Answer:
Step-by-step explanation:
I think the quotent is 5, but I recommend waiting for sumone else to answer. Because 31.5 divided by 1.4 equals 22.5 but I'm not sure.
The remainder from the division of the algebraic equation is -53/8.
<h3>What is the remainder of the algebraic expression?</h3>
The remainder of the algebraic expression can be determined by using the long division method.
Given that:
![\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%20%5Cdfrac%7Bx%5E3%20-%206x%5E2%20%2B%203x%20-%201%7D%7B2x-3%7D%7D)
where:
Using the long division method, we have:
![\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D%20%2B%5Cdfrac%7B-%5Cdfrac%7B9x%5E2%7D%7B2%7D%2B3x%20-1%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20%2B%5Cdfrac%7B-%5Cdfrac%7B-15x%7D%7B4%7D-1%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20-%5Cdfrac%7B15%7D%7B8%7D%2B%5Cdfrac%7B-%5Cdfrac%7B53%7D%7B8%7D%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20-%5Cdfrac%7B15%7D%7B8%7D-%5Cdfrac%7B53%20%7D%7B8%282x-3%29%7D%7D)
Therefore, we can conclude that the remainder is -53/8.
Learn more about the division of algebraic equations here:
brainly.com/question/4541471
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Answer:
158.4 pounds
Step-by-step explanation:
first find the volume of the tank
![V = 30 \times 30 \times 80](https://tex.z-dn.net/?f=V%20%3D%2030%20%5Ctimes%2030%20%5Ctimes%2080)
![V = 72000 cm^3](https://tex.z-dn.net/?f=V%20%3D%2072000%20cm%5E3)
to convert this to m^3 we know that 1m = 100cm
![V = 72000 cm^3 \times \left(\dfrac{1\,\text{m}}{100\,\text{cm}}\right)^3](https://tex.z-dn.net/?f=V%20%3D%2072000%20cm%5E3%20%5Ctimes%20%5Cleft%28%5Cdfrac%7B1%5C%2C%5Ctext%7Bm%7D%7D%7B100%5C%2C%5Ctext%7Bcm%7D%7D%5Cright%29%5E3)
![V = 72000 cm^3 \times \left(\dfrac{1\,\text{m}^3}{100^3\,\text{cm}^3}\right)](https://tex.z-dn.net/?f=V%20%3D%2072000%20cm%5E3%20%5Ctimes%20%5Cleft%28%5Cdfrac%7B1%5C%2C%5Ctext%7Bm%7D%5E3%7D%7B100%5E3%5C%2C%5Ctext%7Bcm%7D%5E3%7D%5Cright%29)
the cm^3 cancel out.
![V = \dfrac{72000}{100^3} m^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B72000%7D%7B100%5E3%7D%20m%5E3)
![V = 0.072\,m^3](https://tex.z-dn.net/?f=V%20%3D%200.072%5C%2Cm%5E3)
by simply converting the side-lengths to meters beforehand can give you this answer directly:
![V = 0.3 \times 0.3 \times 0.8 = 0.072 m^3](https://tex.z-dn.net/?f=V%20%3D%200.3%20%5Ctimes%200.3%20%5Ctimes%200.8%20%3D%200.072%20m%5E3)
it is given that 1 meter cube of water weighs about 2200 pounds.
![1\,m^3 = 2200 \,\text{lb}](https://tex.z-dn.net/?f=1%5C%2Cm%5E3%20%3D%202200%20%5C%2C%5Ctext%7Blb%7D)
multiply both sides with 0.072 to find our answer:
![1\,m^3 \times 0.072 = 2200 \times 0.072 \,\text{lb}](https://tex.z-dn.net/?f=1%5C%2Cm%5E3%20%5Ctimes%200.072%20%3D%202200%20%5Ctimes%200.072%20%5C%2C%5Ctext%7Blb%7D)
![0.072\,m^3 = 158.4 \,\text{lb}](https://tex.z-dn.net/?f=0.072%5C%2Cm%5E3%20%3D%20158.4%20%5C%2C%5Ctext%7Blb%7D)
hence the weight of the water in the tank would be 158.4 pounds!
9:1 because you divide both sides by 8. Hope this helps :)