Evaluate the Expressions
Evaluate the expression.
8(x-3)+4 when x=4
8(x-3)+ 4
8( 4-3) + 4
8(1) + 4
8 + 4
12
Consider the sequence below.
94, 87, 80, 73, …
a.) Describe the sequence in words.
b.) What is the value of the 8th term?
a.) starts at 94 & Subtracts 7
b.) 45
A group books a venue for an event for $2500. The cost of renting the venue will be split equally among all of the attendees. However, they have decided that the planning committee, consisting of 5 people, should not have to contribute to the cost.
a.) If a total of 105 people attend (including the planning committee), what is the cost per person?
105 - 5 (the community members) = 100 people
2,500 / 100 = $25 per person
If expressions A and B are equivalent, what must the value of c be?
Expression A: 8(x+4)-2(x-2)
Expression B: 3(cx+12)
**Hint: distribute the first**
Expression A: 8(x+4)-2(x-2)
8x + 32 - 2x + 4
6x +36
Expression B: 3(cx+12)
3 x __ = 6
c = 2
Evaluate the expression.
3y - 4(2y+5) when y=-3
3y - 4(2y+5) when y=-3
3(-3) -4( 2(-3) +5 )
-9 -4( -6 +5)
-9 -4(-1)
-9 + 4
-5
The 7th, 8th, and 9th terms of an arithmetic sequence are 20, 15, and 10 respectively. What is the first term of the sequence?
Term Number
9 10
8 15
7 20
..... ...
2 45
1 50
A group books a venue for an event for $2500. The cost of renting the venue will be split equally among all of the attendees. However, they have decided that the planning committee, consisting of 5 people, should not have to contribute to the cost.
b.) If a total of 45 people attend (including the planning committee), what is the cost per person?
45 - 5 (the community members) = 40 people
2,500 / 40 = $62.50 per person
The first two terms of a sequence are 2 and 6. Give the next term in the sequence and explain your answer if the sequence is Arithmetic.
2 , 6 , 10
--> -->
+4 +4
Starts with 2 then adds 4
Evaluate the expression.
(8z) / 4 when z=12
(8z) / 4 when z=12
(8*12) / 4
96/ 4
24
The 3rd and 5th term of a geometric sequence are 12 and 432 respectively. What is the common ratio of the sequence?
12 , _72_ , 432
--> -->
x 6 x 6
---------->
x 36
Common ratio = 6
Part of John’s workout routine is a circuit of 30 squats, followed by 20 deadlifts and then followed by 10 lunges. He completes multiple rounds of this circuit in the same sequence.
a.) After 3 full rounds of the circuit, how many squats has he done?
30 Squats x 3 circuits = 90 Squats
The first two terms of a sequence are 2 and 6. Give the next term in the sequence and explain your answer if the sequence is Geometric.
2 , 6 , 18
--> -->
x 3 x 3
Starts with 2 then multiplies by 3
Evaluate the expression.
-4(2d + 7) + 3(d - 9) when d = -3
-4(2d + 7) + 3(d - 9) when d = -3
-4(2(-3) +7 ) + 3( -3-9)
-4(-6+7) + 3(-12)
-4(1) + -36
-4 - 36
-40
Jenna is going out of town and a friend is going to feed her dog when she is gone. The dog needs to be fed 80 grams of food per day. Jenna’s bin of dog food contains 2000 grams when she leaves for her trip.
a.) Fill out the table
Day 0 1 2 3
Food 2000
Remaining (g)
b.) Write an explicit rule to find the amount of food left on the nth day.
c.) How much food will remain after 7 days?
a.) Fill out the table
Day 0 1 2 3
Food (g) 2000 1,920 1,840 1,760
b.) an= 2000 - 80(n-1)
c.) 2000 - 80(7-1)
2000-80(6)
2000-480
1,520
Part of John’s workout routine is a circuit of 30 squats, followed by 20 deadlifts and then followed by 10 lunges. He completes multiple rounds of this circuit in the same sequence.
a.) If John has done 100 squats, how many deadlifts has he done?
100/30 = 3.3 sets
** Since John has half way through the squats during set 4, he only has 3 sets of dead lifts completed **
20 dead lifts x 3 sets = 60 Deadlifts
The table below represents an arithmetic sequence.
a.) Fill out the table below
Term Number 1 2 3 4 5 6 7
Term Value 2 __ 8 __ 14 __ __
b.) Write an explicit formual to find the nth term of the sequence
Term Number 1 2 3 4 5 6 7
Term Value 2 _5_ 8 _11_ 14 17 20
b.) an= 2 + 3(n-1)