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I got the tank is 1900 tons since when its 75% full its 3700 and when its 25% full it weighs 2500 so 3700-2500 is 50% of fuel which is 1200 tons. So 25% would be 600 tons. 2500-600=

1900 tons. 

😅😅😅😅

Hmm cal ty! But i know that i need to find out how much the tank weighs! I never thought of that so it might help.

Yep! That's the same answer that I got. Good job!

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

That is incorrect. Try to explain how you got 1/2 and 4.

7 and -3

Good job! I never thought of that approach to the question. 

24 girls= 30% of girls

8 girls= 10% of girls

80 girls=100% of girls

80 people: 40 % of class

20 people: 10% of class

200 people: 100% of class

200 people in the class, 80 girls, so 120 boys.

As it was written by the Guest, ako correctly points out that this equation has no solutions. However, I will take it that they forgot parentheses(important!) around the denominator and numerator. I'll then solve it with this interpretation:

\({x\over x-5} = {4 \over x-4}\)

Cross multiplying ,we get

\(4x-20 = x^2-4x\)

Rearranging, we get:

\(x^2-8x + 20 = 0\)

Realizing that our roots are imaginary because of the discriminant(but the problem never limits the value of x, so I'll continue), we can use the quadratic formula to find:

\(x = {8 \pm \sqrt{-16} \over 2}\)

\(x = {8 \pm 4i \over 2} = 4\pm2i\)

If 3/10 of 2/5x = 24, then 6/50x = 24. x = the class. Then, we can multiply both sides by 50/6 and get that x = 200. Using that 2/5 of the class is girls, 3/5 of the class is boys. So, 200 * 3/5 = 120 boys.

A + B = 1/2 + 4 = 9/2.

No,  (2x+2)(x+1) multiplies out to 2x² + 4X + 2 

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

By partial fractions, A = 1 and B = 2, so B/(x + 1) - A/(x - 2) = 2/(x + 1) - 1/(x - 2) = (x - 5)/((x - 2)(x + 1)).

We can solve this using a system of equations. 

Let \(x=\)tickets bought at the door

Let \(y=\)tickets bought in advance

Our equations are 

\(10y+15x=1390\)

\(y+x=120\)

We can solve elimination (Feel free to use a different strategy):

Multiply the bottom equation by \(10\)

\(10y+10x=1200\)

Subtract the bottom equation

\(5x=190\)

Divide both sides by \(5\)

\(x=38\)

Plug that value into the bottom equation (or the top if you want)

\(y+38=120\)

Subtract \(38\) from both sides

\(y=82\)

\(82\) tickets were bought at the door.

Hope this helped!!!

-Ako

Because we have the roots of this quadratic given as : 

\(x = {-5 \pm \sqrt{c} \over 2}\), by vietas, we can write:

\({-5 + \sqrt{c} \over 2} * {-5 - \sqrt{c} \over 2}\) = c

Expanding, we get:

\({25-c\over4} = c\), because the square roots cancle out

then, this gives us:

\(4c = 25-c\) when we multiply by 4 on both sides

\(5c = 25\)

Dividing by 5 on both sides, we get:

\(c = 5\)

That's a unique way to solve it!

By simiilar trianlges, DE = 16.

Here is how I solve it:

Say all the tix were bought in advance: that would mean 1200 dollars were sold. For each ticket we turn into bought at the door, we gain 5 dollars. The difference of 1390 and 1200 is 190. So 190/5 38 were bought at the door. So 82 were bought in advance.

Check

38*15=570

82*10=820

820+570=1390