Need help w/ solving (X-1)^2-6=0, writing 7-t^2/2 - t/3 in standard form, etc

[User123789]

Hello, I have been absent from school due to sickness and the work hasn't stopped piling up. I have an unhelpful teacher and a book tht is of no aid. These are the questions I need help with and am completely clueless. If I could see the answers and steps taken to arrive, it would be appreciated tremendously.Thank you!

1. Solve: (X-2)^2-6=0
2. Write expression in standard form.
7- t^2/2 - t/3
3. Solve: x^2 + 3x + 4=6
4. Put in form a+bi:
square rt of -8 + 3 square rt-18
5. A rectangular piece of paper is 2 inches longer than it is wide. A one-inch square is cut from each corner, and the paper is folded up to make an open box with volume 80 cubic inches. Find the dimensions of the rectangle.

 

[Deleted member 4993]

Hello, I have been absent from school due to sickness and the work hasn't stopped piling up. I have an unhelpful teacher and a book tht is of no aid. These are the questions I need help with and am completely clueless. If I could see the answers and steps taken to arrive, it would be appreciated tremendously.Thank you!

1. SolveX-2)^2-6=0
2. Write expression in standard form.
7- t^2/2 - t/3
3.solve: x^2 + 3x + 4=6
4. Put in form a+bi:
square rt of -8 + 3 square rt-18
5.a rectangular piece of paper is 2 inches longer than it is wide. A one-inch sq is cut from each corner, and the paper is folded up to make an open box with volume 80 cubic inches. Find the dimensions of the rectangle.

These are not topics that you would miss in one or two days. You have missed "training" for multiple days. You must attempt these problems and show us your attempts - so that we know where to start.

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[stapel]

Hello, I have been absent from school due to sickness and the work hasn't stopped piling up. I have an unhelpful teacher and a book tht is of no aid. These are the questions I need help with and am completely clueless. If I could see the answers and steps taken to arrive, it would be appreciated tremendously.Thank you!

You already have loads of worked examples with "the answers and steps taken to arrive" at them in your class notes (gotten from fellow students) and your textbook. These, you say, haven't helped at all, and you remain "completely clueless".

Completing this homework set will not solve that problem. While we can provide help with specific exercise, this assistance requires that the student have at least a basic grasp of the underlying material, something you say is missing. Unfortunately, we cannot here replace the missing hours or weeks of classroom instruction. Are you open to online self-study?

1. Solve: (X-2)^2-6=0

3. Solve: x^2 + 3x + 4=6

These are "quadratic" equations. Do you know how to multiply polynomials? Do you know how to factor quadratics? If so, then we can start you off with lessons on solving by taking square roots, solving by factoring, and solving with the Quadratic Formula. Otherwise, we'll need to start further back.

2. Write expression in standard form.
7- t^2/2 - t/3

Does the above represent the following?

. . . . .\(\displaystyle 7\, -\, \dfrac{t^2}{2}\, -\, \dfrac{t}{3}\)

How does your book define "standard form"?

4. Put in form a+bi:
square rt of -8 + 3 square rt-18

Does the above represent the following?

. . . . .\(\displaystyle \sqrt{\strut -8\,}\, +\, 3\, \sqrt{\strut -18\,}\)

Are you familiar at all with "complex" numbers, being numbers containing the "imaginary" number "i"? If so, where are you stuck? If not, are you familiar with simplifying radicals?

5. A rectangular piece of paper is 2 inches longer than it is wide. A one-inch square is cut from each corner, and the paper is folded up to make an open box with volume 80 cubic inches. Find the dimensions of the rectangle.

Use what you learned back in beginning algebra:

a) If "w" stands for the width, what expression stands for the length? Draw a picture with this labelling.

b) If one-inch squares are cut from the corners, then what will be the width of the part they fold up? In other words, how deep will the box be? So what is the value of the height "h" of the box?

c) If one-inch squares are cut from the corners, then what will be the new width and length of the base of the box?

d) What is the formula for the volume V of a box with width w, length L, and height h?

e) Plug the given information, along with your expressions, into the "volume" formula.

Then, the only new part, which is:

f) Solve.

Thank you!

