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p(1,-1)  =  1 - 2(-1)  = 3

p(-5,2)  = -5 -2(2)  = -9

So  we have

p (3, -9)   =    3 - 2 (-9) =  3  -18  =   -15

B

              2

A                   C

If tan B  = 5.....then  the ratio of AC / BA =  5/1  ....so  ....   AC = 5BA 

Using the Pythagorean Theorem

BA^2 + AC^2=  BC^2

BA^2  +  (5 BA)^2 =  2^2

BA^2  + 25 BA^2   =  4

26 BA^2 =  4

BA^2  = 4 /26  =  2 /13

BA  = sqrt  (2/13) =   2sqrt (13) / 13  ≈  .392

                                     Y

                                                 W

     X                                                     Z

Angle YXZ  =  60°

Angle  XYZ =   45°

So angle  XZY  =  180 - 60 - 45  =  75°  = angle XZW

Since XW bisects angle YXZ.....then angle  WXZ =  30°

Then in triangle XWZ ,angle WXZ = 30°   and angle XZW = 75°

So angle XWZ =  180  - 30  - 75    =  75°

x = -2y^2 -3y + 5 - y^2  + 6               simplify as

x =  -3y^2 - 3y + 11

This is a parabola that opens to  the left.....the line will intercept the parabola at  its vertex

The y coordinate of the vertex =  - (-3) / ( 2 * -3)  = 3/ -6  = -1/2

The x coordinate is     -3(-1/2)^2 -3(-1/2) + 11  =   -3/4 + 3/2  + 11  =  11+3/4 = 11.75

The equation of the line  is     x =  the x cordinate of the vertex =  11.75

500 * 5 =  $2500  = total money taken in = revenue

1(750) + 2(250) + 5(125)  = $1875   =  prize money paid out

Profit =  2500 - 1875  =  $625  

% of revenue that was profit =    625  /   2500  =    .25  =  25 %

Expand and simplify and see what you get.

let r = # of pennies ryan has

let n = # of pennies nathan has

n = (5/6)r

r - (5/10)r = n - 50

r - (5/10)r = (5/6)r - 50

.5r = (5/6)r - 50

solve for r, r = 150

This IS a thread, and you started it.  

77x9/11=63. 

77-63=\(\boxed{14}\)

how many ounches makes 1liter  

I used https://www.sciencemadesimple.com/conversions.html  

1 liter equals 33.81 ounces (US, fluid)  

1 liter equals 35.20 ounces (British, fluid)  

_.

Parabola

Take \(ab + c = 2\). From the first words, we know that c must be 1, because if c was 2, \(ab = 0\), which is not possible with positive integers. 

This means \(c = 1 \), and \(ab = 1\). 

The only positive integers that satisfy this are: \(a = b = c = 1 \). 

Thus, \(a + b + c = \color{brown}\boxed{3}\)

He spent 4/5, so he has 1/5 left.

spent 4 parts,   left 1 part

spent $28          left  ?

Can you work it out now?

Base 6==3 3223
Base 7==1 6323
Base 11==3523
Base 25==7923
Base 40==2.35.23

Note: I only checked numbers from 2 to 40!.

https://web2.0calc.com/questions/find-a-base-7-three-digit-number-which-has-its-digits-reversed-when-expressed-in-base-9-you-do-not-need-to-indicate-the-base-with-a-subscr

Wish I found this link before spending 30 min on this....

15 , 60 , 135 , 240 , 375 , 540 , 735 , 960>>Total==8 such integers

Let  two points on the line  be  (0, 18)  and (x , 0)

We can solve this

[ 0 -18 ] / [ x - 0 ]  = 3/7

-18  / x  = 3/7

-18 (7/3)  =  x

(-18/3)(7)  = x

-42  = x   =   the   x intercept

t^2 -9t - 36 + t^2 - 5t + 14        simplify  as

2t^2  - 14t  - 22

The t that produces a min  is the  x coordinate of the  vertex of this parabola given by

- (-14)  / (2 * 2)  =   14/4  =  7/2  =   3.5

 1.2n-4.4<5.2+1.1n        multiply through by 10 to clear the decimals

12n - 44 < 52  +11n

12n - 11n  < 52 + 44

n < 96

The sum of the positive integers from  1  to 96 inclusive is

[96] [ 97] /  2  =

48 * 97  =  

4656

help

A non-graphical method

The center of the circle  = (0,0)

The equation of the line in standard form  is

2y =  3x + 7

3x - 2y + 7  =  0                 using (0,0) for (x,y).....the distance  from  the circle's center  to the  line is  given  by

l  3(0)  - 2(0)  + 7 l                    7

_________________  =       _________        (1)

     sqrt  [ 3^2 + 2^2]              sqrt (13)

We can  form  a right  triangle  with a hypotenuse of 5, one  leg  = (1)   and the  other leg 1/2 the  chord length

So......the length of the  whole  chord is

2sqrt   [ 5^2 - (7/sqrt(13))^2 ]  =

2sqrt [  25  -  49/13 ]  =

2sqrt [ 276/13 ] ≈   9.215 =  9.22 (rounded to the  nearest hundreth )

Note     1/a^2  + 1/b^2 =      [a^2 + b^2 ] / [ ab ] ^2

The sum of the roots =   11/5  =  a + b

Square both sides

121/25 =  a^2 + 2ab + b^2

The product of the roots =    4/5 = ab     so.....2ab =  8/5        and [ab]^2 = 16/25

So 

121/25 = a^2 + 2(4/5) + b^2

121/25 = a^2 + 8/5 + b^2

121/25  - 8/5 = a^2 + b^2

121/25 - 8/5 = a^2 + b^2

121/25 - 40/25 = a^2 + b^2

81/25 =  a^2 + b^2

So

1/a^2  + 1/b^2 =   [ 81/25] / [ 16/25 ] =    81 / 16

The equation factors to: \((m+4)(n-1) = 36\)

Now, recall the factor of 36: 1,2,3,4,6,9,12,18,36

We need to find the number of pairs of integers that satisfy this. 

For example, 1 pair is \((32,2)\), because 36 x 1 = 36. 

Can you take it from here?