CPhill

(-9 1/4, -7 1/2), (-4, 5)

First, let's simplify the fractions by getting one common denominator  = 4

-[9 + 1/4]  = -[ 37/4]

-[7 + 1/2]  = -[ 15/2]  = -[30/4]

 5  = 20/4

-4  = -16/4

So  we would have

( -37/4, -30/4) , ( -16/4, 20/4)

sqrt  [  ( -37/4 -  - 16 /4)^2  + ( -30/4 - 20/4)^2  ]  =

sqrt [ ( -21/4)^2  + (-50/4)^2 ]  =

sqrt [ 441/16 + 2500/16 ] =

sqrt [ 2941/16]       we can split this up as :

sqrt [2941] / sqrt [16]  =

sqrt [2941] / 4  =

about 13.56  units

sqrt(54)/6  + 2/3   =

[3*sqrt(6)] / 6  + 4/6  =

[ 3*sqrt(6) + 4 ] / 6

Capital "P"

Since BC meets AB at right angles, the slope of BC would be the negative reciprocal of that of AB.

The slope of AB =  [0- -2] / [ -3 - 3] = 2/-6   = -1/3

So...the slope of BC   = 3

We are looking for the measure of an angle - in this case, y -  whose sine = 2/3......so we have

arcsin(2/3)  = y  = about  41.81°

f(x) = −3 cos(4x + π) + 6

Rewrite as

f(x)  = -3 cos4(x + pi/4) + 6

The amplitude is  l -3 l   = 3

The period - call it, m -  is found by solving this: 

4m = 2pi     divide both sides by 4   m = pi/2

The phase shift is pi/4 units to the left

Here's the graph :  https://www.desmos.com/calculator/1slz9abnpw

We can't give any hard and fast rules, here.....for example :

20  = 3x + 5

We would subtract the 5 and divide by 3 to find x

However

20 = 3(x + 5)

We would divide by 3  and then subtract 5 to find x

So....it depends upon what you are given as to the order of operations.......

A 20% discount means that the volleyball just sold for 80% of its normal cost....so

35 * .80   = $28          [the discount was $7 ]

30 * 25.98   = 779.4     [ no rounding necessary ]

I think that we're trying to solve for "x" here and m is denoting meters....so we have

91 = (2x+3)(x+2)    simplify on the right

91  =  2x^2 + 3x + 4x + 6    

91 = 2x^2 + 7x + 6     subtract 91 from both sides

2x^2 + 7x - 85  =  0    factor

(2x + 17) (x - 5)   = 0 

Set each factor to 0 

2x + 17 = 0                                          x -  5   =  0

subtract `17 from both sides            add 5 to both sides

2x = -17                                               x  = 5

divide both sides by 2                     

x = -17/2

So...the solutions are  x = -17/2   or  x = 5