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4 years ago

PLEASE HELP! WILL MARK BRAINLIEST!

Mathematics

1 answer:

Korolek [52]4 years ago

7 0

<h3>Answer:</h3>

y = 1644.245(1.098x); 4,598

<h3>Explanation:</h3>

A suitable graphing calculator (or spreadsheet program) can do this regression for you.

_____

<em>Comment on doing it by hand</em>

If you're going to do this by hand, you need to work with the logarithms of the values. Then find the line of best fit to those in the usual way.

The equation of the line is best written in point-slope form, with the point being the mean of x (which is 5.5) and the mean of y. The slope is the ratio of the covariance of x and y to the variance of x (which is 8.25). (Here, y refers to the logs of the numbers in your table.)

This equation for a line will give the logarithm of the market value, so will need to be put back into exponential form for comparison to the answer choices.

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3 years ago

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The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic

- Rewrite the equation in the general form,

Ax² + Bxy + Cy² + Dx + Ey + F = 0

- Identify the values of A and C from the general form.

- If A and C are nonzero, have the same sign, and are not equal

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- If A and C are equal and nonzero and have the same sign, then

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- If A and C are nonzero and have opposite signs, and are not equal

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- If either A or C is zero, then the graph is a parabola

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

(x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

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