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3 years ago

What is the value of x in the rhombus below?

Mathematics

1 answer:

NeX [460]3 years ago

7 0

Answer:

no rhombus?

Step-by-step explanation:

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Ezpress 3x + 11/x² + 6x + 9<br>as partial fractions,

andreev551 [17]

Answer:

$\frac{3}{x + 3} + \frac{2}{(x+3)^2}$

Step-by-step explanation:

Given

$\frac{3x + 11}{x^2 +6x + 9}$

Required

Express as partial fraction

$\frac{3x + 11}{x^2 +6x + 9}$

Expand the numerator

$\frac{3x + 11}{x^2 +3x +3x+ 9}$

Factorize

$\frac{3x + 11}{x(x +3) +3(x+ 3)}$

Factor out x + 3

$\frac{3x + 11}{(x +3)(x+ 3)}$

$\frac{3x + 11}{(x +3)^2}$

As a partial fraction, we have:

$\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}$

Take LCM

$\frac{3x + 11}{(x +3)^2} = \frac{A(x+3) + B}{(x + 3)^2}$

Cancel out (x + 3)^2 on both sides

$3x + 11 = A(x+3) + B$

Open bracket

$3x + 11 = Ax+3A + B$

By comparison, we have:

$Ax = 3x$ ===> $A = 3$

$3A + B = 11$

Substitute 3 for A

$3*3 + B = 11$

$9 + B = 11$

Solve for B

$B = 11-9$

$B =2$

Substitute: $A = 3$ and $B =2$ in

$\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}$

$\frac{3x + 11}{(x +3)^2} = \frac{3}{x + 3} + \frac{2}{(x+3)^2}$

Hence, the partial fraction is:

$\frac{3}{x + 3} + \frac{2}{(x+3)^2}$

7 0

2 years ago

What is (5^7)(5^9) as a number to a single<br> power?

Advocard [28]

Answer:

$5^{16}$

Step-by-step explanation:

Exponential rules: add the exponents

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3 years ago

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Betty bought a new dress for 30% off. The original price of the dress was 45 dollars. How much was the sale price?

wolverine [178]

It'll Most Likely Be... C. $31.50

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3 years ago

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Solve for x. 2 ( x + 1 ) = 12

Evgen [1.6K]

2 ( x + 1 ) = 12

Use distributive property:

2x + 2 = 12

Subtract 2 from both sides:

2x = 10

Divide both sides by 2:

X = 5

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3 years ago

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What is the measure of angle CBA?

Rzqust [24]

Answer:

Step-by-step explanation:

yes

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3 years ago