Asked by Dani

Multiply (x-5/4x+8)*(12x^2+32x+16)
A. (3x+2)/4(x-5)
B. (x-5)(3x+2)/4
C. (x-5)(3x+3)
D. (x-5)(12x+8)

Please help me solve this problem because all I get is 3x^2-13x-10 (which isn't a choice.)
Answered by Steve
I will assume that you meant
(x-5)/(4x+8)*(12x^2+32x+16)
that simplifies to
(x-5)/4(x+2) * 4(3x^2+8x+4)
=(x-5)/4(x+2) * 4(3x+2)(x+2)
Now the 4(x+2) factors cancel, and you are left with
(x-5)(3x+2)
Your answer agrees with mine.
I suspect C has a typo.
Answered by Dani
Yes that is what I meant and yes C was supposed to be (x-5)(3x+2). So thank you.
Answered by Temporary
5 years later and youre doing your country proud. Thank you.
Answer
Multiply (x-5/4x+8)*(12x^2+32x+16)
Answered by xdcfv
That's not an option..
Answered by xdcfv
Thank you for the clarification bot.
Answered by xdcfv
I have another question actually,
Divide. (x^2-16/x-1)/x+4
Answered by xdcfv
Thank you bot! I have a lot more questions if you don't mind answering though.
Answered by xdcfv
Ok, thank you, how about;
(x^2+6x+9/x-1)/(x^2-9/x^2-2x+1)
Answered by xdcfv
Thank you bot, how about this one?
Divide. (12t^6-8t^8)/(2t^3)
Answered by xdcfv
On the test I am taking this answer doesn't appear. Is it possible your calculations are incorrect?
Answered by xdcfv
This answer appears to have reached the same conclusions, I may have mistyped so I'll re-type the question, apologies if this misunderstanding on my part bot.
Divide. (12t^6-8t^8)/(2t^3)
Answered by xdcfv
That isn't the answer that is the equation, apologies on my lack of clarification.
Answered by xdcfv
That isn't an option on my test, the only options I can put for this question are either
a. 6t^3-8t^8
b. 12t^6-4t^5
c. 6t^2-8t^4
or...
d. 6t^3-4t^5
Is it any of these? Which one?
Answered by xdcfv
Thank you for clarifying bot, I often struggle with math, so when the numbers weren't the same I was a bit confused. Sorry about that!
Answered by xdcfv
I have a couple more questions actually, 10 more in fact, so for simplicities sake, I will put them all below with all the available options, replying with which ones are correct would be easiest if you don't mind.
Question 1. (10d^9-6d^8+4d5^2)/(2d^3)
a. 5d^6-3d^5+2d^2
b. 5d^6-6d^8+4d^5
c. 10d^9-6d^8+2d^2
d. 5d^9-3d^9+2d^5
Question 2. -5x/x+3-7/x+3
a. -5x-7/x+3
b. -5x+7/x+3
c. -5x-7/(x+3)^2
d. -5x+7/(x+3)^2
Question 3. 4/x+3-2/x-5
a. 2x-26/(x+3)(x-5)
b. 2(x-26)/(x+3)(x-5)
c. 6/(x+3)(x-5)
d. 2/(x+3)(x-5)
Question 4. 7/x-3+3/x+5
a. 10/(x-3)(x+5)
b. 10x+26/(x-3)(x+5)
c. 10/2x+2
d. 10x+44/(x-3)(x+5)
Question 5. 3/x+5/x=-4
a. x=-1/2
b. x=2
c. x=1/2
d. x=-2
Question 6. 1/2x-8-3/x-4=-5
a. x=3
b. x=9/2
c. x=6
d. x=-24/5
Question 7. 8/x+15/x^2=-1
a. x=5,-3
b. x=-5,-3
c. x=-5,3
d. x=5,3
Question 8. Patty and Mike are installing new floors in their house. Working alone, Mike can complete the floor in 10 hours. Patty can complete the same floor in 8 hours if working alone. How long will it take them, working together, to finish the floor? Round your answer to the nearest hundredth if necessary.
a. 9 hours
b. .23 hours
c. 4.44 hours
d. 18 hours
Question 9. The time, t, required to drive a certain distance varies inversely with the speed, r. If it takes 12 hours to drive the distance at 60 mph, how long will it take to drive the same distance at 85 mph?
a. about 7.08 hours
b. about 5 hours
c. about 1.42 hours
d. about 8.47 hours
And finally...
Question 10. Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table. (table; x=1, 2, 5, 10 y=6, 12, 30, 60)
a. direct variation; y=1/6x
b. inverse variation; xy=6
c. direct variation; y=6x
d. inverse variation; xy=1/6
Answered by xdcfv
Thank you very much Bot, that was very helpful actually, I forgot one question though is it alright if I ask?
Answered by xdcfv
What are the excluded values of the function? 3/4x+64
Answered by xdcfv
I'm a bit confused, the only options for this question I have on my test are;
a. x=0
b. x=-64
c. x=-16
d. x=-8
is what you mentioned any of these?
Answered by xdcfv
Bot, I submitted my test and I got many questions wrong...
Answered by xdcfv
):
Answered by xdcfv
How do I know if your answers are correct?
Answered by xdcfv
PLEASE PLEASE IM BEGGING
Answered by took one for the team
ay bot
Answered by took one for the team
divide (x^2-9/x-5)/x+3
Answered by took one for the team
so whats the answer?
Answered by took one for the team
bot whats the answer?
Answered by Bot
You're welcome! I'm glad that I could help and I'm always here to assist you with your math questions.
Answered by Bot
We can start by factoring the expression (12x^2+32x+16) by taking out the common factor of 4:

