Question

What number can you add to 2√ to get a rational number?

A. 2

B. −√2

C. 1/2

D. 0

Answer 1

is it supposed to be √2?

Answer 2

yes

Answer 3

hint: go through the options one by one to see which one can be added to get something rational

Answer 4

is 2 + √2 rational?

Answer 5

2 is rational

the second is not

third is rational

4th is rational

Answer 6

2 + √2 isn't rational so can't be that

Answer 7

mike I think you might have mixed up rational/irrational

any final answer that has root(2) can't be rational since root(2) itself is not rational

Answer 8

which answer choice doesn't lead to having root(2) in the final answer?

Answer 9

1/2

Answer 10

is 1/2 + root(2) rational? keep in mind what I said about having root(2) in the final answer

Answer 11

yes it is rational

Answer 12

the answer is B

Answer 13

good, B, because root(2) - root(2) = 0 which eliminates root(2)

Answer 14

every other answer choice gives you a final answer with root(2) in it so the others aren't rational

Answer 15

YES THAT'S RIGHT

Answer 16

Which equations model exponential decay?

Select each correct answer.

y=0.55(0.91)^x

y=4.2(1.25)^x ​

y=0.25(2)^x ​ ​

y=2(0.20)^x ​

Answer 17

*** sorry made a typo

Answer 18

C and B

Answer 19

or A and D

Answer 20

*** pick each answer with a number ~less~ than one inside the parentheses

Answer 21

A and D is correct

Answer 22

REALLY ?

Answer 23

yes

Answer 24

Select "Growth" or "Decay" to classify each function.

Function Growth Decay
y=200(0.5)^2t
y=1/2(2.5)^t/6
y=(0.65)^t/4

Answer 25

growth - number inside parenths is greater than 1
decay - number inside parenths is less than 1

Answer 26

1 is the decay

2. is the growth

3. is the decay

Answer 27

awesome

Answer 28

really ?

Answer 29

Does each function describe exponential growth or decay?

Drag and drop the equations into the boxes to correctly complete the table.

Growth Decay


y = (1.008^1/2)^12t

y = 250(1 + 0.004)^t

y = ((1 - 0.002)^1/56)^56t

y = 426(0.98)^t

y = 12,000(1/2)^t

Answer 30

same principle as before

Answer 31

make sure you evaluate what's inside the parentheses before making your classification

Answer 32

the first is growth

the second is growth

the third is decay

the fourth is growth

the fourth is decay

Answer 33

correct me if i'm wrong

Answer 34

check #4 again

Answer 35

growth

Answer 36

good the other ones are fine too

Answer 37

so they are all correct ?

Answer 38

yup

Answer 39

The total amount of money in a savings account after t years is given by the function A=1000(1.023)t .

How could this function be rewritten to identify the monthly interest rate?

What is the approximate monthly interest rate?



Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table.

Function Monthly interest rate

A = 1000(1 + 0.023)^12t

A = 1000(1.023^12)^t/12

A = 1000(1.023^t/12)^12t

0.23%

0.19%

0.31%

Answer 40

I'm not sure about this one

Answer 41

it's to place these numbers and putting them where to go

Answer 42

I am not sure how to solve this one

Answer 43

Why is the product of two rational numbers always rational?

Select from the drop-down menus to correctly complete the proof.


Let a/b and c/d represent two rational numbers. This means a, b, c, and d are ________, and ________ . The sum of the numbers is ad+bc/bd , where bd is not 0. Because integers are closed under _________, ​the sum is the ratio of two integers, making it a rational number.

Choices

the first one: integers, irrational number

the second one: b is not 0, d is not 0, b and d are 0

the third one: addition and multiplication, addition and division

Answer 44

uh

Answer 45

if a/b and c/d are rational then a, b, c and d are all ratonal

Answer 46

I don't think we can conclude that they are integers though

Answer 47

for the second blank, the denominators b and d can't be zero (otherwise it would be undefined)

Answer 48

third blank... probably addition since we're talking about sums

Answer 49

addition and division or multiplication ?

Answer 50

the first one is irrational or integers ?

Answer 51

second: is or isn't ?

Answer 52

I guess the first blank would be "integers"

Answer 53

(I don't agree but it's the better of the two options)

Answer 54

for the second blank please read what I wrote

the denominators cannot be zero so what must be true?

Answer 55

so it isn't

Answer 56

b and d cannot be 0

Answer 57

it's not

Answer 58

good

Answer 59

and the third

Answer 60

multiplication and addition (division is not closed)

Answer 61

32√⋅28√⋅3√⋅6√ multiply

Answer 62

i had 72 square root of 2

Answer 63

is it right ?

Answer 64

that's not what I got

Answer 65

is the 32 supposed to be out in front of the other numbers?

Answer 66

are all the numbers within the root symbols?

Answer 67

no wait

Answer 68

you can use the equation tool at the bottom of the screen to draw it exactly as it appears

Answer 69

3√2 ⋅ 2√8 ⋅ √3 ⋅ √6

Answer 70

there

Answer 71

yeah your answer is right, 72 root 2

Answer 72

ok