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That's great! If you still have any questions, feel free to still ask.

- Daisy

I found a video on how to do it thanks for the help

No problem! 

- Daisy 

ok thanks for the tip 

Hi Guest, I think it is better if you look up your question online. Depending on your actual equation, there will be examples that might help. 

- Daisy

\( 3x - 7≤5x + 9\) is our equation, and we want to move all the variables to one side. We can simplify the equation to  \( -2x ≤ 16\). Then, we need to divide each side by \(-2\). Since we are dividing/multiplying the equation by a negative number, we need to flip the sign. By doing this, we get \(x ≥ -8\). Since the problem is asking for an interval, we can get \([-8, +∞]\). Please correct me if I made a mistake!

- Daisy

Bringing x, and the numbers to one side, we get: \(-7-9\leq5x-3x=-16\leq2x\), so x is greater than or equal to -8. Try to see how you can form an interval.

[-8, infinity)

We have \({a}^{2} - {b}^{2} = 8\), which we can square both sides to get \(a^4 + b^4 - 2a^2b^2 = 8^2\). Since \(ab = 2\), we can square both sides again to get \(a^2b^2 = 2^2\). Then, we can subsitute that value into the equation; \(a^4 + b^4 - 2(4) = 8^2\) -> \(a^4 + b^4 - 8 = 64\) -> \(a^4 + b^4 = 72\).

- Daisy

5x + 8y  = -9

In the form  ax + by  = c, the slope of this line  is   -a/b = -5/8

So...a perpendicular line will have a negative reciprocal slope  = - (-8/5)  = 8/5

So......the equation of a line with  a slope of  8/5  passing through (10,10) is

y =(8/5)(x - 10) + 10

y  =(8/5)x - 16 + 10

y = (8/5)x  -  6

So.....m =  8/5    and   b   = -6  =  -30/5

So....m + b   =     8/5  - 30/5  =    -22/5

Maybe an easier way.....but.....

A  = (0, 4)

F = (3, 0)

slope of AF = -4/3

equation of line containing AF    ....   y  = (-4/3)x + 4

E  = ( 0, 2)

B = (7,0)

slope of EB  = -2/7

equation of line containing EB  ...  y = (-2/7)x + 2

Find the x coordinate of D by setting these two functions equal

(-4/3)x + 4  = (-2/7)x + 2

4 - 2 = (-2/7  + 4/3)x

2  = [-6 + 28] /21 x

2 = [22/21]x

42/22   =x

21/11   = x

And the associated y coordinate  is  (-2/7)(21/11) + 2  = 16/11

So  D  = (21/11 , 16,11)

And the equation of the line joining AB  is  y  =   (-4/7)x + 4

Write this is standard form  ....   4x + 7y  - 28   =   0

Now...using the  equation to find the distance from  a point to a line we can find the altitude of triangle ABD

l   4(21/11) + 7(16/11)  - 28  l                   l  -112/11 l              112/11

_______________________   =           __________  =        _____

     √[ 4^2 + 7^2 ]                                         √65                       √65

And considering AB to be the base, its length is  √ [4^2  + 7^2]  = √65

So...the area  of triangle ABD  =  (1/2) √65  * (112/11) / √65  =

(1/2) (112 / 11)  =

112 /22  =

56 /21  units^2

As tertre and Melody said, this will be undefined whenever the denominator   = 0

And the denominator factors as ( x + 2) ( x - 2)

So   either

x +  2   =  0  ⇒  x  = -2

or

x  - 2   = 0 ⇒   x  =  2

So   [ -2,  2  ]  make the expression undefined

So...I assume that we want to know how much paint we need to cover the kitchen wall and the bathroom

We can solve this with a proportion

4 / 120    =     x  /  ( 67 + 53)      where x is the amount of paint we need

4 /120  =  x  / 120

So....it appears that  x   =  exactly 4 quarts

Thanks Tertre,   

More of a hint: you cannot divide by 0, that is impossible. So if the bottom is 0 the answer would be undefined.

We can factor the denominator first: (a+2)(a-2), and leave the numerator as it is: a+3. Now, think about what undefined means, and see what value of x can fit in.

Suppose you graphed every single point of the form $(2t + 3, 3-3t)$ . For example,  when $t=2$ , we have $2t + 3 = 7$ and $3-3t = -3$, so $(7,-3)$ is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.

we have a graph defined by the locus of all points (2t+3, 3-3t)

so

x= 2t +3  (1a)        and         y=3-3t     (2a)

I am going to sove these simultaneously in order to eliminate t.

3x=6t+9   (1b)      and         2y=6-6t     (2b)

add equations    2a and 2b

3x+2y=15

This is the equation of a line.

All points on this line will satisfy the given condtion and no point that is not on this line will satisfy it.

Hi Oldtimer,

If x is in degrees then this doesn't work the same. The only solution would be  x=0

For any higher mathematics it should always be assumed that angles are in radians.

If for some reason, degrees are required then the degrees sign should be displayed.

Of course for many questions it does not matter but here it does matter.

Here are the graphs if degrees are used.

Nevermind, I understand now

I'm a bit confused, would I expand the two polynomials then multiply the answer all by 10?

10x^2  + 20x  - 80   take out the  greatest common factor, 10

10  (x^2  + 2x  - 8)

To factor the polynomial, we need two numbers that add to 2  and multiply to  -8.....

4  and -2    seem to be  just right....so we have

10 ( x + 4) ( x - 2)

First we can expand \(-3(-x + 5)\) and \(-10(x-3)\). By doing this, we get \(3x - 15 + 20 = -10x + 30 + 4\). Then, we can get \(3x +5 = -10x + 34\). After this, we need to isolate the variable; \(13x = 29\). From here, we can get \(x = \frac{29}{13}\) or \(x = 2\frac{3}{13}\)​.

- Daisy

Thanks

I believe it is quadrant 4

Note if  x   = 3  and  y  = -4...they must intersect at  (x, y) =   (3, -4)  ⇒  4th quadrant

Thanks both of you!

Thanks!