NinjaDevo

So basically what we have here is a rectangle on the bottom part, and then a half circle on the upper part. We'll need to add these two areas together to get the total area.

For the area of the rectangle, simply multiply 6 in times 2 in (base times height), giving you \(12\; in^2\).

For the half circle, we know that the area of a circle is pi times the radius^2. Well, we don't know the radius but we do know the diameter of this circle, which is 6 in. The radius is always half the diameter, so the radius is 3 in.

Meaning, the area of this half circle is 1/2(pi((3 in)^2)) =

\(\frac{9}{2}\pi\; in^2\)

or aproximately 

\(14.13\; in^2\)

Adding these together we get aproximately

\(28.13\; in^2\)

Which, if we're rounding to the nearest inch, would come out to

\(28\; in^2\)

Thanks for the question dude. If you have any additional questions or don't understand how I did this, or even see a mistake of mine, feel free to let us know and me or another forum member would love to help!

Whenever I think geometric series I think multiplication. So that means the first 1st times a number (lets just call it x) equals the 2nd number. And the 2nd term times this same number x equals the 3rd term, so on and so forth.

So you'll know that the number in inbetween 35 and 875, otherwise the multiplication doesnt work. This rules out b and c.

455 looks a little to big to be multiplied so d. Seems like the best answer.

Let's prove it though.

To find the number that needs to be multiplied between terms, divide our suspected answer -175 by the first term.

-175/35 = -5.

Ok great now lets multiply -175 by -5 and see if we get 875 (our 3rd term)

-175 x -5 = 875.

Boom! Nailed it!

Thanks for the question, let us know if it helped or not and I'm sure me or another member would be happy to help more if you need it. 

Well, you'd just have to add 12 * (#number of hours passed) to find how many minutes your clock is behind at 2:00pm

Then find the amount of hours passed and add that to it

Since 5 hours have passed, and 12*5 = 60 mins, add one hour to 2:00 and...The correct time is 3:00pm!

First we're going to want to factor these out.

f(x)=x^3+x^2-42x

f(x) = (x)(x^2+x-42)   ---this second part can be factored

f(x) = (x)(x+6)(x-7)    

Now that this is factored completely, we can find the zeros. The "zeros" of a polynomial funtion like we have here are the numbers you could put in for x to make f(x) = 0. 

For instance, if we put in -6 for x, we would get this:

f(x)=(-6)(-6+6)(-6-7)

f(x)=(-6)(0)(-13)       ---anything and everything multiplied by zero is zero.

f(x) = 0

Basically you find the opposites of the numbers next to x.

So the zeros are 0, -6, and 7.

Why don't you try this on the website's calculator my friend?

I'm thinking you mean 

$$log_3(2x-1) = 2$$

To do this, we need to rewirte this is exponential form!

What $$log_3(2x-1) = 2$$ is saying, is that $$3^2 = 2x-1$$

Now that we have it like this its pretty easy to solve.

3^2 = 2x-1

9 = 2x-1

10=2x

x=5

Neighbor Malia has 126 inches of lumber, but the problem is we need to know how many feet of lumber this is!

To do this, we need to know how many inches are in a foot.

It turns out there are 12 inches in a foot, so $$126\div12$$ will tell us how many feet of lumber Malia has.

$$126\div12=10\frac{1}{2}$$

add this to the lumber Jim gave her, which is 8 feet.

$$10\frac{1}{2}+8 = 18\frac{1}{2}$$

So...Jenna won't have enough for her fence yet, but she does have $$18\frac{1}{2}$$ feet of lumber so far.

Well, the area of the known side is height*length, 7.5*9, and thus 67.5.

Well, since there are two of these sides on a rectangle, we can do 67.5*2 = 135

Now subtract this from the total surface area: 399-135 = 264

Now this is where it'll be a little tricky. We know there's four sides left and 264 more surface area left...but not all of these sides are necessarily the same area.

If you think about it, one of the sides lengths of two of these squares will have to be 7.5, and one of the side lengths of the other two squares will be 9. Also, the other side legnth for all four of these squares will be the width (or x, because we don't know this yet)

So what we can do is set up an equation! Woohoo!

We'll end up with something like

2(7.5*x) + 2(9*x) = 264      (x = width)

2(7.5x)+2(9x)=264

15x+18x=264

33x=264

x = 264/33

x = 8

Nice! The width is 8 cm!

To find the percent that 11/14 would be, divide 11 by 14 and see what you get

$$\frac{11}{14} \approx .79$$

Well, to turn this into a percent, move the decimal over two places to the right and add a percent sign

$$.79 = 79 \%$$

So it looks like Cindy got the better mark, because her percentage is higher and Johns.

Well, the common ratio in a geometric sequence is what your multiplying each of these numbers by to get the next number. So, in this case, the comon ratio would be a^4, because whenever you multiply two numbers with exponets and they have the same base you add the exponets. for example,

$$a^{-6} \;\times\;a^{4}\;=\;a^{-6+4}\;=\;a^{-2}$$

And to find the next four terms, you would just multiply a^2 by a^4 and that would be your next term, then you would multiply that answer by a^4 and so on.

Try it out and let me know if you can get it. If you can't post again and me or another forum member should be able to help you out :)

$$-4 \div 4 = \frac{-4}{4} = \frac{-1}{1} = -1$$