CPhill

(x + 1)^2  = √(5/4)     take the square root of both sides.....remember that, on the right side, we have to take both roots.....so we have....

x + 1 = ±√(√(5/4)   which we can simplify to....

x + 1 =  ± ⁴√(5/4)      subtract 1 from both sides

x = -1 ± ⁴√(5/4) 

I think that the problem is supposed to say that "square of the difference of the 4th and the 1st term is 225"  rather than 255......when I tried 255 I get a strange square root which doesn't allow for any "integer" answers [If I didn't make a mistake, that is !!!!].....I'm working this one assuming 225 is correct...

The first term is just a1

Let the 4th  term be given by:

a4 = a1 + d(4 -1)   =  a1 + 3d

And the difference between the 4th and 1st terms is just 3d

And the square of this difference  = 225

So  (3d)^2  = 225 →  9d^2 = 225  →  d^2  = 225/9  →   d =  15/3   so d =5 [since all the terms are positive]

And we're told that    [ (a1 + d(7) ) - (a1 + d(3)) ] / [a1 + d (14) ]  = 4/15  simplify   

[d(7) - d(3)] /[ a1 + d(14)] = 4/15   and sustituting 5  for d we have

[5(7) - 5(3)] /[ a1 + 5(14)] = 4/15

5*4  = [4/15]  (a1 + (5)*14)     multiply through by 15

5*4*15 = 4[a1 + 70]

300 = 4a1 + 280

20 = 4(a1)

So a1  = 5

So

2015 = 5 + 5(n -1)

2010 = 5(n -1)

402 = n - 1    add 1 to both sides

403    which is answer "3"

6x^2−102x+432=0 .....  factor out the 6, first

6 (x^2 - 17x + 72) = 0   divide both sides by 6

x^2 - 17x + 72 = 0      factor, again

(x - 9) (x - 8)  = 0    and setting each factor to 0, x =8  or x = 9

Depends upon the pocket.....!!!

Just divide both sides by 1.03......

x = 600/1.03  =  ????

[3/4 x 2/3 - (1/2-1/3)] *12     perform the multiplication in the brackets, first

[ 1/2 - (1/2 - 1/3)]  *12       perform the subtraction inside the parentheses  inside the brackets

[ 1/2 - (1/6)] * 12         subtract inside the brackets, again

[1/3] *12   multiply

4

See what i just did, here : 

(-2,1) and (4,5)....let's get the slope, first

First, subtract the y coordinates in any order  [ 5 - 1]  = 4

Next, subtract the x coordinates in the same order  [4 - (-2)]  = [4 + 2] = 6

Put the first thing over the second → 4/6  = 2/3    and this is the slope

Now....just choose  one point [I'll use (4,5)]    and set up the following "formula".....

y - [y coordinate of our point] - (slope)* [ x - ( the  x coordinate of our point)]

Let's fill in the "blanks"

y - 5  = (2/3)(x - 4)      add 5 to both sides

y = (2/3)(x - 4) + 5   and this is the equation of the line in "slope-intercept" form

9/16  = .5625