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4 years ago

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

Read 2 more answers

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