ElectricPavlov

....as a further interpretation of the cost line   When x= 0  (this is when you have produced 0 cupcakes) your start-up, or fixed cost are $36  (the y-axis intercept)

The slope is defined as  how much the graph rises over how much the graph 'runs' horizontally

rise / run  = slope       if you graphed this line and looked at an x point then went 10 points to the right, you would see the graph would go up 9  units higher......

This tells you that to produce 10 more cupcakes....it costs 9 more dollars.

DO the stuff in parentheses first then the exponents then the multiplication then the addition or subtraction.

 3(-3)^2-5(-3-2)^2

=3(9) - 5(-5)^2

=27 - 5 (25)

=27-125

= -98

Equation for a line is  y = mx + b  where  m = slope  and  b = y-axis intercept

You are given two points on the line    100, 126        and     120, 144

Slope =  (y1-y2) / (x1-x2) ====   rise/run  =====    (126-144)/(100-120) =  -18/-20  = 9/10 = slope

so, so far    y = 9/10 x + b   

Substitute in either one of the points to calculate 'b'

126 = 9/10 ( 100)  +  b

126 = 90 + b

b = 36  = y- axis intercept                                    y= 9/10  x    +   36     is your line        

I agree with Melody ....Mostly....

y = mx + b   is the equation of a line with slope  m   and  y-axis intercept   b

you are given 'm' = 0.5     so your line equation becomes   y = .5 x + b

you are given the 'x' axis intercept....(this is where y = 0) as  28, 0   so substitute this value into your equation to find 'b'

y = .5x + b

0 = .5 (28 ) + b

-14 = b    

so your line equation becomes:

y = 0.5 x - 14   

.9775^2 = .9555      

\(\sqrt{.9555}\)   would be another way

As Guest 1 pointed out   .9775 = 391/400

so radical form of .9775  would be   \(\sqrt{(391/400)^2}\) =      \( \sqrt{152881/160000}\)

3/5  x ( - 15/1)  =   -45/5 = -9

Often unclear what is being asked :

(-2)^2  = -2 x -2 = 4

-(2^2)  = -(2 x 2) = -4

A nanometer is 1 x 10^(-9) meter (one billionth)

it is 1 x 10^(-12) of a kilometer

(1 x 10^(-12)  )^2   = 1 x 10^(-24) sq km

3  2/3     or   11/3