SparklingWater2

Lets say she rows x miles in each direction.

When she rows against the current, she travels for $\frac{x}7$ hours.

When she rows with the current, she travels for $\frac{x}{11}$ hours.

In total, she rows $\frac{11x+7x}{77}=\frac{18x}{77}$ hours.

She rows 2x miles in $\frac{18x}{77}$ hours, so the average speed Judy rows is $2x\cdot\frac{77}{18x}=\boxed{\frac{77}{9}}$

Let S be the sum and a is the first term:

S = S/5 + a = 16

5S = S + 5a = 80

4S = 5a

4 x 16 = 5a

64 = 5a

a = $\boxed{\frac{64}5}$

1/3 of 36 = 1/3 x 36 = $\boxed{12}$

15

base 2: 1111

base 4: 33

Let a be the speed the jet travels, and let b be the speed the wind travels. 

$9(a-b)=6930$

$a-b=\frac{6930}9=770$

$6(a+b)=6060$

$a+b=\frac{6060}6=1010$

$a+b=770$

$a-b=1010$

You can finish the rest :)

$\sqrt{25}=5$

$\sqrt{72}=\sqrt{4\cdot9\cdot2}=6\sqrt2$

so $\frac{\sqrt{72}}{\sqrt{25}}=\boxed{\dfrac{6\sqrt2}{5}}$

Yes I do, and sorry about not mentioning the fact that this is answered. I will wait one or two more days, and see if anyone comes up with an answer :)

hint: similar triangles

It's one thing to be able to draw it, and it's another to prove it using words :)

If the coefficient of x is 1, then the factorized form would be something like (x-a)(x-b) for roots a and b. In this case, the roots are -2 and 3, so it would be (x+2)(x-3)=$\boxed{x^2-x-6}$