gwenspooner85

We find the number of ways where the two numbers on the dice rolled add up to 7.

We can have:

1 6

2 5

3 4

4 3

5 2

6 1

The total number of sums we can get is 6 x 6=36.

So the probability of rolling a sum of 6 is 6/36=1/6.

0.999... is a repeating decimal, so:

Let x represent the fraction that 0.999 is equal to.

x=0.999...

10x=9.999....

10x-x=9.999...-0.999....

9x=9

x=1

@DeluxeVegan, I remember you sent this as a message to me and I responded. Why don't you check that? If my answers were wrong, you should've told me.

\((\frac{4x}{x})^3=(6x-5x)+(11\cdot5+2^2)\\ 4^3=x+55+4\\ 64=x+59\\ \boxed{x=5}\)

We can factor x^2-20x-69=0 to (x+3)(x-23)=0. 

Then x+3=0 so x=-3

and x-23=0 so x=23.

Therefore the roots are -3 and 23.

69 has another meaning that you probably don't want to know.

The area of the entire large rectangle is (x+7)(x+5). The hole is (2x-3)(x-2). Not including the area of the hole, the area of the large rectangle would be (x+7)(x+5)-(2x-3)(x-2).

(x+7)(x+5)-(2x-3)(x-2)

=x^2+12x+35-2x^2-7x+6

=-x^2+19x+29

This is simple. x^2-4x+1 is not factorable so we plug it into the quadratic equation.

\(x = \frac{-b \pm \sqrt{b^2-4ac}} {2a}\\ x=\frac{4\pm\sqrt{(-4)^2-4(1)(1)}}{2(1)}\\ x=\frac{4\pm\sqrt{12}}{2}\\ x=\frac{4\pm2\sqrt{3}}{2}\\ x=2\pm\sqrt{3}\)

Cube the two roots.

\((2+\sqrt{3})^3+(2-\sqrt{3})^3\\ =\boxed{52}\)

We first convert 4x+2y=8 into slope intercept form.

4x+2y=8

2y=-4x+8

y=-2x+4

Parallel lines have the same slope, so -2 y=-2x will remain the same for the parallel line's equation. However, the y intercept will not and we let it be the variable b. We plug in the given point, (0,1).

y=-2x+b

1=0+b

b=1

So the equation is y=-2x+1.