a homeowner has just installed a swimming pool with a capacity of 3.5 x 10⁴ gallons.of the pool is initially empty, how many hou
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A= 3, and 4. (c & d)
1. Solve the Equation: , to get
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1a. Use the distributive property to multiply 3 by x−1.
1b. Add −3 and 4 to get 1.
1c. To find the opposite of x+3, find the opposite of each term.
1d. Subtract 3 from 2 to get −1.
1e. Add x to both sides.
1f. Combine 3x and x to get 4x.
1g. Subtract 1 from both sides.
1h. Subtract 1 from −1 to get −2.
1i. Divide both sides by 4.
1j. Reduce the fraction 4−2=−0.5 to lowest terms by extracting and canceling out 2.
or x = -21
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Now that you know the answers, solve the others:
2. A= 1, so this is wrong. How I solved it is shown below:
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1a. Add −3 and 4 to get 1.
3x+1=2−x+3
1b. Add 2 and 3 to get 5.
3x+1=5−x
1c. Add x to both sides.
3x+1+x=5
1d. Combine 3x and x to get 4x.
4x+1=5
1e. Subtract 1 from both sides.
4x=5−1
1f. Subtract 1 from 5 to get 4.
4x=4
1g.Divide both sides by 4.
x=44
1h. Divide 4 by 4 to get 1.
x=1
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3. A= .5, so it is Correct. Work below
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3a. Add x to both sides.
3b. Combine 3x and x to get 4x.
3c. Subtract 3 from both sides.
3d. Subtract 3 from 5 to get 2.
3e. Divide both sides by 4.
3f. Reduce the fraction 42=0.5 to lowest terms by extracting and canceling out 2.
(A = 1/2 or .5)
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4. A= .5, so it is correct. Work below. Now we have our 2, so we don't need to do it again.
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4a. Add −1 and 4 to get 3.
4b. Add 2 and 3 to get 5.
4c. Add x to both sides.
4d. Combine 3x and x to get 4x.
4e. Subtract 3 from both sides.
4f. Subtract 3 from 5 to get 2.
4g. Divide both sides by 4.
4h. Reduce the fraction 42=0.5 to lowest terms by extracting and canceling out 2.
The 400th term is 425.
There are floor(√400) = 20 squares in the range 1..400, so the 400th term will be at least 420. There are floor(∛420) = 7 cubes in the range 1..400, so the 400th term may be as high as 427. However, there are![\lfloor\sqrt[6]{427}\rfloor=2](https://tex.z-dn.net/?f=%5Clfloor%5Csqrt%5B6%5D%7B427%7D%5Crfloor%3D2)
numbers that are both squares and cubes. Consequently, the 400th term will be 427-2 = 425.
There are floor(√400) = 20 squares in the range 1..400, so the 400th term will be at least 420. There are floor(∛420) = 7 cubes in the range 1..400, so the 400th term may be as high as 427. However, there are