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We get the maximum when A = B = C = D.  This gives a maximum value of ABCD = 256/625.

2-digit: 14

3-digit: 108

4-digit: 1004

W   *     10 W   = 264

W^2 = 26.4

W = 5.138      L = 51.38   units

10 = 2x^2 -31x + 25            (10 is  10 000 in thousands)

2x^2 -31x +15 = 0    Quadratic formula shows x = 15 months       ( 1/2 month also shows as a possible....but unlikely)

Jared’s stock portfolio grows according to the formula a=2x^2-31x+25, where a is the amount in the portfolio, in thousands, and x is the amount of time the money has been in the portfolio, in months. When will Jared’s portfolio be at a value of 10,000 dollars?

Hello Guest!

You either have to enter the investment time or the invested capital.

Friendly greeting

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How many gallons of 20% alcohol solution should be added to 40 gallons of a 50% alcohol solution to make a 30% solution?

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Wie viele Gallonen einer 20%igen Alkohollösung sollten zu 40 Gallonen einer 50%igen Alkohollösung hinzugefügt werden, um eine 30%ige Lösung herzustellen?

\(40gal\cdot0.5+x\cdot0.2=(x+40gal)\cdot0.3\\ 20gal+0.2x=0.3x+12gal\ |\ -0.2x-12gal\\ 8gal=0.1x\ |\ /0.1\)

\(80gal=x\)

80 gallons of 20% solution must be added to the 40 gallons of 50% solution.

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If \(\frac{3x^2-4x+1}{x-1}=m, \)  and x  can be any real number except 1 , what real values can  m NOT have?

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\((m(x)=\frac{3x^2-4x+1}{x-1})\color{blue}\in\mathbb R\ |\ x\neq 1\\ m(1)\ is\ not\ 2\\ \color{blue}2\notin \{m(x)\} \)  

By stars and bars, the number of polynomials is C(12,3) = 220.

Uisng the quadratic formula, m can be any value except 4.

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That was easy.

Can you find the coordinates of the 2 remaining vertices? 

x = pens

y = pencils

(2/3)x = 2* (2/5)y

x = 50 + y

(2/3)(50 + y) = 2*(2/5)y

100/3 + 2y/3 = 4y/5

500 + 10y = 12y

y = 250

x = 300

550.

using the triangle inequality, a triangle with sides 5, 11, and 7 can be formed

Use distance formula to find distance between the two points....this is the diagonal of the square

s^2 + s^2  = diagonal ^2         s= side length

    2 s^2 = diagonal ^2

       s^2 = diagonal^2  / 2         = area      beause    (Area = side x side = s^2)

Re-arrange to 

x^2 - 7x - 44 = 0

then factor to

(x-11)(x+4) = 0               x = 11    and  -4

y = x^2 - 18x - 33        Is a bowl shaped parabola...

     the zeroes occur    at    x = 19.677  ~~ 20 units will produce zero or very minimal profit

Multiplying by a constant will not conver the imaginary number to a real number so

f(1+i) =    2 + 2i

f(2+ 2i) =   4 + 4i

f(4+4i) =   8 + 8i

f(8+8i)  = 16 + 16i

Any number that makes a denominator equal to zero (not allowd) will not be in the domain,,,

   64         8 and -8          4         sqrt 8   and   - sqrt 8

Aww thank you so much cat! <3

The following graph should help:

-7 is less than -5 so   f(-7)=3

You can try the other 2    

set all of his money as x.

3/5x is 4 highlighters, so 3/10x is 2 highlighters.

he only spent 1/10x of his money buying 10 rulers, which answers the first question given.

(b) he spends all his money buying rulers. which means ignoring the free rulers, he could buy 100 rulers. but then, since there are 8*12 = 96, we know he gets an extra 8 rulers and hence have 108 rulers if he spent all his money at first on rulers.

What is the coefficient of x^3 when 24x^4 + 6x^3 + 4x^2 + 7x - 5 is multiplied by 6x^3 + 3x^2 - 3x + 4 and the like terms are combined?

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\((24x^4 + 6x^3 + 4x^2 + 7x - 5)\cdot ( 6x^3 + 3x^2 - 3x + 4)\\ =144x^7+108x^6-30x^5+132x^4+{\color{blue}3x^3}-20x^2+43x-20\)

\(The\ coefficient\ of\ x^3\ is\ 3.\)

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40x + 40(x - 0.5) = 130

x = 1.875

40x = 75