
Define the Variable
The sum of three numbers is 110. The second
number is twice the first. The third number is
equal to three times the first minus one half the
first. Find the numbers.
#2
#3
Do with your group.
Define the Variable
The sum of three numbers is 110. The second
number is twice the first. The third number is
equal to three times the first minus one half the
first. Find the numbers.
#2
x
y
z
x = 2z + 7
x+ y =19
2
x + y + 2z = 58
Set up a system of eqns/solve
Answer the problem
z
x
y
Define the Variable
z
x = 2z + 7
x+ y =19
2
x + y + 2z = 58
Set up a system of eqns/solve
y = 11 in.
x = 27 in.
z = 10 in.
Answer the problem
An isosceles trapezoid has shorter base, longer base, and
two congruent legs. The perimeter of the trapezoid is 58
inches. The average of the bases is 19 inches and the
longer base is twice the leg plus 7. Find the lengths of the 4
sides of the trapezoid then find the area of the trapezoid.
x
z
#4
z
y
An isosceles trapezoid has shorter base, longer base, and
two congruent legs. The perimeter of the trapezoid is 58
inches. The average of the bases is 19 inches and the
longer base is twice the leg plus 7. Find the lengths of the 4
sides of the trapezoid then find the area of the trapezoid.
Define the Variable
z
Answer the problem
14,400 bottom seats
10,100 middle seats
24,500 upper seats
x + y + z = 49000
35x+30y+25z=1,419,500
x+y=z
Set up a system of eqns/solve
Answer the problem
#4
Let
x = bottom seats
y = middle seats
z = upper seats
Define the Variable
Set up a system of eqns/solve
An isosceles trapezoid has shorter base, longer base, and
two congruent legs. The perimeter of the trapezoid is 58
inches. The average of the bases is 19 inches and the
longer base is twice the leg plus 7. Find the lengths of the 4
sides of the trapezoid then find the area of the trapezoid.
There are 49,000 seats in a sports stadium. Tickets for the
seats in the upper level sell for $25, the ones in the middle
level cost $30 and the ones in the bottom level are $35 each.
The number of seats in the middle and bottom levels
together equals the number of seats in the upper level.
When all of the seats are sold for an event, the total revenue
is $1,419,500. How many seats are there in each level?
Define the Variable
#4
#3
27
10
h(b1 +b2 ) 6(11+ 27)
=
2
2
6
114 inches2
Area =
10
11
Find the area of the trapezoid.
#4
Set up a system of eqns/solve
Answer the problem
You do NOT have to copy the
problems out of the book.
Define the Variable
Do these problems just like the notes!
p. 147; 27, 40, 41, 42, 43a, 52
p. 171; 7, 20a, 20b, 21, 23
Homework
#4