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BartSMP [9]
2 years ago
14

(Please Hurry!) Which expression is equivalent to the following complex fraction?

Mathematics
1 answer:
galben [10]2 years ago
6 0

Answer:

The expression equivalent to the given complex fraction is

\frac{-2x+5y}{3x-2y}

Step-by-step explanation:

An easy way to solve the complex fraction is to solve the numerator and denominator separately.

Numerator:

\frac{-2}{x} + \frac{5}{y}\\ = \frac{-2y + 5x}{xy}

Denominator:

\frac{3}{y} + \frac{-2}{x}\\ = \frac{3x - 2y}{xy}

Solving the complex fraction:

[\frac{-2}{x} + \frac{5}{y}] / [\frac{3}{y} + \frac{-2}{x}]\\= [\frac{-2y + 5x}{xy}] / [\frac{3x - 2y}{xy}]

=\frac{-2y + 5x}{xy} * \frac{xy}{3x - 2y}

Common terms in the numerator and denominator cancels each other(Cross multiplication) :

= \frac{-2y + 5x}{3x - 2y}

You might be interested in
Find the next number in the sequence 32, 48, 56, 60, 62
Kruka [31]

Answer: divide 2 from what you got from the last one

Step-by-step explanation:

32+16=48 so then divide 16 by 2 or subtract 8

8 0
3 years ago
Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)
zavuch27 [327]

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

4 0
2 years ago
Can someone PLEASE help? i need this done!
iren [92.7K]
It would be .43, rounded. You get this answer by taking all of the 10th graders (14) and looking at how many prefer sporting events (6). Then, you simply form a decimal from 6/14, and that comes out to .428, and .43 rounded up. I hope this helps! :) 
3 0
3 years ago
A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and
mr Goodwill [35]

Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

\mu = \frac{3X_{1} + 4X_{2}  }{8}

Now

Bias for the estimator = E(μ bar) - μ

                                    = E( \frac{3X_{1} + 4X_{2}  }{8}) - 4.5

                                    = \frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5

                                    = \frac{3(4.5) + 4(4.5)}{8} - 4.5

                                    = \frac{13.5 + 18}{8} - 4.5

                                    = \frac{31.5}{8} - 4.5

                                    = 3.9375 - 4.5

                                    = - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

                                                             = Var(μ bar) + [Bias(μ bar, μ)]²

                                                             = Var( \frac{3X_{1} + 4X_{2}  }{8}) + 0.3136

                                                             = \frac{1}{64} Var( {3X_{1} + 4X_{2}  }) + 0.3136

                                                             = \frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})]  }) + 0.3136

                                                             = \frac{1}{64} [{3(57.76) + 4(57.76)}]  } + 0.3136

                                                             = \frac{1}{64} [7(57.76)}]  } + 0.3136

                                                             = \frac{1}{64} [404.32]  } + 0.3136

                                                             = 6.3175 + 0.3136

                                                              = 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

6 0
3 years ago
I don't know how to solve it.
Nataly [62]

Step-by-step explanation:

Take the first derivative

\frac{d}{dx} ( {x}^{3}  - 3x)

3 {x}^{2}  - 3

Set the derivative equal to 0.

3 {x}^{2}  - 3 = 0

3 {x}^{2}  = 3

{x}^{2}  = 1

x = 1

or

x =  - 1

For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).

For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.

Since we are going to Positve to negative slope, we have a local max at x=-1

Plug in -1 for x into the original function

( - 1) {}^{3}  - 3(  - 1) = 2

So the local max is 2 and occurs at x=-1,

For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.

Since we are going to decreasing to increasing, we have minimum at x=1,

Plug in 1 for x into original function

{1}^{3}   - 3(1)

1 - 3 =  - 2

So the local min occurs at -2, at x=1

8 0
1 year ago
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