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this the one you cant read 

We have a slope (2) and a point (1, 0)

We could use something known as the point - slope equation to get to the slope-intercept form, but here's a faster way. Note that, if the slope is 2, this means that everytime x changes by a positive 1, y changes by a positive 2. And everytime x changes by a negative 1, y changes by a negative 2. So, when x changes from 1 to 0, it changes by a negative 1, so y changes by negative 2.... from 0 to -2. So (0, -2) is on the graph...so the y intercept is at -2.

So......the slope intercept form  is given by:

y = mx + b     where m is the slope and b is the y intercept.   So we have

y = 2x - 2     and that's slope-intercept form

To get standard form, get x and y on one side of the equation and the constant on the other

So we have   (noting that y  = 1y)

 y = 2x - 2   or  1y = 2x - 2           subtract 1y from both sides  and add 2 to both sides....so we have,,,

2 = 2x - 1y     or      2x - 1y = 2       and that's standard form

Alan I don't understand  " b " 

Don't forget the minus sign!

Here's another way to do (a)

lim x → 0⁺  √[1 - cos(x)] / x        multiply top and bottom by √[1 + cos(x)]   so we have

lim x → 0⁺  √[1 - cos^2(x)] /[ (x) √[1 + cos(x)]    =

lim x → 0⁺  sin(x) /[ (x) √[(1 + cos(x)]  =

lim x → 0⁺  [sin(x) / (x)] * [1/ √[1 + cos(x)]      and, using an identity...... lim x → 0⁺  [sin(x) / (x)]  = 1

So we have

lim x → 0⁺  [1/ √[1 + cos(x)]       and taking the limit, we have

[1/ √[1 + 1]  =  1 / √2

0.002 is the answer.

a.  The x intercept is the value of x at which y = 0.   2x - 3*0 = -6, x=-3

b. The y intercept is the value of y at which x = 0.  2*0 - 3y = -6,  y = 2.

The equation can be rewritten as y = (2/3)x + 2

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Is this just a random blurt out?

It can be confusing, but you honestly just need to study

2.5 can be written as 2 1/2 or 2 5/10

Couldn't read your third one, but the first two are:

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4k² - 8 = 4k - 8

k² = k

k = 0 or k = 1

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Suppose he was going to paint each of rooms A, B and C a different colour.

1. If he decided that A= red, B=blue and C= green was a different combination from A=blue, B=green and C=red, then there would be smile478's 6840 possibilities.

2. However, the way the question is phrased, it sounds more like he would count these as the same combination of colours, in which case there would only be Chris's 1140 possibilities.

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Press the 2nd button, then choose asin

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If you really meant 2*7<18 then, as a Boolean expression, it is true.

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You got as far as a|6 - b| = 0.  This must mean that either a = 0 or b = 6.

If a = 0 then the function would reduce to f(x) = -1, a constant.  Since f(x) clearly isn't a constant we can't have a = 0, so we must have b = 6.

So the function is f(x) = a|x - 6| - 1

Use the point (0, 11) to find a.

11 = a*|0 - 6| - 1

11 = a*6 - 1

12 = a*6

a = 2

Finally,

f(x) = 2|x - 6| - 1

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Just use the on site calculator....it will give you the decimal equivalent....

23% = .23      "of" means multiply.....so.....

.23 x $20 = $4.60

I surely did understand it. Thank you both. 

As for anonymous. My name is Kim and I'm not good at math. 

We have 20 colors and we want to choose 3 of them....so we have

C(20, 3) = 1140 combinations

@smile478, It's ok.

@CPhill. Yes it does help! Thank you!

thank you melody 

6840.  20*19*18=6840