CPhill

x =  cost for lb of  beans

y =cost  for lb of peppers

3x  +  2y =  7.05        multiply through by  3  ⇒  9x + 6y  =  21.15

4x  +   3y =  9.83      multiply through by  -2  ⇒ -8x  - 6y  = -19.66     add  these and we have

x = 1.49    

And

3(1.49)  + 2y = 7.05

4.47 + 2y  = 7.05

2y = 7.05  - 4.47

2y = 2.58  divide  each side by 2

y = 1.29

Yep.....always true

B =  2pi  / period     

First one....the  scale  factor  for  the dilation can be found  by a comparison of any similar sides....so, for instance:

C'E'  / CE  = 2.5 / 5   =    1/2

We  have  this form :

y = A cos (Bx)  +  C

A  = the amplitude  = 5

B =   2pi / period =      2pi  [ (6/5) pi ]  =  2 / (6/5)   =    2 (5/6)  =  10/6 =   5/3

C   = the vertical  shift   =   -6

If each cat  eats  1/4  of a tin per day.....then in one day  they  eat  1/4 + 1/4  =  1/2  of a tin per day

So.....the  number of days  that 9 tins will last  is

9 / (1/2)   =

9 * (2/1)   =   

9 * 2   =

18 days

Look  at    f(x)

Note  that this  is a line with a y intercept  of  -3

Thus....the second graph MUST be  the correct  one

The   x values that  make f(x)  = g(x)   are at  x   = 0    and  x  = 3

The  factors of  10  are  the integers  that divide 10......these  are  2  and  5

  sec A  =  r / x

We  can  find  r  as   √ [ (-6)^2  + (3)^2  ] =  √  [36 + 9]  =  √ 45  =  √ [9 * 5 ] = 3√ 5

So

sec A  =  3√ 5 / -6  =   √ 5 / -2   =  -√ 5  /  2

f(x)  is a parbola   that opens downward......

g(x)  is  the square root graph   shifted  down  one unit

The second graph is therefore correct

The  x  where f(x)  =g(x)   occurs at  x  =  4 

See here  :

https://web2.0calc.com/questions/a-good-math-question