Which system of equations is consistent and dependent?

Mathematics

1 answer:

Bad White [126]4 years ago

5 0

Answer: The answer is the third option

Step-by-step explanation:

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(cotx+cscx)/(sinx+tanx)

Butoxors [25]

Answer: $\bold{\dfrac{cot(x)}{sin(x)}}$

<u>Step-by-step explanation:</u>

Convert everything to "sin" and "cos" and then cancel out the common factors.

$\dfrac{cot(x)+csc(x)}{sin(x)+tan(x)}\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)}{1}+\dfrac{sin(x)}{cos(x)}\bigg)\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg[\dfrac{sin(x)}{1}\bigg(\dfrac{cos(x)}{cos(x)}\bigg)+\dfrac{sin(x)}{cos(x)}\bigg]\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)}{cos(x)}+\dfrac{sin(x)}{cos(x)}\bigg)$

$\text{Simplify:}\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)+sin(x)}{cos(x)}\bigg)\\\\\\\text{Multiply by the reciprocal (fraction rules)}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)cos(x)+sin(x)}\bigg)\\\\\\\text{Factor out the common term on the right side denominator}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)(cos(x)+1)}\bigg)$

$\text{Cross out the common factor of (cos(x) + 1) from the top and bottom}:\\\\\bigg(\dfrac{1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)}\bigg)\\\\\\\bigg(\dfrac{1}{sin(x)}\bigg)\times cot(x)}\qquad \rightarrow \qquad \dfrac{cot(x)}{sin(x)}$

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4 years ago

What is 56 as a reduced fraction?

Gala2k [10]

56 reduced as a fraction is 56/100 or 14/25

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4 years ago

Read 2 more answers

|3k-2|=2|k+2| how do I do this when the 2 is on the other side??

grin007 [14]

|3k-2|=2|k+2l
Do Distributive Property and take 2 times by everything in the parenthesis. That will leave you with |3k-2|=2k+4. Then add like terms. 3k+2k=5k. Then -2+4=2. So you end up with 5k+2. I believe I'm right. If not please tell me.

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3 years ago

Elliot spent 3/5 of his money on stereo equipment and 1/6 of the money he had left on lunch. He left the house with $24. How muc

riadik2000 [5.3K]

$24/5 = $4.8 x 3 = $14.4
$24/6 = $4 x 1 = $4
$14.4 + $4 = $18.4
$24 - $18.4 = $5.6

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3 years ago

What are the solution(s) to the quadratic equation 50 - x2 = 0?

jekas [21]

Answer:

x = $5\sqrt{2}$