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3 years ago

4 - 4y = -2 - 9x - 4y = -3

Mathematics

1 answer:

arsen [322]3 years ago

7 0

Answer:

x = -1/3 , y = 3/2

Step-by-step explanation:

Solve the following system:

{4 - 4 y = -2

-9 x - 4 y = -3

Express the system in standard form:

{0 - 4 y = -6

-9 x - 4 y = -3

Express the system in matrix form:

(0 | -4

-9 | -4)(x

y) = (-6

-3)

Write the system in augmented matrix form and use Gaussian elimination:

(0 | -4 | -6

-9 | -4 | -3)

Swap row 1 with row 2:

(-9 | -4 | -3

0 | -4 | -6)

Multiply row 1 by -1:

(9 | 4 | 3

0 | -4 | -6)

Divide row 2 by -2:

(9 | 4 | 3

0 | 2 | 3)

Divide row 2 by 2:

(9 | 4 | 3

0 | 1 | 3/2)

Subtract 4 × (row 2) from row 1:

(9 | 0 | -3

0 | 1 | 3/2)

Divide row 1 by 9:

(1 | 0 | -1/3

0 | 1 | 3/2)

Collect results:

Answer: {x = -1/3 , y = 3/2

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Alex_Xolod [135]

Answer:

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Step-by-step explanation:

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3 years ago

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Ulleksa [173]

5^-3 is 1/125

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For example,

9^2 = 81

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3 years ago

How do you complete the square to rewrite y= x^ -6x + 15 in vertex form

Vaselesa [24]

Vertex form of a quadratic equation is $y=a(x-h)^{2}+k$
where (h, k) is the vertex.

Our aim is to write the expression $y=x^{2} -6x+15$ in the form
$y=a(x-h)^{2}+k$

$y=x^{2} -6x+15$

$y=x^{2} -2*3*x+15$

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$y=(x-3)^{2}+6$

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3 years ago

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

motikmotik

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$