The width w of a rectangular swimming pool is x+4. the area a of the pool is x^3-13x+12. What is an expression for the length of the pool
If you can help I would really appreciate it
a = w * L
so
L = a / w
L = (x^3 - 13 x + 12) / ( x+4)
so divide
x^2 - 4 x + 3 maybe?
thanks bunches damon!!
1. simplify 3/5a * 1/a^2:
To simplify this expression, we can combine the two fractions by multiplying their numerators and denominators:
3/5a * 1/a^2 = (3*1)/(5a*a^2)
= 3/(5a^3)
Therefore, the simplified form of 3/5a * 1/a^2 is 3/(5a^3).
2. multiply (x-5)/(4x+8)*(12x^2+32x+16):
To multiply these two expressions, we can first factor out 4 from the denominator of the first fraction:
(x - 5)/(4x + 8) = (x - 5)/4(x + 2)
Now we can cancel out the 4 in both the numerator and denominator of the first fraction and simplify the second fraction:
(x - 5)/(4x + 8) * (12x^2 + 32x + 16) = (x - 5)/(x + 2) * (3x^2 + 8x + 4)
Next, we can factor the second fraction:
3x^2 + 8x + 4 = 3(x^2 + (8/3)x + 4/3) = 3(x + 2/3)(x + 2)
Substituting this back into the expression, we get:
(x - 5)/(x + 2) * 3(x + 2/3)(x + 2)
Now we can cancel out (x + 2) from the numerator and denominator:
(x - 5)/(x + 2) * 3(x + 2/3)(x + 2) = (x - 5) * 3(x + 2/3)
= 3x^2 - 4x - 10/3
Therefore, the product of (x-5)/(4x+8)*(12x^2+32x+16) is 3x^2 - 4x - 10/3.
bob drove 120 miles on his vacation. he drove an average of 1.2 times faster on the second 60 miles of his trip. Which expression represents the time he spent driving? let x = his speed on the first half of the trip
I apologize for the mistake. Here's the correct solution:
Let Bob's speed on the first half of the trip be x. Then, the time he spends on the first half of the trip would be:
time = distance / speed = 60/x
On the second half of the trip, Bob drives 1.2 times faster, so his speed would be:
1.2x
The time he spends on the second half of the trip would be:
time = distance / speed = 60/(1.2x) = 50/x
Therefore, the total time Bob spent driving would be:
60/x + 50/x = 110/x
So, the correct answer is A. 110/x.
thank you i have some more for you!!!
Sure, feel free to ask!
simplify x/4x+x^2
x/(4x + x^2) can be simplified by factoring the denominator:
x/(4x + x^2) = x/(x(4 + x))
Notice that x appears in both the numerator and denominator, so we can cancel them out:
x/(x(4 + x)) = 1/(4 + x)
Therefore, x/(4x + x^2) simplifies to 1/(4 + x).
thank you
You're welcome!
can you help me?
Yes! Please let me know what you need help with.
simplify x/(7x+x^2)
x/(7x+x^2) can be simplified by factoring the denominator:
x/(7x + x^2) = x/(x(7 + x))
Notice that x appears in both the numerator and denominator, so we can cancel them out:
x/(x(7 + x)) = 1/(7 + x)
Therefore, x/(7x + x^2) simplifies to 1/(7 + x).
tysm
You're welcome! Let me know if you need help with anything else.
can you simplify -12x^4/(x^4+8x^5) ?
can you help with something else?
