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Thank you I get it now.

Thank you

Good job, CalculatorUser....!!!!

Remember GM....if x - 4 is a factor then 4 is a root

This is where the Remainder Theorem comes in handy

So....if  4 is a root....then  putting 4 into the function will return 0....so....

(4)^2 +  k(4) - 52 = 0   simplify

16  + 4k   - 52 = 0

-36 + 4k = 0      add 36 to both sides

4k =  36           divide both sides by 4

k = 9

So....we have    x^2 + 9x - 52

Notice that this factors  as  ( x - 4) (x + 13)

Note that (x - 4) is a factor

Thank you for going indepth about how I would go so forth in solving. I was confused about it but with your explaination t\it all makes sense now thank you!

Thank you!

1. First add 5 to both sides

\(x^2-11x+19+5=-5+(5)\)

So you get \(x^2-11x+24=0\)

2. Then factor

Since 3 and 8 add up to 11 and they multiply to 24. The factored version of the left side of the equation is \((x-3)(x-8)=0\)

3. Solve

You multiply each side by (x-3) or (x-8) to get \(\boxed{x=3, x=8}\)

....and now I learned another graphing tool/ method in Desmos ....Thanx  Chris !

I did it way different than you. Idek how to do it the way you did

g(x) =  -2x ,  x ≥3

Let's just pick two x values ≥ 3   and stick them into the function

When x = 3,  y = -6.....so....(3, -6) is on the graph

When x = 4, y = -8.....so.....(4, -8) is on the graph

Plot  (3, -6)

Then...plot (4, -8).....draw a ray startting at (3, 6) and extend it through (4, -8)

g(x) = -(1/3)X - 5,  x ≤3

Again..let's pick x = 3   and put it into the function....and we have (-1/3)(3) - 5 = -1 - 5  = -6

So....the point (3, -6) is on the graph

Now.....pick anoher x value < 3.......0 is good

So   (-1/3)(0) - 5 =  -5

So (0, -5) is on this graph

Draw a ray from (-3, 6) through (0, -5)

The graph will look like this :

Of course...the lines (rays) will have "arrows" at their ends  

That is a graph of y= cos x         at 0 it is equal to one.....it is sinusoidal and the period is 2pi  (it appears)

So basically you are trying to find $60.00 plus 50% of $60.00 again because you are trying to find the total cost of 2 tickets with the deal.

50% is 1/2 off....

so 1 ticket costs 60  and the next one costs 30 for a total of $90

SInce they are lines , you only need two points to draw each one....just make sure ONE of the points for both lines is the common point

3,-6

$15 x 40  x   1.10 = $660 /wk

C  1 and III  only

they both look like sine waves don't they?   Yah......

wouldnt it be marked as incorrect if I do need plot all the points? 

What do you want to do with that?  

Then just plot the whole numbers in the list.....and connect the dots as I explained....the lines will be the same....GLuck !

The dowel will be the hypotenuse of a right triangle with legs 180 and 195 mm

d^2 = 180^2 + 195^2        d = 265.38   is the amount of dowel in the paint     remainder out of the paint

    is equal to  270 - 265.38 =4.62 mm

the points without whole numbers I cannot graph . this is the only space I have it doesnt let me choose middle points.

40 -10 = 30 dollars      now he gets a 20% discount form 30 dollars

30 - .2(30) = $24    Final price

that is 16 dollars off full price     16/40 x 100% = 40% off

The shoes have an original price of $40 but are $10 off, this means that the sale this week is $30.

An additional 20% off means that it is basically 80% of the shoe being sold this week. So \(30*\frac{8}{10} = 24\)

Since the shoes he is going to buy are $24 dollars out of the $40 original price. The price dropped $16.

What percent of 40 is 16? You can convert it into a fraction by dividing 16 by 40. So \(\frac{16}{40} = \frac{4}{10}\)

Since \(\frac{4}{10}\) is easily recognized as 40%. The total percent discount is 40%