derpiiXD

It is a 2x3

You are missing some numbers...

XD

Hmm...

I think what Guest meant to do was divide the first quadratic by 4, which gets us

\(\frac{1}{4}x^2+2x+1\)

a=1/4

b=2

So add them up and get

1/4+2=9/4, or 2.25

XD

We know the amount of girls that play soccer and the percentage, so set them equal

30% of the girls in the class is 24 girls.

You can create a proportion to find the total amount of girls in the class

out of       3 girls who play soccer       =  24 girls

there are 10 girls in the total class     =  80 girls

There are 80 girls in the class.

To find the number of BOYS, create another proportion to find the students.

4 girls       =  80 girls

10 students    =  200 students

There are 200 students in the class.

Now subtract the amount of girls to find the boys

200-80=120 boys.

I wonder... How many boys play soccer??

XD

For this quadratic to have a double root(where there is only one solution for x), the disriminant must be 0

In the quadratic formula, the discriminant is the stuff in the square root, which is \(\sqrt{b^2-4ac}\)

To find a, b, and c, put the quadratic in the form ax^2+bx+c(it is already in this form)

So,

a=2

b=3

and c=k

Now plug the numbers in to get

\(\sqrt{3^2-4(2)(k)}\)

which equals

\(\sqrt{9-8k}\)

The stuff inside must equal zero, so the equation becomes

\(9-8k=0\)

Then solve for k:

Subtract nine on both sides

-8k=-9

k=9/8

or 1.125

XD

Thanks!

Use the quadratic formula:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
x^2+5x+c=ax^2+bx+c

a=1

b=5

c=?

Plug it into the formula and we get

\(x = {-5 \pm \sqrt{5^2-4(1)c} \over 2(1)}\)

and solve to get

\(x = {-5 \pm \sqrt{25-4c} \over 2}\)

now, we know that everything is the same except for the discriminant(the stuff in the square root), and we also know that the disriminant is c

Set them equal to get

25-4c=c

Now solve to get

25=5c

and c=5

XD

srry for the mess, this is my first post

XD

Here's the answer: 10

6xyz+30xy+21xz+2yz+105x+10y+7z=812

We can group them and factor:

6xy(z+5)+21x(z+5)+2y(z+5)+7z=812

(z+5)(6xy+21x+2y)+7z=812

Now if we add 35 to both sides, we can put 7z into parenthesis too,

(z+5)(6xy+21x+2y)+7z+35 --> 7(z+5)=812+35

(z+5)(6xy+21x+2y+7)=847

This simplifies to

(z+5)(3x+1)(2y+7)=847.

Now we can find the factors of 847, which are:

1, 7, 11, 77, 121, 847.

Now, we must find three positive integer values that multiply to 847. There are three of them, which are

and 7x11x11(they don't have to be distinct)

(z+5)(3x+1)(2y+7) take the place of the three integers.

Now we must test all three possibilities.

z+5=1

z=-4

Since it is negative, 1 does not work

3x+1=1

3x=0

x=0

But zero is neither positive or negative, so 1 does not work for this one either

2y+7=1

2y=-6

y=-3

Since this is also negative, it does not work

This means that 

1x7x121

1x11x77

do not work.

That means that (z+5)(3x+1)(2y+7)=7x11x11

BUT...

Which is which?

We must test again...

z+5=7

z=2 This works...

3x+1=11

3x=10

x=10/3

This does NOT work because z must be an integer.

So

z+5 must equal 11

z=6

Now we need to find the other 11 and the 7

This is easy, because we already know that 3x+1 cannot equal 11, so it equals 7.

3x+1=7

3x=6

x=2

This means that

2y+7=11

2y=4

y=2

NOW WE JUST ADD THEM UP

2+2+6=10

The answer is 10

XD