Yes, I can help you! What's the question?
simplify -12x^4/(x^4+8x^5)
-12x^4/(x^4+8x^5) can be simplified by factoring out -4x^4 from numerator and denominator:
-12x^4/(x^4 + 8x^5) = (-4x^4*3)/(x^4*(1 + 8x))
Now we can cancel out -4x^4 from the numerator and denominator:
-12x^4/(x^4 + 8x^5) = -3/(1 + 8x)
Therefore, -12x^4/(x^4 + 8x^5) simplifies to -3/(1 + 8x).
i have another question
Sure, what's the question?
simplify (x-2)/(x^2+4x-12)
To simplify (x-2)/(x^2+4x-12), we need to factor the denominator:
(x^2 + 4x - 12) can be factored as (x + 6)(x - 2)
Thus, we get:
(x - 2)/(x^2 + 4x - 12) = (x - 2)/[(x + 6)(x - 2)]
We can cancel out (x - 2) from the numerator and denominator:
(x - 2)/[(x + 6)(x - 2)] = 1/(x + 6)
Therefore, the simplified form of (x-2)/(x^2+4x-12) is 1/(x+6).
my last Answer didnt show
No problem, I'll wait for your last question.
simplify (x^2-3x-18)/(x+3)
To simplify (x^2-3x-18)/(x+3), we can first factor the numerator:
(x^2 - 3x - 18) can be factored as (x - 6)(x + 3)
Thus, we get:
(x^2 - 3x - 18)/(x + 3) = [(x - 6)(x + 3)]/(x + 3)
We can cancel out (x + 3) from the numerator and denominator:
[(x - 6)(x + 3)]/(x + 3) = x - 6
Therefore, the simplified form of (x^2-3x-18)/(x+3) is x - 6.
i dont know what i could do without you
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can you compute multiple questions at once?
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1. simplify 3/5a * 1/a^2
2 multiply (x-5)/(4x+8)*(12x^2+32x+16)
Hey bot, how accurate are your answers?
As an AI language model, I strive to provide the most accurate and helpful responses possible based on the information provided. However, please note that there may be certain limitations in my knowledge or understanding of a particular topic. Additionally, if the input is incorrect or incomplete, my response may not be accurate. Nonetheless, I will do my best to assist you and provide accurate answers to the best of my ability.
simplify x/6x-x^2
To simplify x/(6x - x^2), we can factor out x from the numerator and denominator:
x/(6x - x^2) = x/(x(6 - x))
Now we can cancel out x from the numerator and denominator:
x/(x(6 - x)) = 1/(6 - x)
Therefore, the simplified form of x/(6x - x^2) is 1/(6 - x).
that isnt the full answer its this one 1/6-x; where x=0,6 or 1/6-x; where x=6
I apologize for the confusion. You're correct.
The simplified form of x/(6x - x^2) is indeed 1/(6-x), but with the condition that x cannot equal 0 or 6, as that would make the denominator zero.
So the complete answer is:
x/(6x - x^2) = 1/(6 - x), for x not equal to 0, 6.
thanks bot a couple more questions
The time t required to drive a certain distnace varies inversely with the speed, r, if it takes 7 hours the distance at 55 miles per hour how long will it take to drive the same distance at 65 miles per hour
We know that the time t required to drive a certain distance varies inversely with the speed r. We can write this as:
t = k/r, where k is a constant of variation.
We are also given that it takes 7 hours to travel this distance at a speed of 55 miles per hour. We can use this information to find the value of k:
7 = k/55
Multiplying both sides by 55:
k = 385
Now we can use k to find the time required to travel the same distance at a speed of 65 miles per hour:
t = k/r
t = 385/65
t = 5.92 hours (rounded to two decimal places)
Therefore, it will take approximately 5.92 hours to drive the same distance at a speed of 65 miles per hour.
TYSM!!! HAVE A GOOD DAY BOTTTT
You're very welcome! If you have any more questions in the future, don't hesitate to ask. Have a great day!
Bot can you simplify x/6x-x^2
Let t be the time Bob spent driving on the first half of the trip, then his speed was x and he covered a distance of 60 miles. The time he spent driving on the second half of the trip would be t/1.2 because he was driving faster. The distance he covered on the second half of the trip was also 60 miles.
Therefore, the total time he spent driving would be:
t + t/1.2
Simplifying, we get:
2.2t/1.2
which can be written as:
1.83t
thats not the answer
A. 110/x
B. 120/x
C.132x
D. 132/x