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fgiga [73]
2 years ago
5

Review the work showing the first few steps in writing a partial fraction decomposition.

Mathematics
1 answer:
allochka39001 [22]2 years ago
7 0

Answer:

8/(x + 2) - 4/(x + 6)

Step-by-step explanation:

4x + 40 = Ax + 6A + Bx + 2B

Equating coefficients of x

4 = A + B      (1)

Equating constant terms:

40 = 6A + 2B    (2)

Multiply  equation (1) by -2:

-8 = -2A - 2B   .. (3)

Add (2) and (3):

32 = 4A

A = 32/4

A = 8.

4 = 8 + B

B = 4 - 8

B = -4.

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64.80-0.08=59.62

59.62 is the original price of the pants
8 0
3 years ago
Two employees are painting a boat. One uses ¾ gallon of paint each hour, one uses 1 ⅔ gallon of paint every 2 hours. How much pa
Ad libitum [116K]
<h2>Hello!</h2>

The answer is:

First employee: 3 gallons

Second employee: 3 1/3 gallons

Total: 3+3\frac{1}{3}=3+\frac{10}{3}=\frac{19}{3}

<h2>Why?</h2>

From the statement we know:

First employee uses 3/4 gallon each our, for 4 hours the will use:

\frac{3}{4}*4=\frac{12}{4}=3 gallons

Second employee uses 1 2/3 (5/3) gallon every 2 hours, meaning 5/6 gallon each hour.

\frac{5}{6}*4=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}gallons

Remember, to sum (algebraic sum) fractions we should follow the next steps:

First: Multiply both fractions denominators by each other in order to get the denominator of the new fraction.

Second: Multiply the numerator of the first fraction by the denominator of the second fraction.

Third: Multiply the denominator of the first fraction by the denominator of the second fraction.

Fourth: Sum (algebraic sum) each result and divide it into the number obtained from the first step (denominator of the new fraction).

Example:

3+\frac{1}{3} =\frac{(3*3)+(1*1)}{3*1}=\frac{9+1}{3}=\frac{10}{3}

Have a nice day!

5 0
3 years ago
Casey has n number of movies in her collection. James has 1 1/2 times as many movies as Casey. James has 42 movies. Complete the
scoundrel [369]

Answer:

n=28

Step-by-step explanation:

Casey has n number of movies. James has 1 1/2 times or 1.5n movies. Since James has 42 then 1.5n = 42. Solve for n to find Casey's. Casey has 28.


8 0
3 years ago
The mean of four positive integers is 5 . The median of the four integers is 6 . What is the mean of the largest and smallest of
lapo4ka [179]

Answer:

4.

Step-by-step explanation:

The sum of all the integers =  4 * 5 = 20.

The median is 6 so that means that the mean of the 2 middle numbers is 6.

So the sum of the largest and smallest numbers is 20 - 12 = 8.

Therefore the mean of these 2 numbers is 4.

7 0
3 years ago
write a number sentence that shows an estimate of each answer. Then write the exact answer. 1) 65 +25= 2) 259+43 = 3) 2,009 +995
Hunter-Best [27]
<span>Part 1:
65 + 25 can be estimated as 70 + 30 = 100.

The exact answer of 65 + 25 = 90.


Part 2:
259 + 43 can be estimated as 260 + 40 = 300.

The exact answer of 259 + 43 = 302


Part 3:
2,009 + 995 = can be estimated as 2,000 + 1,000 = 3,000.

The exact answer of 2,009 + 995 = 3,004.
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3 0
3 years ago
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