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thank you!

By pythagoras' theroem, the ladder reaches up √(10² - 2²) = √96 = 4√6 m

we can use pythagorean theorum: 10^2-2^2=h^2=96

h=$\sqrt96$=$\boxed{4\sqrt6}$

$\boxed{f(x)=x^2+2}$

A=1000(1+0.0125/4)^(18x4)=~$\boxed{2446}$

Because CPQ=QDC=90 and PC=CD=2, we know that PQ=QD. and for the exact same reasons,PQ=QA, or QD=QA. if we mark a point E bisecting CD, we can find AD by pythagorean theorum in triangle BCE:$\sqrt{9-1}=\sqrt{8}=2\sqrt2$, and AD/2=AQ=QD=PQ, so we have

PQ=$\frac{2\sqrt2}2=\boxed{\sqrt2}$  

Because of opposite angles, e = 66^o 

This means f = 180 - 66 = 114^o

Finally, since d is supplement to the 90^o angle next to it, which means it's 180 - 90 = 90^o as well

Which means d = 90^o, e = 66^o, f = 114^o

They are both going at 2 miles per hour.

The product is 16.

the area of the black shaded region is:$\pi+25\pi-9\pi=17\pi$

the area of the white shaded region is:$9\pi-\pi+49\pi-25\pi=32\pi$

therefore, the ratio of the black area to white area is $\boxed{\frac{17}{32}}$

The question asks for 7 percent of 43.99. 

7% = .07

Can you do .07*43.99?

I hope this helped. :))

=^._.^=

the diameter of the circle will be the diagonal of the square, which is 12$\sqrt2$, and the area of the circle is $\pi$(d/2)$^2$=$K\pi$=72$\pi$, so therefore, the value of $K=\boxed{72}$

We can start by looking at the angles, and we see that each interior angle is 120$^\circ$. this means that  we can find so 30-60-90 triangles.

we can start by looking at the top half(notice we are cutting the hexagon from one of its diagonals), and if we draw two straight lines as heights, we can two 30-60-90 triangles on the side, and we get 1/2 as the base of the triangle. we can do the same for the other triagle, which also has a base of 1/2, and the length between these two triangles is 1, so 1/2+1/2+1=2, which is the length of one diagonal.

there are 6 diagonals in total, so 2 $\cdot$ 2 $\cdot$ 2 $\cdot$ 2$\cdot$ 2 $\cdot$ 2 = 2$^6$=$\boxed{64}$

the degree with an arc is marked (3x)$^\circ$, and we know that a striaght line consists of 180 degrees in total, so 180-82.5=3x+2x=97.5

5x = 97.5

x = 19.5

3x = 19.5 $\cdot$ 3 = $\boxed{58.5^\circ}$

To find the intersection, we must find the point satisfying both equations. Hence we must solve the system

\(\begin{align*} y&=-4x, \\ y-2&=12x. \end{align*}\)

Substituting the expression for \(y\) in first equation into the second equation, we obtain \(-4x-2=12x\). Solving for \(x\) we find that \(x=-1/8\) 

Plugging this into the first expression for \(y\) above, we find that \(y=-4\cdot -\frac{1}{8}=\frac{1}{2}\) . So the intersection is \(\boxed{\left(-\frac{1}{8}, \frac{1}{2}\right)}\).

amount of green M&Ms=3x+4 how to solve for x: total M&Ms = sum of amount of M&M's per color.

59 = 16+3x+4+2x-1 = 19+5x

5x=40

x=8

3x+4=24+4=$\boxed{28}$

5 chickens x 4 donkeys x 7 emus = $\boxed{140}$

we can use pythagorean theorum to solve this problem, so PR^2 = PS^2+SR^2.

those two lengths are the hypotenuses of triagnles APS and SDR, so

PS^2+SR^2 = 2AP^2+2SD^2.

we also know that AP^2+SD^2=200, so AP^2+2SD^2=2(200)=400.

this means that PR^2=400, so PR=$\boxed{20}$

How about this,

You roll a D6 five times, and get five numbers. The order they appear does not matter. What is the probability that there are three adjacent numbers among them?

I'll do that the next times :)

Thanks!

n=3(mod 7)

2n=6(mod7)

2n+1=0(mod 7)

so the answer is $\boxed0$

The volume of a pyramid is 1/3 times the sidelength cubed (square pyramid), so 1/3(1^3)=1/3

Someone check this please

An even number has a factor of 2, so we can represent it as 2x. 

The other number will be 2x + 2. 

So we're tryign to prove that

(2x+2)^2-(2x)^2 = multiple of 4

4x^2+8x+4-4x^2

8x+4

4(2x+1). 

The number has to have a factor of 4, making it a multiple of 4. 

I hope this helped. :)))

=^._.^=

-16t^2 + 44t      = h       max h will occur at t = - b/2a =  -  44/(2*-16) =  1.375 sec  

     Use this value of t to calc height

-16 ( 1.375)^2 + 44 ( 1.375) = 30.25 ft max