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sqrt  (4x^2)  -  sqrt (x^2)  =  16

sqrt (4) * sqrt (x^2)  -  sqrt (x^2)  =  16

2 sqrt (x^2)  -  sqrt (x^2)  =   16

sqrt (x^2)  =  16         square both sides

x^2  =  256        take  both roots

x = 16     or  x  =  -16

Midpoint    coordinates

(2 - 6) /2   =  - 2

(15 + 3) / 2   =   9

Can you take it from there   ????

d =  the  midline  =  (25 + 15)/2   =   20

a  = the amplitude   =   25 - 20   =   5

The period   =     13pi/ 6    -   pi/6   =   12pi/ 6  =   2pi

b = the periods  in 2pi  =   1

We  can find  the  phase  shift thusly

13pi/6  -  pi/2    =   13pi/6  - 3pi/6  =  10pi/6  =  5pi/3  =    c

0   =  5 sin ( x - 5pi/3)  +  20

Here's the graph :  https://www.desmos.com/calculator/qd5aqbj53w

Dropped 'x ' from the last line ....if you READ and UNDERSTOOD the solution method ...YOU would have seen slight error rather than just looking for an answer !

2x - y -4 >= 0

It's wrong!

x = time goal

16% = .16

.16 x = 32

x = 32/.16 = ___________ minutes

Shaded area is everything less than and including the line .

Equation of a line    y = mx + b

Line slope    m = rise / run =  4/2 = 2           b = -4

     y = 2x -4    is the line equation

y <= 2x-4       re-arrange to requested form

-2x + y +4  <= 0    multiply by -1

2 - y -4 >= 0

Solution:    1x100+ 2x100+3x100 +4x100 + 5x100+6x100

+7x100+8x100+9x100

=4500

Cross multiply (multiply the numerator and denominator of opposite sides and vice versa.)

This gives us $2x(x+4) = -6(x+2) \rightarrow 2x^2+8x = -6x-12 \rightarrow 2x^2+14x+12 = 0 \rightarrow x^2+7x+6 = 0$. 

Now we have to look for two numbers that add to $7$ and multiply to $6$. These numbers are clearly $1$ and $6$, so we can rewrite our equation as $(x+1)(x+6) = 0$. Thus, our answers are $\boxed{x = -1,-6}$. 

Seriously. You just posted an answer here so that you could say that?

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Rather conveniently, from the first equation, we have $4x = 4y \rightarrow x = y$. 

Thus, we can plug this into the second equation to get $y = 2y+6$. Solving this equation gives us $\boxed{y = -6}$, which is our solution. 

OMG TYSM!!

12.5%  discount   =   100  -  12.5  =   87.5%

So

64  (.875)  =   $56   =  his  cost

25%  of  his cost =   56  /4  = $14

So.......

Marked Price ( 1.00  - .20)  -  Cost  =  14

Marked Price   ( .80)  -  Cost     =    14

M  (.8)  -   56   =  14

M(.8)  =   70

M  = 70/ .8     =   $87.50  =  Marked Price  

From the graph, we can see that the line passes through the points $(0,-3)$ and $(-3,3)$. 

Standard form is $y = mx+b$, where $b$ is a constant and $m$ is the slope of the line. 

The slope of the line is given by $\frac{y_1-y_2}{x_1-x_2}$. Thus, the slope of this line is $\frac{-3-3}{0-(-3)} = -2$

Plugging a point into our new equation of $y = -2x + b$ gives $-3 = 0 + (-3)$, meaning $b = -3$. 

Thus, our final equation is $\boxed{y = -2x-3}$  

$2 \cdot \frac{1}{3} + 2 \cdot \frac{1}{4} + 1 \cdot \frac{1}{2} + 1 \cdot \frac{1}{4} = \frac{23}{12}$.

We take the remaining fraction of the paint in each jar and add them together, thus, our answer is $\boxed{\frac{23}{12}}$ 

we  have  the  points   (0 , - 3)     and    (-1, - 1)  on the  graph

The slope   is      ( -1 - -3)  / ( -1 - 0) =  2/-1  =  -2

Using  (0, - 3).....the  equation is

y  =  -2x  -  3

Standard form

2x  + y  +  3   =    0

A  +  B  +  C  =   180

Let  A  =  x

B  =  C    =   5x

So

x + 5x  +  5x   =  180

11x =  180

x  =  180 / 11

B = 5 (180 / 11)  ≈  81.81°

(x , y)   reflected  in x  axis  =   ( x , - y)

(x, -y)    after    90°    counterclockwise   rotation  =   ( y, x)

(y, x)   reflected  across  y = x      =    ( x, y)

Arc LPM = 360º - 72º   

Let me turn this not-so-smart question into an interesting one:

Points L and M lie on a circle centered at O, and the measure of arc LM on this circle is 72 degrees.  The circle passing through points O, L, and M is drawn.  Find the measure of arc LOM on the larger circle, in degrees.

Using the midpoint rule  :

(x  + 1)  / 2   =   3                 (y  - 8)  / 2   =  5

x + 1     =    6                        y -   8   =   10

x =  6 - 1   =  5                     y  =  10 + 8  =  18

xy  =  5*18    =  90

diameter  of  20  =   radius of 10

diameter of  15  =   radius  of  7.5

To  find the  savings.......take  the  difference in surface areas  =

4pi   ( 10^2  - 7.5^2)  =

4pi  ( 100  - 56.25)  =

4 pi  * 43.75  cm^2     =   

 175 pi   cm^2

Simplify the  second  equation  as

9a  + 12b   =  k

Notice  that  the left side   is  just  3 ( 3a + 4b)

So.....to provide  infinite solutions, the equations must be the  same which means that 3* 7   =  k   =  21

3^(2x - 1)  =   36  * 2 (1 - 2x)

Note  that we  can  write     2 ^(1-2x)   =  [ 2^(-1) ] ^(2x - 1)  =    1 /  [ 2^(2x - 1)]

So   we  have  that

3^(2x - 1)  =  36  /  [ 2^(2x - 1)]         multiply  both sides by  2^(2x - 1)

3^(2x - 1)  *  2^(2x - 1)   =   36

3^(2x)/3  *  2^(2x)  / 2  =    36

9^x   * 4^x  /   6     =  36          multiply both sides  by  6

9^x  * 4^x   =   216

(9 * 4)^x   =  216

36^x   =  216

(6^2)^x   =  6^3

6^(2x)  = 6^3           equate  exponents

2x  =  3

x   = 3/2

Let me correct this question:

Let X, Y, and Z be points such that XZ/ZY = ZY/XY = 2/3. If Y = (1, 7), Z = (-1, -9), then what is the sum of the coordinates of X?