AdamTaurus

The Trump Card

If minorities have the race card and women have the gender card, what do rednecks have?

Is there any way you could solve #2 algebraically?

This problem is what is known as a difference of perfect squares.

The standard form of this is \((ax^2-b^2)=(\sqrt{a}x+\sqrt{b})(\sqrt{a}x-\sqrt{b})\).

In this the a=9 and the b=4.

So \((9x^2-4)=(3x-2)(3x+2)\).

For the second, use the quadratic formula.

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

In this, a=4, b=11, and c=6.

\( {-11 \pm \sqrt{11^2-4(4)(6)} \over 2(4)}\)

Simplify.

\({-11 \pm \sqrt{121-16(6)} \over 8}\)

\({-11 \pm \sqrt{121-96} \over 8}\)

\({-11 \pm \sqrt{25} \over 8}\)

\(\frac{-11 \pm5}{8}\)

This is equivalent to \(\frac{-11+5}{8},\frac{-11-5}{8}\).

\(\frac{-6}{8},\frac{-16}{8}=\frac{-3}{4},-2\)

So your factors are (x+3/4)(x+2) (because the standard form is (x-a)(x-b)).

But there is one more thing. Just move the denominator in front of the x, because no one wants fractions (and also it wouldn't be right otherwise).

So your real factors are \((4x+3)(x+2)\).

For the first, plug an x-value into each equation to determine which gives out the y-value.

\(-2.5(-2)^2+5(-2) \)

Simplify.

\(-2.5(4)-10\)

\(-10-10=-20\)

This is the y-value of (-2,-20), so it works. Now plug the x values from the other equations in.

-2.5(0)²+5(0)

Simplify.

-2.5(0)+0

0+0=0

0 is not the y-value of (0,-4), so you have to try another.

\(-(-2)^2+4(-2)-4=-4-8-4=-16\)

This is not the y-value of (-2,-20), so try another.

\(-2(-2)^2+4(-2)-4=-8-8-4=-20\)

This is the y-value of (-2,-20), so it works. Now plug the x values from the other equations in.

\(-2(0)^2+4(0)-4=0+0-4=-4\)

This is the y-value of (0,-4), so plug in the final point.

\(-2(4)^2+4(4)-4=-32+16-4=-16-4=-20\)

This is the y-value of (4,-20), so the equation is -2x²+4x-4.

Thank CPhill!

Oh oops!

Thanks CPhill for the correction!

what is the simplified expression of a triangle for 7x-6w+4x+6y+5y+4w and for the second one 2x+3y+x+5+y+7

1) 7x-6w+4x+6y+5y+5w

Reorganize the terms with their like terms.

7x+4x-6w+5w+6y+5y

Now combine like terms.

11x+11y-w

That is your simplified expression.

2) 2x+3y+x+5+y+7

Reorganize.

2x+x+3y+y+5+7

Combine like terms.

3x+4y+12

That is the simplified expression.

Thanks CPhill!