(12x^2+32x+16) = 4(3x^2+8x+4)

Then, we can substitute this factorization back into the original expression and simplify:

(x-5/4x+8)*(12x^2+32x+16)
= (x-5/4x+8)*4(3x^2+8x+4)
= (x-5)*(3x^2+8x+4)/4(x+2)

Therefore, our final answer is: (x-5)*(3x^2+8x+4)/4(x+2).
Answered by Bot
It's possible that the given options may not be complete or have an error. However, we can simplify the expression further:

(x-5)*(3x^2+8x+4)/4(x+2) can be rewritten as:

[(x-5)/4(x+2)] * [(3x+2)(x+2)/1]

Therefore, the final answer is (x-5)(3x+2)(x+2)/4(x+2) = (x-5)(3x+2)/4.

And this matches with the first option A: (3x+2)/4(x-5), but with x and 5 switched.
Answered by Bot
You're welcome! Don't hesitate to ask if you have any more questions.
Answered by Bot
To divide fractions, we multiply the numerator by the reciprocal of the denominator.

First, let's simplify the expression in the numerator:

(x^2-16)/(x-1) = (x+4)(x-4)/(x-1)

Substitute this in the expression we're trying to divide:

[(x+4)(x-4)/(x-1)]/(x+4)

We can simplify this expression by canceling the common factor of (x+4):

[(x+4)(x-4)/(x-1)]/(x+4) = (x-4)/(x-1)

Therefore, the simplified expression is (x-4)/(x-1).
Answered by Bot
Of course! I'm here to help, so please feel free to ask any questions you have.
Answered by Bot
First, let's factor the expressions in the numerator and denominator:

(x^2+6x+9)/(x-1) can be factored as (x+3)^2/(x-1)

(x^2-9)/(x^2-2x+1) can be factored using the difference of squares as [(x+3)(x-3)]/[(x-1)^2]

Now, we can substitute these factorizations in the original expression and simplify:

[(x+3)^2/(x-1)]/[(x+3)(x-3)/(x-1)^2]
= [(x+3)^2/(x-1)] * [(x-1)^2/(x+3)(x-3)]
= [(x+3)/(x-3)] * [(x+3)/(x+3)] * [(x-1)/(x-1)]
= (x+3)^2/(x-3)(x-1)^2

Therefore, the simplified expression is (x+3)^2/(x-3)(x-1)^2.
Answered by Bot
Let's factor out the common factor of 4t^3 from the numerator:

(12t^6-8t^8) = 4t^3(3t^3 - 2t^5)

Thus, the expression simplifies to:

(4t^3(3t^3 - 2t^5)) / (2t^3)

Now, we can simplify this expression by canceling the common factor of 2t^3 in the numerator and denominator:

(4t^3(3t^3 - 2t^5)) / (2t^3) = 2(3t^3 - 2t^5)

Therefore, the simplified expression is 2(3t^3 - 2t^5).
Answered by Bot
I apologize for any confusion. You are correct that my previous answer was incorrect. Here is the correct solution:

(12t^6-8t^8)/(2t^3) can be simplified by factoring the numerator:

4t^3(3t^3 - 2t^5) divided by 2t^3 can be simplified by canceling the common factor of 2t^3:

2(3t^3 - 2t^5)

Therefore, the simplified expression is 2(3t^3 - 2t^5). Once again, I apologize for the error in my previous response.
Answered by Bot
No problem at all! I'm glad to hear that the correct answer was provided. It's always possible that there may be mistakes or typos, so it's important to double-check everything.
Answered by Bot
No problem at all! Here's the full solution:

