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enot [183]
4 years ago
8

Ms. Baker was measuring yarn for a project and

Mathematics
1 answer:
laiz [17]4 years ago
7 0

Answer:

2.4/3

8 Feet of yarn

This is because we're asking of one third of the original amount so we divide it by three.

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What two rational expressions sum to 2x+3/x^2-5x+4
Anni [7]

Answer:

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

Step-by-step explanation:

Given the rational expression: \frac{2x + 3}{x^2 - 5x + 4}, to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

x^2 - 5x + 4

x^2 - 4x - x + 4

(x^2 - 4x) - (x + 4)

x(x - 4) - 1(x - 4)

(x- 1)(x - 4)

Thus, we now have: \frac{2x + 3}{(x- 1)(x - 4)}

Step 2: Apply the concept of Partial Fraction

Let,

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

Multiply both sides by (x - 1)(x - 4)

\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) = (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)

2x + 3 = A(x - 4) + B(x - 1)

Step 3:

Substituting x = 4 in 2x + 3 = A(x - 4) + B(x - 1)

2(4) + 3 = A(4 - 4) + B(4 - 1)

8 + 3 = A(0) + B(3)

11 = 3B

\frac{11}{3} = B

B = \frac{11}{3}

Substituting x = 1 in 2x + 3 = A(x - 4) + B(x - 1)

2(1) + 3 = A(1 - 4) + B(1 - 1)

2 + 3 = A(-3) + B(0)

5 = -3A

\frac{5}{-3} = \frac{-3A}{-3}

A = -\frac{5}{3}

Step 4: Plug in the values of A and B into the original equation in step 2

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

7 0
3 years ago
Chose a prize and explain your reasoning:
Ainat [17]

Answer:

1st prize

Step-by-step explanation:

Not all people use a car. Some people walk, take a bike, etc. So, if you won free gas for life, you might not be able to use it.

7 0
3 years ago
Read 2 more answers
What is the approximate volume of the cylinder?
OverLord2011 [107]
The answer would be 3,799.4 I don’t know how to get it to the nearest hundredth because I used my phone calculator but to find the answer you would take radiusxradiusxheightxpi so 11x11x10x3.14
4 0
3 years ago
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the u.s.s harry truman is an aircraft carrier that is 1,092 feet long. find the length in ft and in please help
kodGreya [7K]
The U.S.S Harry Truman is 1,092 feet (333 m) long, 257 feet (78 m) wide and is as high as a twenty-four-story building, at 244 feet (74 m)
3 0
3 years ago
Instructions: Using the image, find the distance between the points given on the graph.​
9966 [12]

Answer:

d = 2.54951

Step-by-step explanation:

For:

(X1, Y1) = (4, 2)

(X2, Y2) = (4.5, 4.5)

d = \sqrt {(4.5 - 4)^2 + (4.5 - 2)^2}

6 0
3 years ago
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