Which expression is equivalent to 10√5<br>A. √500<br>B.√105<br>C.√50<br>D.√15

Find the major axis for the ellipse <br> x² + 16y2-96y + 128 = 0

Softa [21]

The major axis for the ellipse, x² + 16y² - 96y + 128 = 0 is the x-axis

To answer the question, we need to write it in the standard form of the equation of an ellipse

<h3>Equation of an ellipse</h3>

The equation of an ellipse centered at (h,k) is

(x - h)²/a² + (y - k)²/b² (1) where a > b and the major axis is parallel to the x axis

Given x² + 16y² - 96y + 128 = 0, we convert it into the standard equation of an ellipse.

So, x² + 16y² - 96y + 128 = 0

Dividing through by 16, we have

x²/16 + 16y²/16 - 96y/16 + 128/16 = 0/16

x²/16 + y² - 6y + 8 = 0

Completing the square in y by adding and subtracting (-6/2)² = (-3)²

x²/16 + y² - 6y + (-3)² - (-3)² + 8 = 0

x²/16 + (y - 3)² - 9 + 8 = 0

x²/16 + (y - 3)² - 1 = 0

x²/16 + (y - 3)² = 1

x²/4² + (y - 3)²/1² = 1 (2)

Comparing equations (1) and (2), we have that a = 4 and b = 1.

Since a = 4 > b = 1, the major axis for the ellipse is the x-axis

So, the major axis for the ellipse, x² + 16y² - 96y + 128 = 0 is the x-axis

Learn more about ellipse here:

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8 0

2 years ago

When jeremy gets his allowance he agrees to save part of it his savings and expenses are in the ratio of 7:5 if his daily allowa

nignag [31]

He saves $ 1.75 each day from his allowance.

<u><em>Explanation</em></u>

The ratio of his savings and expenses is 7 : 5

Lets assume, his savings = 7x dollar and his expenses is 5x dollar

Given that, his daily allowance is $3. So....

$7x+5x=3\\ \\ 12x=3\\ \\ x=\frac{3}{12}= \frac{1}{4}= 0.25$

So, the amount of his savings each day $=7x= (7*0.25)dollar= 1.75 dollar$

8 0

3 years ago

Five less than twelve times a number is represented by:

Paraphin [41]

Option ( 1 )

.....................

5 0

3 years ago

4x-10y=-16 and -7x+20y=23 elimination

mixas84 [53]

(-5/8, 27/20) is the answer.

6 0

4 years ago

Part C

makkiz [27]

a = 1, b =14 and y-coordinate is 6 when x = 0.

Solution:

Let us first write the equation of a line.

Take the points are (2, 2) and (6, 10).

Slope of the line:

$$m=\frac{y_2-y_1}{x_2-x_1}$

$$m=\frac{10-2}{6-2}$

$$m=\frac{8}{4}$

m = 2

Point-slope formula:

$y-y_1=m(x-x_1)$

y - 10 = 2(x - 2)

y - 10 = 2x - 4

Add 10 on both sides,we get

y = 2x + 6

Equation of a line is y = 2x + 6.

To find (a, 8), substitute x = a and y = 8 in the equation,

8 = 2a + 6

Subtract 6 from both sides, we get

2 = 2a

a = 1

To find (4, b), substitute x = 4 and y = b in the equation,

b = 2(4) + 6

b = 8 + 6

b = 14

Substitute x = o in the equation.

y = 2(0) + 6

y = 6

The y-coordinate is 6 when x = 0.

7 0

3 years ago

Which expression is equivalent to 10√5A. √500B.√105C.√50D.√15