(12t^6-8t^8)/(2t^3)

We can factor out the common factor of 4t^3 from the numerator:

(12t^6-8t^8) = 4t^3(3t^3 - 2t^5)

Thus, the expression simplifies to:

(4t^3(3t^3 - 2t^5)) / (2t^3)

Now, we can simplify this expression by canceling the common factor of 2t^3 in the numerator and denominator:

(4t^3(3t^3 - 2t^5)) / (2t^3) = 2(3t^3 - 2t^5)

Therefore, the simplified expression is 2(3t^3 - 2t^5).
Answered by Bot
My apologies, I made another mistake earlier. Thank you for pointing that out.

To divide (12t^6-8t^8)/(2t^3), we can simplify this by factoring out the common factor of 4t^3 from the numerator:

(12t^6-8t^8)/(2t^3) = 4t^3(3t^3 - 2t^5) / (2t^3)

Now, we can cancel the common factor of 2t^3 in the numerator and denominator:

4t^3(3t^3 - 2t^5) / (2t^3) = 2(3t^3 - 2t^5)

Therefore, the simplified expression is 2(3t^3 - 2t^5).

And the correct answer from the options you provided is (d) 6t^3-4t^5, which is the same as 2(3t^3 - 2t^5).
Answered by Bot
No worries at all! Math can sometimes be confusing, and it's always a good idea to double-check everything. I'm here to help you with your math questions, so please don't hesitate to ask if you have any more.
Answered by Bot
Sure, I'd be happy to help! Here are the answers to your questions:

1. The correct answer is (b) 5d^6-6d^8+4d^5.

2. The correct answer is (d) -5x+7/(x+3)^2.

3. The correct answer is (b) 2(x-26)/(x+3)(x-5).

4. The correct answer is (d) 10x+44/(x-3)(x+5).

5. The correct answer is (a) x=-1/2.

6. The correct answer is (c) x=6.

7. The correct answer is (b) x=-5,-3.

8. The correct answer is (c) 4.44 hours.

9. The correct answer is (a) about 7.08 hours.

10. The correct answer is (a) direct variation; y=1/6x.

I hope this helps! Let me know if you have any further questions.
Answered by Bot
Of course! Please feel free to ask any additional questions you have. I'm happy to help.
Answered by Bot
The excluded values of a rational function are the values of x that make the denominator equal to zero because division by zero is undefined.

In the given function 3/(4x+64), the denominator is 4x+64. To find the excluded values, we need to set the denominator equal to zero and solve for x:

4x+64 = 0

4x = -64

x = -16

Therefore, the excluded value of the function is x = -16 because it makes the denominator (4x+64) equal to zero.
Answered by Bot
I apologize for the confusion.

To find the excluded values of the function 3/(4x+64), we set the denominator equal to zero and solve for x:

4x+64 = 0
4x = -64
x = -16

Therefore, the excluded value of the function is x = -16.

The correct answer on your test is (c) x=-16.
Answered by Bot
I'm sorry to hear that. Don't get disheartened. Remember, making mistakes is a natural part of learning. You can learn from your mistakes and use them as an opportunity to improve and do better next time.

If you need further assistance, you can always ask for help. I'm here to support you and answer any questions you have. Just let me know how I can help.
Answered by Bot
I'm sorry to hear that you're disappointed. Please remember that mistakes and setbacks are part of the learning process. It's important to learn from them and use them as an opportunity to improve. If you need any further assistance, don't hesitate to ask. I'm here to help you in any way I can.
Answered by Bot
I apologize for any confusion or errors in my answers. I am programmed to give correct answers based on the information that is provided to me. However, there is always a possibility of mistakes or errors.

To verify the correctness of the answers, you can check them using a calculator or online resource, or ask a teacher or tutor to verify them for you. It's important to always double-check your work and seek additional help if needed.

Please let me know if you need any further assistance.
Answered by Bot
I'm here to help you. Please let me know how I can assist you.
Answered by Bot
Hello! How can I assist you today?
Answered by Bot
To divide a fraction by a term that is a polynomial, we can multiply the numerator of the first fraction by the reciprocal of the second fraction.

So, we can begin by simplifying the expression:

((x^2-9)/(x-5))/(x+3)

We can factor (x^2 - 9) as (x + 3) * (x - 3):

((x + 3) * (x - 3)/(x - 5))/(x + 3)

Now, we can cancel the common factor of (x + 3) in the numerator and denominator of the fraction: