Question

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The graph shows the maximum height, in inches, reached by a pendulum on each swing.

On what swing did the pendulum's maximum height dip below 1 in. for the first time?

A. the 3rd swing

B. the 4th swing

C. the 5th swing

D. the 6th swing

Answer 1

@Vocaloid

Answer 2

select the first x-coordinate where the matching y-coordinate is less than 1

Answer 3

C

Answer 4

you're getting closer but there's one x-coordinate less than 5 that has as y-coordinate less than 1

Answer 5

ok i worked it out it's either B or D because A is out of the question and C

Answer 6

so since i checked the graph, it's D

Answer 7

oh B

Answer 8

good

Answer 9

https://static.k12.com/nextgen_media/assets/8078569-NG_AL1_J_03_U06_Quiz_01.png

The graph shows a car's value as a function of its age.

Select from the drop-down menus to correctly describe the graph.


The graph shows exponential __________. decay or growth

As the value of the car decreases, time ____________. increases or decreases

Answer 10

is the value of the car going up or down as the age increases?

Answer 11

UP

Answer 12

no down

Answer 13

good so it should be decay and decreases

Answer 14

https://static.k12.com/nextgen_media/assets/8078622-NG_AL1_J_03_U06_Quiz_06.png

The points on the curve represent the number of teams remaining in a tournament as a function of the number of games that have been played.

What is the number of teams who began the tournament?


Enter your answer in the box.

__________

Answer 15

hint: what is the number of teams when games played = 0

Answer 16

8

Answer 17

remember that games played is on the x-axis

Answer 18

4

Answer 19

each coordinate is (games played, teams remaining)

so what is the y-value when x = 0?

Answer 20

4

Answer 21

64

Answer 22

good, (0,64) means 64 games at the start so 64 = your answer

Answer 23

https://static.k12.com/nextgen_media/assets/8078571-NG_AL1_J_03_U06_Quiz_07.png

The graph shows the processing speeds of computers as a function of time since 1980.

Which statements are true about the function?

Select each correct answer.

The practical domain is x > 0 , so the processing speed increases over time.

The graph is ascending, indicating that the processing speed increases over time.

The practical range is y ≥ 16 , so the processing speeds are always positive.

The point (0, 16) represents an initial processing speed of 16 MHz.

The point (10, 256) represents the maximum processing speed.

Answer 24

well first off is the graph increasing or decreasing?

Answer 25

decreasing

Answer 26

increasing

Answer 27

good

since 0 is included in the domain, statement 1 is actually false since x > 0 excludes 0 from the domain

Answer 28

statement 2 we said was true (increasing graph)

Answer 29

for statement 3, the minimum y-value is 16 so statement 3 is true

Answer 30

1st one right and 2

Answer 31

wrong

Answer 32

statement 4 is true since this represents the speed when x = 0

Answer 33

statement 5 is false because the graph has no maximum (notice how the graph increases past (10,216)

Answer 34

https://static.k12.com/nextgen_media/assets/8078624-NG_AL1_J_03_U06_Quiz_12.png

After being dropped from a platform, a ball bounces several times. The graph shows the height of the ball after each bounce.

What does the end behavior for x increasing without bound represent?

A. The height of the platform is unknown.

B. The ball will never stop bouncing.

C. The end behavior for x decreasing without bound is meaningless in this situation.

D. The height of each bounce will approach 0 m.

Answer 35

as a hint, notice how the height gets closer and closer to 0 as the # of bounces increase

Answer 36

which answer choice matches this statement?

Answer 37

B

Answer 38

key phrase: "height gets closer to 0"

Answer 39

D

Answer 40

good, d

Answer 41

What is the recursive rule for an = 4n − 1?

A. a1 = 4;an = an−1 − 1

B. a1 = 3; an = an−1+ 4

C. a1= −1; an = an− 1 + 4

D. a1 = 3; an = an −1 −1

Answer 42

first step is to calculate a1 using n = 1

when n = 1, what does 4n - 1 equal?

Answer 43

3

Answer 44

good, now calculate 4n - 1 when n = 2

Answer 45

7

Answer 46

good, and if you continue this pattern, the term increases by 4 each time

making B the only answer that matches the initial term and rate of change

Answer 47

Haylee opened her savings account with $440 in Week 1. Each week after this, she deposited $65 in her account.

How much money will Haylee have in her savings account after Week 25?



Enter your answer in the box.

$__________

Answer 48

general formula for sequences

an = a1 + (n-1)d

a1 = first term
d = common difference
n = number of terms

Answer 49

in this case, 440 is the first term, d is the rate of increase (65)

Answer 50

so our formula becomes

an = 440 + (n-1)*65

let n = 25 and find an

Answer 51

5 • (13n + 75)

Answer 52

440 + (n-1)*65

replace "n" with "25" and calculate this

Answer 53

2000

Answer 54

good that's it.

Answer 55

What is the 8th term in the sequence?


an = 25 − 3n


Enter your answer in the box.

___________

Answer 56

my answer is 1

Answer 57

good that's it.

Answer 58

What is the explicit rule for the sequence?

15.5,13,10.5,8,5.5,3,...


A. an=18 − 2.5n

B. an=15.5 + 2.5n

C. an=15.5 − 2.5n

D. an=18 + 2.5n

Answer 59

MY ANSWER IS A

Answer 60

nvm that's right

Answer 61

What is the common difference, d, of the sequence?

−92, −74, −56, −38, −20, ...


Enter your answer in the box.

d = _____

Answer 62

my answer is 18

Answer 63

good

Answer 64

What is the value of a3 in the sequence?

2,5,10,17,...



A. 2

B. 5

C. 10

D. 17

Answer 65

MY ANSWER IS D

Answer 66

a3 means the third term

Answer 67

counting from the left, the third term is 10

Answer 68

really are you sure?

Answer 69

Which answer describes the type of sequence?


99,89.9,78.8,68.7,...

A. geometric

B. neither arithmetic nor geometric

C. arithmetic

Answer 70

my answer is B

Answer 71

good.

Answer 72

Which answer describes the type of sequence?

1,6,7,13,...

A. arithmetic

B. neither arithmetic nor geometric

C. geometric

Answer 73

is there a common difference or a common ratio?

Answer 74

common ratio

Answer 75

is 13/7 equal to 7/6?

Answer 76

no

Answer 77

good so there must be no common ratio making the sequence not geometric and not arithmetic

Answer 78

so B

Answer 79

Which answer describes the type of sequence?

3,4,5,6,...

A. arithmetic

B. neither arithmetic nor geometric

C. geometric

Answer 80

is there a common difference or ratio?

Answer 81

common difference

Answer 82

good so arithmetic (A)

Answer 83

What is the value of a1 in the sequence?

−4,−2,− 1/2,− 1/4,...



A. ​ −1/4

B. ​ −1/2 ​

C. −4

D. ​ −2 ​

Answer 84

what's the first number in the sequence?

Answer 85

C

Answer 86

good

Answer 87

What is the explicit rule for this geometric sequence?

2/9, 2/3, 2, 6,...



A. an = 3(2/9)^n

B. an = 3(29)^n−1

C. an = 2/9 ⋅ 3^n

D. an = 2/9 ⋅ 3^n−1

Answer 88

in this case your first term is (2/9) and the common ratio is 3

Answer 89

substitute these values into the formula and pick the answer that matches

Answer 90

the answer is B and C

Answer 91

there is only one correct answer

Answer 92

a = (2/9) and r = 3

which answer choice matches the correct formula?

Answer 93

D

Answer 94

good.

Answer 95

What is the recursive rule for this geometric sequence?

3, 3/2, 3/4, 3/8,...

A. a1 = 3; an =1/2 ⋅ an−1

B. a1 = 3/2;an = 1/2 ⋅ an−1

C. a1 = 1/2; an = 3/2 ⋅ an−1

D. a1 = 1/2; an = 3 ⋅ an−1

Answer 96

the first term (a1) is 3 so there is only one answer choice that matches

Answer 97

A

Answer 98

good

Answer 99

What is the explicit rule for this geometric sequence?

a1 = 4; an = 1/3 ⋅ an−1



A. an = 1/3 ⋅ 4n

B. an = 1/3 ⋅ 4n−1

C. an = 4(1/3)n−1

D. an = 4(1/3)n

Answer 100

first term is 4, common ratio is (1/3) so using the formula from earlier find the explicit formula

Answer 101

B

Answer 102

hint: the common ratio is the part that gets raised to the n - 1power

Answer 103

the first term is on the left of the formula

Answer 104

D

Answer 105

the exponent is n - 1 not just n

Answer 106

c

Answer 107

good, c.

Answer 108

use the geometric formula where first term = 100 and common ratio = 11/2, for n = 5

Answer 109

A company earns a profit of $100 the first month it is in business. Every month after that, the company earns a profit that is 1 1/2 times the previous month's profit.

What will the company's profit be in the fifth month?

Answer 110

sorry typ

Answer 111

my answer is $506.25

Answer 112

good.

Answer 113

What is the common ratio for the geometric sequence?

54,36,24,16...



Enter your answer in the box.

___________

Answer 114

just divide the 2nd term by the first term

Answer 115

36/54 and reduce to the lowest terms

Answer 116

2
— = 0.66667
3

Answer 117

good, if you can enter it as 2/3 I would recommend that

otherwise I guess you could round to 0.6667 or whatever

Answer 118

the answer is 3/2

Answer 119

correct ?

Answer 120

it is 2/3

Answer 121

What is the recursive rule for this geometric sequence?

7, 21, 63, 189, …



A. a1 = 7; an = 3 ⋅ an−1

B. a1 = 3; an = 7 ⋅ an−1

C. a1 = 7;an = 1/3 ⋅ an−1

D. a1 = 21;an= 7 ⋅ an−1

Answer 122

hint - what's the common ratio? what's the first term?

Answer 123

7

Answer 124

good, first term is 7 and what is the common ratio?

Answer 125

21

Answer 126

to find the common ratio divide the 2nd term by the 1st term

Answer 127

21/7 = ?

Answer 128

3

Answer 129

3

Answer 130

3

Answer 131

good, so pick the answer choice where a1 = first term = 7 and an = common ratio * a^(n-1)

Answer 132

D

Answer 133

a1 must be 7 not 21.

Answer 134

C

Answer 135

the common ratio is 3 not 1/3

Answer 136

A

Answer 137

good.

Answer 138

can we close this and open a new question, it's getting laggy

Answer 139

YES