CPhill

The third one is correct.....

−3.5(3)^2 − 0.5(3) + 65  =  32 in

For the second one, we need to replace t  with 8   [ 2018 is 8 years after 2010 ]

1.65(8)^2 + 18.25(8) + 155  = 406.6   =  $407,000

"A" is correct....

"B"  is the correct answer.....

[  Generated from this website  : http://keisan.casio.com/exec/system/14059932254941 ]

Halving the string length doubles the frequency and vice-versa....

So....doubling the string length halves the frequency....so....the new frequency is

220 Hz

"B"  is the correct  answer

2.

x - y = 10       multiply through by 2  ⇒  2x  - 2y  =  20   (1) 

5x + 2y = 12    (2)

Add  (1)  and (2)

7x  =  32      divide both sides by  7

x  =  32 / 7

Using  (1)  to solve for  y

(32/7)  -  y  =  10         multiply through by 7

32 - 7y  =   70             subtract 32  from both sides

-7y  =  38                   divide both sides by  -7

y  = -38/7

3.

5/2x + 2y = -2   multiply through by 2 to clear the fraction ⇒  5x + 4y  = -4  (1)

-x + y = 2   multiply through by  5  ⇒  -5x + 5y  = 10  (2)

Add  (1) and (2)

9y  =  6      divide through by  9

y  =  6/9  =  2/3

Put this into     -x  + y  =  2

-x +  (2/3)  = 2      subtract  2/3 from both sides

-x  =  2 - 2/3   =  4/3        

-x  =  4/3

x  =  -4/3

I count 9

BTW  ....

There is actually a   formula for the total number of rectangles  [ including squares ] on a N x N   grid  :

[ Here......"grid" refers to  N squares by N squares...so....using this definition, you have a 2 x 2 grid ] 

(N)^2  ( N + 1)^2   /  4   =    (2)^2 * (3)^2  / 4  =   4 * 9  /  4   =   36 / 4    =   9   

EDIT......as hectictar points out....there is also an additional square created by connecting the "mid-point"   vertices of each side....so.....the correct answer seems to be 10....!!!!!

The stuff in red goes into each respective blank

 Whole

 Note, werty.....that the second blank can be interpreted like this :

A /  [ pi r^2 ]   =   θ / [ 2pi ]           [ multiply both sides by pi r^2  ]

A  =  [ θ / 2 ]  r^2  =    (1/2)r^2 θ

The linear combination method is also known as the "addition" method

1.    We can pick either variable to eliminate....I'll pick  y

4x + y = 4      (1)

2x + y =  6     multiply this through by  -1   ⇒  -2x  -  y  =  -6     (2)

Add (1)  and (2)

2x   =  - 2         divide both sides by  2

x  =  -1

And using  (1)  to solve for  y  we have

4(-1)  + y  = 4

-4 +  y   =  4       add 4 to both sides

y  =  8