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duck  =  2 legs  =  (1)(9)  = $9

spider  = 8 legs  =  (4)(9) = $36

bee = 6 legs  = (3) (9)  = $27

Each pair of legs is worth $9

So....a cat would get   2(9)  =  $18

A cat will go after ducks, spiders, and bees so it receives $72.

We can use the concept of Egyptian Fractions to solve this

6/7    divide  7/6  and take the ceiling of this result  =  2

Take the reciprocal of this  =   1/2

So 

6/7  =  1/2 +  remainder

6/7 - 1/2  =  remainder

12/14 - 7/14  =  

5/14  = remainder

divide 14/5  and take the ceiling of this  = 3

Take the reciprocal of this   =1/3

So

6/7  =  1/2  + 1/3  + remainder

6/7  =  5/6 + remainder

6/7 - 5/6  = remainder

36 / 42  - 35/42  = remainder

1/42  =  remainder

So

6/7  =  1/2  + 1/3  + 1/42

a          b         c
42         3        2
3          42       2
42         2        3
2          42       3
3          2        42
2          3        42
a + b + c =42 + 3 + 2 = 47

Look at this similar problem for help with this one https://www.quora.com/If-1-a-1-b-1-c-1-then-what-is-the-value-of-a-b-and-c

I believe it is -1.

Let  the  distance from the apartment bldg.  to the car park  =  x

Let the distance from the car park to the office  =  42-x

Since they take the same amount of time we have that

x / 60 + (42 - x) / 4  =  x/ 40 + (42 - x) / 12    simplify

[4x + 60(42 - x)]  / 240  = [12x + 40(42 - x) ] / 480

[4x + 2520 - 60x ] / 240  =  [12x + 1680 - 40x ] / 480

[ 2520 - 56x] / 240  =  [ 1680 - 28x] / 480

[2520 - 56x] / 240  =  [ 840 - 14x ] / 240

2520 - 56x  =  840 - 14x

1680  =  42x

x =  1680 / 42   = 40

So....the total time  (in hours)  =   

40/60  + (42 - 40) / 4  =

2/3 hrs   +  2/4  hrs  =

2/3 hrs  + 1/2  hrs  =

40 mi + 30 min  =

70 min  =   

7:10AM

I don't exactly understand how this is geometry, but 2+2-2 = 2.

Factoring 1763 we get that that equals 41*43. Hence, the two positive integers are 41 and 43.

https://math.stackexchange.com/questions/829831/find-the-number-of-2-element-subsets-a-b-of-1-cdots-1000-such-tha 

Use this link as reference

Your answer is correct.....the total distance traveled can be deduced from the area of the triangle  formed by the graph

The  base   =  7      

The height   =  4

The area  = The distance traveled  (1/2) (base) (height)   =  (1/2) (7) (4)  =  (1/2)(28)  =  14 m

I don't exactly understand what you need help with here. However, I believe that your answer in the box is correct.

Yes....you are correct   !!!!

I missed that

Maybe  this graph will  help  :  https://www.desmos.com/calculator/wisoaf84zp

It might benefit you to learn about the quadratic equation as well. It is (-b +- √b^2 - 4ac)/(2a). It is commonly used to solve quadratic equations of form ax^2 + bx + c. There are also many other ways to solve, such as completing the square. I'd recommend learning about them, they are very interesting!

THX, ThatOnePerson   !!!!

Apparently 4 is a possible solution as well, according to WolframAlpha. However, I have no idea how to solve it.

2^x  = x^2          take the log of each side

log 2^x  = log x^2      and we can write

x log 2  =  2 log x

Rearrange as

x / log x   =  2 / log 2

And it must be that  x   =   2

First, we add the first and third equations to get -x+3z=8. Then, we multiply the first equation by two and add the third equation to that to get 3y+5z=9. Then, we subtract that from the second equation to get -3x-2y=1. Then, we add the first equation to the second and subtract the third equation from that to get 7y+6z=4. This means that we now have the equations

-x+3z=8

3y+5z=9

-3x-2y=1

7y+6z=4

Looking at the second and fourth equations, we find that y = -2 and that z = 3. Solving for x, we find that x = 1. I'll leave the checking up to you.

You are correct  !!!!

x + 3y + 2z  =  1

-3x + y + 5z  =  10

-2x - 3y + z  =  7

Add  the first and third equations ⇒   -x + 3z  =  8   

Multiply this by 10   ⇒  -10x + 30z  =  80     (4) 

Multiply the second equation by  -3  ⇒   9x -3y  - 15z  = -30

Add this to the first equation ⇒    10x  -13z = -29    (5)

Add (4)  and (5)   ⇒  17z  =  51

Divide both sides by  17

z  =  3

And 

-x + 3(3)  =  8

-x  +  9  = 8

-x  = -1

x  = 1

And

1 + 3y + 2(3)  = 1

1 + 3y + 6  = 1

3y + 6  = 0

3y  = 6

y = - 2

So

{x, y, z}   =  { 1, - 2, 3 }

An archaeology club has 28 members. How many different ways can the club select a​ president, vice​ president, treasurer, and​ secretary?   

Another way to look at it is that there are 28 members who could be chosen for president.        28                 =  28

That leaves 27 members remaining from which to choose the vice president.                             27 x 28         =  756

That leaves 26 members remaining from which to choose the treasurer.                                     26 x 756       =  19,656

And finally, there are 25 members left from which to choose the secretary.                                  25 x 19,656  =  491,400

.

I'm not sure what "slates of candidates" means, but I think this is just 28 choose 4 = 20475.

Let the distance from their apartment to the car Park =D
It takes Betty: D / 60 hours. 
It takes Carl: D / 40  hours.
The distance from the car Park to the office =42 - D
The time it takes Betty to get to the office =42 - D / 4
The times it takes Carl to get to the office =42 - D/12
(42 - D) / 4 + D / 60 = (42 - D) / 12 + D/ 40, solve for D
D = 40 km. Sub this into Betty's time:
(42 - 40) / 4 + 40 / 60 = 7/6 hours, or 70 minutes to get to the office. 6 am + 70 minutes =7:10 am - when both arrive at the office.

Nah sorry. i checked and it was wrong. apparently the answer is 1. thank you though

I think the answer is 1/2.