 

[User123789]

comments

1. Is this a problem where I use the quadratic equation?
2. Standard form is referring to ax^2+bx+c=0. I attempted to get rid of the denominators by multiplying everything by 6 and was left with -3t^2-2t+42. Not sure if that’s correct though.
3. I put this into standard form and got: x^2+3x-2=0. I put that into the quadratic equation and was left with x=-3+- sq root of 1 all over 2. I did not know how to continue from there.
4. I think i^2=-1? I still don’t get how its supposed to look factored though. I got 2i sq rt 2+9i sq rt 2, do I combine for 11i sq rt 2? That doesn’t sound right.
5. Thank you, I guess that was basic.

 

[User123789]

comments

1. Im not sure how to begin this problem. The book has examples but none that are similar enough to this problem that I feel comfortable replicating the steps off a guess.
2. Standard form is Ax^2+bx+c=0. I attempted the problem and multiplied everything by 6 to get rid of the denominators. I was left with -3t^2-2t=42=0 as my answer. I don’t know if this is right..
3. I tried this problem by using the quadratic equation. It left me with x=(-3 plus/minus sq rt of 1)/2. I have no idea how to proceed from that.
4. I thought that i^2= sq rt of -1. So I tried to simplify and came up with 2i sq rt 2 +9i sq rt 2. Combined for 11i sq rt 2. But this is not in the form a+bi so I know im wrong.
5. Yes, thank you, I was overthinking a simple problem.
Ok, my book isn’t useless but for the specific problems I have, theres nothing parallel to reference and I’m simply not keen on picking up math.

 

[Steven G]

Hello, I have been absent from school due to sickness and the work hasn't stopped piling up. I have an unhelpful teacher and a book tht is of no aid. These are the questions I need help with and am completely clueless. If I could see the answers and steps taken to arrive, it would be appreciated tremendously.Thank you!

1. Solve: (X-2)^2-6=0
2. Write expression in standard form.
7- t^2/2 - t/3
3. Solve: x^2 + 3x + 4=6
4. Put in form a+bi:
square rt of -8 + 3 square rt-18
5. A rectangular piece of paper is 2 inches longer than it is wide. A one-inch square is cut from each corner, and the paper is folded up to make an open box with volume 80 cubic inches. Find the dimensions of the rectangle.

If (X-2)^2-6=0, then what do you think (X-2)^2 equals? Hint: when you subtract 6 from it you get 0. Answer this and we will proceed to the next step.

 

[stapel]

1. Solve: (X-2)^2-6=0

Is this a problem where I use the quadratic equation?

Assuming that you mean "the Quadratic Formula" then, yes, this is one method one could apply. It would be the longer method, though, and would require that you know how to multiply polynomials. Do you know how to do this?

2. Write expression in standard form.

. . . . .\(\displaystyle 7\, -\, \dfrac{t^2}{2}\, -\, \dfrac{t}{3}\)

Standard form is referring to ax^2+bx+c=0. I attempted to get rid of the denominators by multiplying everything by 6 and was left with -3t^2-2t+42. Not sure if that’s correct though.

By what logic did you change the original expression? (Since this is not an equation, as it has no "equals" inside it, there is nothing to "multiply through". Just as 12 = 6*2 is not equal to 2, so also 6*(original quadratic expression) is not equal to (original quadratic expression). Why didn't you just rearrange to get things in the form required?

3. Solve: x^2 + 3x + 4=6

I put this into standard form and got: x^2+3x-2=0. I put that into the quadratic equation and was left with x=-3+- sq root of 1 all over 2. I did not know how to continue from there.

Please reply showing your steps, so that we may attempt to locate the errors.

4. Put in form a+bi:

. . . . .\(\displaystyle \sqrt{\strut -8\,}\, +\, 3\, \sqrt{\strut -18\,}\)

I think i^2=-1? I still don’t get how its supposed to look factored though. I got 2i sq rt 2+9i sq rt 2, do I combine for 11i sq rt 2? That doesn’t sound right.

You didn't answer my formatting question. I will assume that I guessed correctly.

What do you mean by "how its[sic] supposed to look factored"? What are you "factoring"? What do you mean when you say that it "doesn't sound right" to combine two "like" terms?

Please be specific. Thank you!