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This graph  confirms your suspicions, AT :

https://www.desmos.com/calculator/e91hazjxx9

x =  1/2 is the only real root

Have fun :) 

https://faculty.math.illinois.edu/~r-ash/ComAlg/ComAlg5.pdf

If you want to read the whole thing,

what is your question?

ff you increase the radius or the height of the cylinder, it will increase the volume

Oh oops!

Thanks CPhill for the correction!

a)  Numerator:         (x²y)²·(xy)³·z²  = (x²y)·(x²y)·(xy)·(xy)·(xy)·z²  =  [x²·x²·x·x·x]·[y·y·y·y·y]·z²  =  x⁷·y⁵·z²

     Denominator:     (xy²)²·y·z  =  (xy²)·(xy²)·y·z  =  [x·x]·[y²·y²·y]·z  =  x²·y⁵·z

    Combining the numerator and denominator:     [x⁷·y⁵·z²] / [x²·y⁵·z]  =  x⁵·z

b)  Numerator:  (12)²·(6³)·5²  =  (2·2·3)²·(2³·3²)·5²  =  (2²·3)²·(2³·3²)·5²​  = 2⁴·3³·2³·3²·5²  =  2⁷·3⁵·5²

     Denominator:     (2·3·3)²·(3·5)  =  (2·3²)²·(3·5)  =  2²·3⁴·3·5  =  2²·3⁵·5

     Combining the numerator and denominator:  [2⁷·3⁵·5²] / [2²·3⁵·5]  =  2⁵·5  =  160

You'll need to answer part c.

C) The bases of a cylinder are circles.

SA  = 

2pi *r * h  +  2 pi * r^2  =

2pi * r  * [ h + r ]  =

2 * 3.14 *  9  * [ 12 + 9 ]  =  1186.9 units^2

How  about

Output  =   4n  + 7   ????

Here's how this is obtained

Slope  =     [ 15 - 11] /  [ 2 - 1 ]   =   4/ 1 =  4

So...using the slope and any  (input, ouput)  point - I'll use (1, 11) -  we have

Output  =  4 ( n - 1) + 11

Output  = 4n - 4 + 11

Output  = 4n + 7

e.   To make factoring easier, rearrange the 25 - 20x + 4x^{2 .}

     $\frac{6x^2-11x-10}{6x^2-5x-6}\cdot\frac{6-4x}{4x^2-20x+25}$

Now we need to factor all the numerators and denominators. Start by splitting their middle terms.

=   $\frac{6x^2+4x-15x-10}{6x^2-9x+4x-6}\cdot\frac{6-4x}{4x^2-10x-10x+25}$

                                                                            Now factor by grouping.

=   $\frac{2x(3x+2)-5(3x+2)}{3x(2x-3)+2(2x-3)}\cdot\frac{6-4x}{2x(2x-5)-5(2x-5)}$

=   $\frac{(3x+2)(2x-5)}{(2x-3)(3x+2)}\cdot\frac{-2(2x-3)}{(2x-5)(2x-5)}$

                                                                           Multiply the fractions together.

=   $\frac{(3x+2)(2x-5)(-2)(2x-3)}{(2x-3)(3x+2)(2x-5)(2x-5)}$

                                                                           Cancel the common terms.

=   $\frac{{\color{red}(3x+2)}{\color{red}(2x-5)}(-2){\color{red}(2x-3)}}{{\color{red}(2x-3)(3x+2)(2x-5)}(2x-5)}$

=   $\frac{(-2)}{(2x-5)}$

=   - $\frac{2}{2x-5}$

And  x  ≠  3/2  or  -2/3   since these cause a zero in the denominator of the original expression.

Thanks. How about when its

Input: 1,2,3,4,n

output: 11,15,19,23?

Output  =  4n

If this is the function........y = (x - 1)^2  + 3

None of the answers are correct

This is the graph of x^2   shifted to the right 1 unit and up 3 units...

Here's the proof :

https://www.desmos.com/calculator/frdqngrnhj

In the form

y = a ( x + h)  + ( - k )   the vertex is  ( -h , -k)

So...we have

y = 3(x + 2)^2  + ( - 3 )

So....the vertex  is ( -2, -3)

Only one answer fits.....the second one

y = 2(x - 3)^2 +   (-  4 )

Because the "2" out front is positive, this parabola turns upward.......the vertex  is  (3, -4)

So....this is the minimum point on the parabola.....and y =  -4  is the minimum

The domain is all real numbers  [  we can put any x value into the function ]

And the range is  [ -4, infinity]   ⇒ all real numbers ≥ 4

The first answer is correct

This graph will help you see this :

https://www.desmos.com/calculator/cmyimyjq0h

In the given ratio,  A = 2B   and C  = 4B

So  

[ 3 (2B) + 2B ]  / [ 4(4B) - 2B ] =

[ 8B ] / [ 14 B ]  =

8 / 14  =

4 / 7

If we let x = 0, then y =  2(0)^2  = 0...so  (0,0)  will be on the graph

This eliminates the middle two graphs

If we let x  = 1, then y =  2(1)^2  =  2

So...( 1 , 2)   is on the graph

So...the first graph is correct.....

1. -2 ( a + 6)  =  -2a  - 2*6  =   -2a  - 12

2.  Whole Numbers, Rational Numbers, Integers 

3. "6 Times the difference of B and p?"  =   6 [ b -  p ]

4. 5(14-2)^2/2  =  5 (12)^2 / 2  =  5 * 144/2  =  5 * 72 =  360

5.  u + xy, if u= 18 and x= 10, AND y=8

    18  + (10) (8)  =

    18  +  80  =

        98

Well... Sadly it was wrong. :( However, thank you for trying. It was actually 165 bikes. :D

.3

There are two ways to solve this problem. Without a calculator, the second is easier, and with a calculator, the first one is. Anyways, here they are:

( 14 / 35 )( .75 )

= .3

OR

( 14 / 35 )( 3 / 4 )

= 42 / 140  

= 21 / 70  

= 3 / 10

= .3

Here's the graph, NSS :

https://www.desmos.com/calculator/fgs3orbcai

The max will be found at a corner point...there's only one at (1.5, 1.5)

Slight typo on the first one

7x-6w+4x+6y+5y+4w =

[7x + 4x] + [ 6y+ 5y ] + [ 4w - 6w ]  =

11x  + 11y  - 2w 

how puck is putting the flower on titania and making Bottom look like a horse. when he wanders in you just know they will falling lover

Probability of taking two red sweets in succession =

(3/8)  (2/7)  =  6 / 56  =  3 / 28

I think this is correct.....

Shape Q is a dilation of P with a scale factor of 3 shifted to the right by 2 units and up 2 units  

To find the percent of discount:

1) calculate the amount of discount:  $17.00 - $13.00  =  $4.00

2) divide this answer by the original amount:  $4.00 / $17.00  =  0.2342941176,,,  --->   rounded:  0.234

3) turn this answer into a percentage:  0.234  --->   23.4%