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We have a quadratic, and since the first step is to find the roots, we can apply the quadratic formula: \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\), where \(a\) is the coefficient of \(x^2\), \(b\) is the coefficient of \(x\), and \(c\) is the constant.

Now to plug in the values. 

\(x = {-1{+\over}\sqrt{13}\over2}\)

The plus operation and the minus operation are the roots p and q, respectively. 

Now I used a calculator, and \(4p^2\) approximates to 6.7889.

\(q^3\) approximates to -12.2111.

Since we are subtracting \(q^3\) from \(4p^2 \), that is 6.7889 - (-12.2111) = 19. 

Thus, \(4p^2 - q^3 = 19\).

Just as builderboi said!

\(\frac{5}{8}\times\frac{1}{5}=\frac{5\times1}{8\times5}=\frac{5}{40} simplify, \frac{1}{8}\)

I think you made a mistake on format you wrote \(\frac{1}{(\frac{1}{3})^2}\) instead of \(\frac{1}{(\frac{1}{3})^3}\)

The question being asked here stated that w + x + z = -4

The question being asked when you google this question stated that w + x + z = 4.

I answered this one where w + x + z = -4, I am not sure if he is asking the same question, or a very similiar question. :)

We have four equations, four unknowns. Fortunately, in each equation the variable has a coefficient of 1, so here is what we can do.

First we add up all 4 equations getting:

\(3w + 3x + 3y + 3z = 25\)

Then we divide both sides of the equation by 3, getting:

\(w + x + y + z = {25\over3}\), let's call this equation5, and the other equations we will list from equation1 - equation4.

Now we take equation5 and subtract it from equation1. We get:

\(w + x + y + z - w - x - y = 25/3 + 6/3\)

This simplifies to \(z = {31\over3}\).

Equation5 - Equation2:

\(y = {37\over3}\)

Equation5 - Equation3:

\(x = {-32\over3}\)

Equation5 - Equation4:

\(w = {-11\over3}\)

Now to multiply:

wx + yz = 352/9 + 1147/9 = \(1499\over9\)

this question was already answered on a web2.0calc post. enter your question on google and you will find it

(This will be a step by step explanation instead of using completing the square formulas/shortcuts)

First we must simplify the original expression.

\(4x^2 - 8x + 9\) this expression looks cleaner.

Since we have to complete the square, we know \(a\), the coefficient of \(x^2\) has to be 4.

If we open the parenthesis of \((x - h)^2\), we get \(x^2 + h^2 - 2hx\). 

Then since we are multiplying 4 to the expression, we have \(4x^2 + 4h^2 - 8hx\). 

\(h\) is a constant. if \(-8hx\) is the only value with \(x^1\), then \(-8h = -8\) in the original expression. Thus \(h = 1\).

The new expression \(4x^2 - 8x + 4\) has a difference of a positive 5 than the original expression \(4x^2 - 8x + 9\). 

Thus \(k = 5\).

Adding up our values, we have a + h + k = 4 + 1 + 5 = 10.

I did it myself and the answer was X= 1/2 and X= 1/3.

I verified it and it is true for both equations.

I posted here because I thought it looked too hard for me at first to do by myself but then I fgured it out. Thank you.

We know the circumference of the circle = the perimeter of the square which is  \(\sqrt{144} =12\times4=48\) (you get 12 and 12 x 4 =48)

\(2\pi r=48\)

\(\pi r=24\)

\(r=\frac{24}{\pi}\)

\(\pi\times\frac{24}{\pi}^2=\frac{576}{\pi}\)

\(576\pi\) is about \(183\)

so 183.

In order to get the smallest value, you want as big of a negative number x as big of a positive number, so the answer is a super small negative. The way we can do this is by having a = -2, and b = 5. 

Plug these values in:

\({({-1 \over 2} + {1\over 5})}* {({1 \over 5} - {-1 \over 2})} \). This yields \(\color{red} -21/100\).

Rather than think about what is similar between the two, think about what can be different between the two.

They are both quadratic funtions.  So they have no holes or anythign like that.   They both have the same basic parabolic shape.  Can aything about them be different?  Are they identical?

12 + 6 = 18

12 - 6 = 6

The x-coordinate of the other x-intercept is \(\color{red} 6\) by symmetry

Think about it... Try and make 2 equations that would intersect at an infinite amount of points. Find similarities between the two equations and apply them to this problem. 

Hi Julia,

These are not equations.  there are not equal signs.  They need   y=   or    f(x)=   or some other funtion name =

I will assume they are   f(x)=     and    g(x)=

a)  f(x)=g(x) then     

-4x2+2x+5=2x2-3x+6

now solve them simultaneously.

b) plug the answers that you get into the original equation to see if they make  f(x) and g(x) equal

You can also put the equations into Desmos graphing calc to see where they both cross.

For the calc call them both y=

How about you discuss it Julia.  What do YOU think?

The other guest got in while I was typing up my correction. 

I'm glad to see that we both obtained the same answer. 

_.

If the ratio of children to adults is 3:53:5 and there are 120120 children at an amateur surfing competition, how many adults are in attendance?  

I think the 3:5 doubled up and I think the 120 doubled up.  I don't know why it would do that.  

So 3 / 5 is the ratio and there are 120 children

                           3 / 5  =  120 / x   

cross multiply      3 • x  =  5 • 120  

                               3x  =  600  

                                 x  =  200 Adults  

_.

If the ratio of children to adults is 3:53:5 and there are 120120 children at an amateur surfing competition, how many adults are in attendance?

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

3/5 = 120/adults

adults = 200

IGNORE THE ABOVE

I misread the question.  I read the total was 120,120.  THAT'S WRONG.  The children are 120,120. 

If the ratio of children to adults is 3:53:5 and there are 120120 children at an amateur surfing competition, how many adults are in attendance? 

I think the the problem is trying to say the ratio is 3:5 and somehow it just got doubled up. 

So the ratio is 3:5.  That means there are 3 + 5 portions, or 8 portions.  

If you can thing of a better word than portions, then use it.  

Divide 120,120 by the total number of portions                 120,120 / 8 = 15,015   

So each portion is 15,015 and the adults have 5 of them.   15,015 • 5 = 75,075 adults  

_.

Thank you so much! <3

Thanks proyaop, you are right! I will correct.

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