1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nataly862011 [7]
3 years ago
11

HELLP!!

Mathematics
1 answer:
Naddik [55]3 years ago
6 0

Answer:

(x - 2)²/2² + (y + 1)²/3² = 1 ⇒ The bold values and signs are the answers

Step-by-step explanation:

* Lets revise the equation of the ellipse  

- The standard form of the equation of an ellipse with center (h , k)  

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k)

- To change the form of the equation of the ellipse to standard form we

 will using the completing square

∵ The equation of the ellipse is 9x² + 4y² - 36x + 8y + 4 = 0

- Lets collect x in bracket and y in bracket

∴ (9x² - 36x) + (4y² + 8y) + 4 = 0

- We will take a common factor 9 from the bracket of x and 4 from the

 bracket of y

∴ 9(x² - 4x) + 4(y² + 2y) + 4 = 0

- Lets make 9(x² - 4x) a completing square

∵ √x² = x ⇒ the 1st term in the bracket

∵ 4x ÷ 2 = 2x ⇒ the product of the 1st and 2nd terms

∵ 2x ÷ x = 2 ⇒ the 2nd term in the bracket

∴ The bracket is (x - 2)²

∵ (x - 2)² = x² - 4x + 4 ⇒ we will add 4 in the bracket and subtract 4

  out the bracket

∴ 9[(x² - 4x + 4) - 4] = 9[(x - 2)² - 4]

- Lets make 4(y² + 2y) a completing square

∵ √y² = y ⇒ the 1st term in the bracket

∵ 2y ÷ 2 = y ⇒ the product of the 1st and 2nd terms

∵ y ÷ y = 1 ⇒ the 2nd term in the bracket

∴ The bracket is (y + 1)²

∵ (y + 1)² = y² - 2y + 1 ⇒ we will add 1 in the bracket and subtract 1

  out the bracket

∴ 4[(y² + 2y + 1) - 1] = 4[(y + 1)² - 1]

- Lets write the equation with the completing square

∴ 9[(x - 2)² - 4] + 4[(y + 1)² - 1] + 4 = 0 ⇒ simplify

∴ 9(x -2)² - 36 + 4(y + 1)² - 4 + 4 = 0 ⇒ add the numerical terms

∴ 9(x - 2)² + 4(y + 1)² - 36 = 0 ⇒ add 36 to both sides

∴ 9(x - 2)² + 4(y + 1)² = 36 ⇒ divide both sides by 36

∴ (x - 2)²/4 + (y + 1)²/9 = 1

∵ 4 = 2² and 9 = 3²

∴ (x - 2)²/2² + (y + 1)²/3² = 1

* The standard form of the equation of the ellipse is

  (x - 2)²/2² + (y + 1)²/3² = 1

You might be interested in
kell works at an after-school program at an elementray school. on monday he work for 1.5 hours and recived 12.6 dollars, on tues
Rina8888 [55]

Answer:

Kell would make more money working 10 hours than Markio.

Step-by-step explanation:

To find how much Kell makes per hour, you have to divide how much he worked by how much he earned. So on Monday, Kell worked 1.5 hours and received 12.6 dollars. Divide 12.6/1.5 and you'll find you're answer.

Monday:   12.6/1.5=<u>8.4</u>

On Tuesday, the problem states that he worked 2.5 hours and received 21 dollars. Divide 21/2.5 and you'll find the answer.

Tuesday:     21/2.5= <u>8.4</u>

On Wednesday, the problem states that he worked 4 hours and received 33.60. Divide 33.60/4 and you'll get you're answer.

Wednesday:    33.60/4= <u>8.4</u>

So we can conclude that Kell makes $8.40 per hour.

Now the problem states, Markio gets paid 7 dollars per hour. To find the answer to the question, you have to multiply how much they make per hour times 10 hours.

Markio:  7x10=70

Kell:  8.4x10=84

So to answer the question, Kell would make more money working 10 hours.


Hope it helps!

3 0
3 years ago
Simplify: 6y + 5z + 8y – 3z
mezya [45]
Combine like terms. 6y + 8y is 14y. 5z - 3z is 2z. so the answer is 14y + 2z.
4 0
3 years ago
Read 2 more answers
. Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds
Dmitriy789 [7]
The fence must have two sides of length 45.45 ft and two sides of length 14.63

To cover each of 45.45 ft long side, he will need 45.45 /  2 = 22.7 slats which approximates to 23. So, they are 2 * 23 = 46 slats.

To cover each of 14.63 ft sides, he will need 14.63 / 2 = 7.3 which approximates to 8 (to not leave any spaces between each slat). So, they are 2 * 8 = 16 slats.

That makes 46 + 16 = 62 slats.

Answer: around 62 slats.
5 0
3 years ago
ABC is a right angled triangle right angled at B . A circle with centre O inscribed in the triangle . AB=6CM BC=8CM . Find the r
Vikki [24]

Answer:

Radius = 2 cm.

Step by step explanation:

By the Pythagoras theorem  the third side of the triangle

= sqrt (6^2 + 8^2)cm = sqrt100 = 10cm.

The formula for the radius of the circle is

r = sqrt [ (s - a)(s-b)(s-c)/ s ]  where a,b,c are side lengths and s = the semi perimeter.

Here s = ( 6+8+10) / 2 = 12

So the radius r  

= sqrt [ (12-6)(12-8)(12-10)/ 12 ]

= sqrt 4

= 2 (answer).

3 0
3 years ago
Simplify the expression (x)^3(x^3y)^2
larisa86 [58]

Answer:

A)

Step-by-step explanation:

(a^{m})^{n} = a^{mn}\\\\x^{3}*(x^{3}*y^{2})^{2}=x^{3}*(x^{3})^{2}*(y)^{2}\\\\\\=x^{3}*x^{3*2}*y^{2}\\\\\\=x^{3}*x^{6}*y{2}\\\\\\=x^{3+6}*y^{2}\\=x^{9}y^{2}

6 0
3 years ago
Other questions:
  • A rectangle has length that is 4 inches longer than its width. It’s perimeter is 36 inches. Which of the following is it’s area?
    6·2 answers
  • The ratio of the volume of fruit juice to the volume of smoothies served at a party was 4 1/2: 2.4. There were 35 liters more fr
    9·1 answer
  • In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probabi
    14·1 answer
  • Which quantity is proportional to 6⁄4?
    15·2 answers
  • Which car can travel at the slowest rate? Plz help fast
    8·2 answers
  • Four students spun a spinner with 16 equal sections, numbered 1 through 16.
    14·2 answers
  • Decide which of the two given prices is the better deal and explain why. You can buy shampoo in a ​6-ounce bottle for ​$2.29 or
    8·1 answer
  • Help please with question 7!!
    15·1 answer
  • 8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the
    8·2 answers
  • \A carpenter is making a wooden window frame that has a width of 1 inch.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!