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3 years ago

If f(x)=|x+2| is changed to g(x)=3f(x)+4, how is the graph of the function transformed?

Mathematics

1 answer:

frozen [14]3 years ago

3 0

Answer:

download photomath it will help u with any type of math

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The equation for the ellipse given is 4x^2+9y^2-16x+18y-11

natita [175]

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

$\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) = 25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

$\dfrac{4\cdot (x - 2)^2}{36} + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}$

$\therefore \dfrac{ (x - 2)^2}{9} + \dfrac{ (y + 1)^2}{4} = \dfrac{ (x - 2)^2}{3^2} + \dfrac{ (y + 1)^2}{2^2} = 1$

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

8 0

2 years ago

find the circumference of each circle with the given radius or diameter round to the nearest tenth use 3.14 for pie r=9 cm

yuradex [85]

Answer:

$C = 2\pi (9)\\C = 56.6 cm$

Step-by-step explanation:

6 0

3 years ago

Find the quotient.<br><br> 0.15)6.435

BARSIC [14]

Answer:

42.9

Step-by-step explanation:

Remember your decimal rules when doing long division

7 0

2 years ago

Emily and Olivia are selling chocolate bars. Emily sold twice as many as Olivia. They sold a total of 48 bars. How many chocolat

Alex_Xolod [135]

Answer:

Olivia sold 16 chocolate bars and Emily sold 32.

Step-by-step explanation:

Let's set the amount of chocolate bars Olivia sold as x.

Since Emily sold twice as many, she would have sold 2x chocolate bars as a result.

Therefore, since the total is 48 bars, the equation would be $x + 2x = 48$ .

$x + 2x = 48$

$3x = 48$

$x = 16$

Hence, Olivia sold 16 chocolate bars.

Substituting the new value into the equation, we would find that Emily had sold 2x = 2(16) = 32 chocolate bars.

Checking the answer, we would find that (16 + 32) chocolate bars is indeed 48 chocolate bars, which fits the question.

Finally, we can arrive at the conclusion that Olivia sold 16 chocolate bars and Emily sold 32.

Hope this helped!

3 0

3 years ago

The graphs of the equations x^2 + y^2 =4 and y = x are drawn on the same set of axes. What is the total number of the points of

Lera25 [3.4K]

Answer:

Step-by-step explanation:

The first equation is a circle. The second equation is a line. If you make the line cross the circle, it'll really only hit 2 points.

5 0

3 years ago