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2 years ago

Simplify 11 to the power of negative 4 over 11 to the power of 8

Mathematics

1 answer:

AlekseyPX2 years ago

7 0

Answer:

1. 1 over 11 to the power of 12

Step-by-step explanation:

$\huge \frac{ {(11)}^{ - 4} }{ {(11)}^{8} } \\ \\ \huge = \frac{ 1}{ {(11)}^{8 + 4} } \\ \\\huge = \frac{ 1}{ {(11)}^{12} }$

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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

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

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

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2 years ago

WILL MAKE U BRAINLIEST!<br><br> Which equation can be used to solve for m∠1?

zlopas [31]

The answer is B.

This is because <span>any angle formed by two chords is equal to half the sum of intercepted arcs.</span>

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tamaranim1 [39]

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2 years ago

Solve and write multiplication equations 2/5g=3/5

Yanka [14]

Answer:

g=1.5

Step-by-step explanation:

you want to eliminates the 2/5 so you do that by dividing it by itself (since you do the opposite equation) you do this on both side (so do 2/5 divided by itself, and 3/5 divided by 2/5) getting you 1.5 therefore all you have on the left side if this equation is g so g=1.5

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3 years ago

Susan can run 2 city blocks per minute. she wants to run 60 blocks. how long will it take her to finish if she has already run 1

Brut [27]

60 blocks in 30 min
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Method 1
60-18 = 42
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Method 2
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3 years ago

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