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Levart [38]
3 years ago
10

Complete the square to put he equation in convenient form for graphing. Then graph the conic section

Mathematics
1 answer:
Maslowich3 years ago
8 0
First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.

You'll basically complete the square for two equations at the same time. Set it up like this:

(16x^2 + 96x) + (9y^2 - 18y) = 9

Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.

(x^2 + 6x) + (y^2 - 2y) = 9/144

then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.

For instance the first one will be 6/2 = 3^2 = 9

The next one will be 2/2 =1^2 = 1

Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.


(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1

Then find a common denominator on the right side of the equals sign and add them all together to get:

(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144

Factor out the two polynomials

(x+3)^2 + (y-1)^2 = 1449/144

the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
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1/2 of a bag of candy is skittles, 1/4 is m and m's, and 3/4 of the rest of it are life savers. The rest are sour patch kids. Wh
m_a_m_a [10]

Answer:

6.25%

Step-by-step explanation:

Total = 1 ; as a decimal

1/2 = skittles

1/4 = M&Ms

Skittles +M&Ms = 1/2 + 1/4 = 3/4

Remainder = 1 - \frac{3}{4}

Remainder = \frac{1}{4}

Sour patch = \frac{1}{4} *\frac{1}{4} =\frac{1}{16}

As a percentage , multiply 1/16 by 100 and it becomes 6.25%

5 0
4 years ago
Help please!<br> - Write a recursive formula for a an =12+(n−1)10.
marta [7]

Answer:

12/(n-1)=10/(n+3). 12n−1=10n+3 12 n - 1 = 10 n + 3

Step-by-step explanation:

8 0
3 years ago
If 3/2 divided by 1/4 =n , then n is between
kari74 [83]
OK, this written in numbers is

\frac{3/2}{1/4} =n

But, fractions can not divide.  So we need to multiply one by the reciprocal of the other.  The reciprocal of a fraction is itself flipped upside down.  For example, the reciprocal of 1/2 would be 2/1.  

So, we will multiply 3/2 by 4/1.  We know how to do this, it is simply 3/2*4=12/2=6.

So, the answer is n = 6.  That would be answer c, because 6 is between 5 and 7.


3 0
4 years ago
Read 2 more answers
Can someone help with this math problem
katrin [286]

Answer:

20 ft long; 12 ft wide

Step-by-step explanation:

Let   w = the width of the garden

Then l = w + 8

       A = lw

       A = (w + 8)w

=====

The sidewalk is 4 ft wide, so, for the big rectangle consisting of garden plus sidewalk:

Width   = w +8

Length = w + 16

   Area = (w + 8)(w + 16)

=====

The <em>difference</em> between the two areas is the area of the sidewalk (320 ft²).

(w + 8)(w + 16) - (w + 8)w = 320     Factor out w + 8

         (w+ 8)(w + 16 – w) = 320      Combine like terms

                     (w+ 8) × 16 = 320      Divide each side by 16

                             w + 8 = 20        Subtract 8 from each side

                                   w = 12 ft

                                    l = 12 + 8

                                   l = 20 ft

The garden is 20 ft long by 12 ft wide.

4 0
3 years ago
2 of 6
Marat540 [252]

Answer:

23.28

Step-by-step explanation:

7 0
3 years ago
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