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The curve is a circle centered at 0 with radius 6, so the area is 36*pi.

Let a, b be the roots.

The the quadratic is x^2 - (a + b) x + ab.

Set a = -(a + b) - 1

b = ab - 1

Substituting, we have

b =b(-b - 2)/2 - 2

b = -b^2/2 - b - 2

b^2/2 + 2b + 2 = 0

b^2 + 4b + 4 = 0

(b + 2)^2 = 0

b = -2
 

Now, a = 0.

The required quadratic is x^2 - (0 + (-2)) x + 0(-2) = x^2 + 2x.

Let m = multiple choice, and s = short response

23m + 10s = 86

28m + 5s = 76

56m + 10s = 152

23m + 10s = 86

-----------------------

33m = 66

    m = 2

28m + 5s = 76

28(2) + 5s = 76

56 + 5s = 76

5s = 20

s = 4

Which means each multiple choice answer is worth 2 points and short responses are worth 4 points :)
 

5       0i

4     -2i 

3     -4i

2     -6i

1     -8i

0    - 10 i          the ninth term is pure imaginary

x = amount of 1       y = amount of  2    z= amount of 3         final amount = x+y+z

.13x   +   .05y    +   .29z    =    .1 (x+y+z)       This is for A

.62x    + .77 y    +  .13 z    =  .5 (x+y+z)          this is for B

.25x   +   .18y    + .58 z     = .4 (x+y+z)           this is for C

I think this is correct......I used wolfram alpha and got no answer !     This problem has no solution that I can fathom !

    Hope someone else can find an answer ....or the same conclusion !!! 

Jason has 4 gallons of hand sanitizer that contains 25% alcohol. He wants to make a hand sanitizer that contains 50% alcohol. How many gallons of pure alcohol should he add?

Hello Guest!

\(4\ gal\cdot 25\%+x=(4\ gal+x)\cdot 50\%\\ 4\ gal\cdot 0.25+x=4\ gal\cdot 0.5+x\cdot 0.5\\ 0.5x=4gal\cdot (0.5-0.25)\)

\(x=\dfrac{4\cdot 0.25}{0.5}gal\)

\(x=2\ gal\)

Jason should add 2 gallons of pure alcohol.

  !

Solve for x

Hello Gast!

First theorem of rays

\(\dfrac{2x-5}{22.5}=\dfrac{x+8+2x-5}{20+22.5}\\ \dfrac{2x-5}{22.5}=\dfrac{3x+3}{42.5}\\ 85x-212.5=67.5x+67.5\\17.5x=280\)

\(x=16\)

  !

a.)  conversion period is  1 year (12 months)   interest is 5% per period

b.)   conversion period is  6 months  or 1/2 year   interest per period    is  4.5 /2 = 2.25 %   (.0225 in decimal form)

            42 months is  42/6 =   7 periods

c.)   conversion period is 1 week   there is 104 periods ( 52 weeks x 2 years)  interest per period is  5.2 /52 = .1%  (this is .001 in decimal)

A = P(1 + r/n)^nt

where,

A = final amount

P = initial investment 

r = interest rate

n = number of times interest is applied

t = number of time periods

Cedric:
A = P(1 + r/n)^nt

   = 12000(1 + 0.05/1)^(1*15)

   = 12000(1.05)¹⁵

   ≈ 12000(2.0789)

   ≈ $24 947.14

Daniel:
A = P(1 + r/n)^nt

   = 12000(1 + 0.07/1)^(1*15)   

   = 12000(1.07)¹⁵

   ≈ 12000(2.759)

   ≈ $33 108.38

33108.38 - 24947.14 = $8161.24, which is your answer :)

(-5x³ - 5x² - 7x + 1)(-x² + 6x + 1) 

To find the coefficient of x², we can just multiply the terms that would have x².

(-5x²)(1) + (-7x)(6x) + (1)(-x²) 

= -5x² - 42x² - x²

= -48x²

Which means your coefficient is -48, which is also your answer :)

ND = NE = NF
6x - 2 = 3x + 7

3x = 9

x = 3

This means NF = 6x - 2 = 6(3) - 2 = 18 - 2 = 16, which is your answer :)

Since they are similar, we can just take the proportions and apply it to each side :)

15/6 = 2.5, which means each side of the triangle LMN are 2.5 times longer than that of the other triangle.

20 ÷ 2.5 = 8

25 ÷ 2.5 = 10

This means the perimeter of triangle XYZ = 6 + 8 + 10, which gives 24cm, which is your answer :)

Hope this helps

The quadratic is x^2 - 5x + 6 > 0, so b + c = (-5) + 6 = -1.

The exterior angles sum to 360

3 /(3+4+5) * 360 = 90

4/12 *360 =  120

5 / 12 * 360 =150

Interior and exterior angles are supplementary (they add to 180)

so the smallest interior will be     150 + 30 = 180          30 degrees

Nice sleuthing guest,

I suspect there are infinitely many solutions if a can be negative......

You could just give the original co-ordinates of the points. 

But if you are are going to ask more questions it is in your interest to play around with the image loader until you can get it to work.

Where is the picture?  Is it an image file  on your computer or is it on the internet?

Can you be a little more specific   ?    "it didn't work"   isn't very helpful.....

here is where you will have to click on after you FIRST click on 'image'

    BTW     I uploaded THESE images this way......so it works....sometimes it fails though....maybe try again?

  Sometimes people just post links to images, though I don't encourage that method.....I won't usually answer if I have to go click -linking around !

I tried that it did not work 

Stat here:

how do i post one ( i am new to this)

Need image....

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