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
Annette [7]
3 years ago
15

Write this equation in standard form 9x^2-4y^2-24y-72=0

Mathematics
1 answer:
Xelga [282]3 years ago
4 0
9x^2-4y^2-24y-72=0\\
\\
9x^2-4y^2-24y=72\\
\\
9x^2-(4y^2+24y+36)=72-36\\
\\
9x^2-4(y+3)^2=36\\
\\
\frac{9x^2}{36}-\frac{4(y+3)^2}{36}=\frac{36}{36}\\
\\
\boxed{\frac{x^2}{4}-\frac{(y+3)^2}{9}=1}
You might be interested in
a cafe offers senior citizens a 15% discount off its regular rice of 8.95 for the dinner buffet. what percent of the regular pri
natta225 [31]

Answer: 85%

Step-by-step explanation:

The regular price is 8.95, with a 15% discount for Seniors. So the senior price would be 100%-15%=85% of the regular price.

4 0
3 years ago
I need help. Please explain the answer. Thanks!
zmey [24]

Answer:

1.25> okay your welcome

5 0
3 years ago
P(x)=5x^2-3x+7(x=1)<br> Pls
kramer

Answer:

9

Step-by-step explanation:

Given

p(x) = 5x² - 3x + 7 ← substitute x = 1

p(1) = 5(1)² - 3(1) + 7 = 5(1) - 3(1) + 7 = 5 - 3 + 7 = 9

4 0
3 years ago
Find the complex factors of the quadratic trinomial x^2 + 8x +17
Naily [24]

Answer: Factoring  x2+8x+17

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +17

Step-1 : Multiply the coefficient of the first term by the constant   1 • 17 = 17

Step-2 : Find two factors of  17  whose sum equals the coefficient of the middle term, which is   8 .

     -17    +    -1    =    -18

     -1    +    -17    =    -18

     1    +    17    =    18

     17    +    1    =    18

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

1

:

 x2 + 8x + 17  = 0

STEP

2

:

Parabola, Finding the Vertex:

2.1      Find the Vertex of   y = x2+8x+17

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -4.0000  

Plugging into the parabola formula  -4.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * -4.00 * -4.00 + 8.0 * -4.00 + 17.0

or   y = 1.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2+8x+17

Axis of Symmetry (dashed)  {x}={-4.00}

Vertex at  {x,y} = {-4.00, 1.00}  

Function has no real rootsvSolving   x2+8x+17 = 0 by Completing The Square .

Subtract  17  from both side of the equation :

  x2+8x = -17

Now the clever bit: Take the coefficient of  x , which is  8 , divide by two, giving  4 , and finally square it giving  16

Add  16  to both sides of the equation :

 On the right hand side we have :

  -17  +  16    or,  (-17/1)+(16/1)

 The common denominator of the two fractions is  1   Adding  (-17/1)+(16/1)  gives  -1/1

 So adding to both sides we finally get :

  x2+8x+16 = -1

Adding  16  has completed the left hand side into a perfect square :

  x2+8x+16  =

  (x+4) • (x+4)  =

 (x+4)2

Things which are equal to the same thing are also equal to one another. Since

  x2+8x+16 = -1 and

  x2+8x+16 = (x+4)2

then, according to the law of transitivity,

  (x+4)2 = -1

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+4)2   is

  (x+4)2/2 =

 (x+4)1 =

  x+4

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x+4 = √ -1

Subtract  4  from both sides to obtain:

  x = -4 + √ -1

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Since a square root has two values, one positive and the other negative

  x2 + 8x + 17 = 0

  has two solutions:

 x = -4 + √ 1 •  i

  or

 x = -4 - √ 1 •  i

6 0
2 years ago
Read 2 more answers
Renata and her family go through an average of more than 15 cans of sparkling water each day. They buy cases of 24 cans at $3.50
DENIUS [597]

Answer:

The inequality required to express the above condition is   x     ≥    18.75

Step-by-step explanation:

Renata and her family go through an average of more than 15 cans of sparkling water each day.

The number of cases of 24 cans of sparkling water.

We can take the number of cases to be x.

Each case is said to cost $3.50.

An inequality for the number of cases that Renata's family go through in 24 days can be written as

       x ≥ \frac{15 \times 30}{24}           ⇒     x    ≥   \frac{450}{24}         ⇒   x ≥     18.75

Therefore the inequality required to express the above condition is

x     ≥    18.75

3 0
3 years ago
Other questions:
  • What Is The Surface Area of the pyramid?
    13·1 answer
  • Can someone help me, please and thank you? I'll give BRAINLEST to the person who gets it right!!! Please have explained how to g
    13·2 answers
  • PLEASE HELP!!
    5·2 answers
  • X = 0<br> x = -1<br> x = -4<br> x = -2<br> x = 1<br> x = 2
    15·1 answer
  • Questions 15 Poge 1 of 1 Tyrone thinks his turtle walks pretty fast compared to other turtles. He wanted to figure out how fast
    10·2 answers
  • Simplify 6^9/6^3<br><br> 20 characters :/
    12·1 answer
  • A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20mph
    5·1 answer
  • Point (-7,-5) is located in which quadrant?​
    9·2 answers
  • A map with a scale of 2:in:350 mi shows two cities to be 6 inches apart. How many miles apart are the cities?
    13·1 answer
  • Help me by today please, brainliest will be given :)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!