Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.
Answers
Answer:
The standard form of the equation for the conic section represented by [tex]x^2\:+\:10x\:+\:6y\:=\:47[/tex] is:
[tex]4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2[/tex]
Step-by-step explanation:
We know that:
[tex]4p\left(y-k\right)=\left(x-h\right)^2[/tex] is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.
Given the equation
[tex]x^2\:+\:10x\:+\:6y\:=\:47[/tex]
Rewriting the equation in the standard form
[tex]4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2[/tex]
Thus,
The vertex (h, k) = (-5, 12)
Please also check the attached graph.
Therefore, the standard form of the equation for the conic section represented by [tex]x^2\:+\:10x\:+\:6y\:=\:47[/tex] is:
[tex]4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2[/tex]
where
vertex (h, k) = (-5, 12)
Related Questions
Arianna went to the store to buy some chicken. The prince per pound of the chicken is $5.75 per pound and she has a coupon for $3 off the final amount. With the coupon how much would arianna have to pay to buy 4 pounds of chicken
Answers
Answer:
$20
Step-by-step explanation:
If you buy 4 pounds of chicken, you multiply 5.75 times 4. That gives you $23. You have a coupon for $3 off the final amount. $23-$3 = $20.
Answer:
20
Step-by-step explanation:
(5.75x4)-3
23-3
20
PLZZZ HELP!! 22 pts!!!
Given P(A)=0.5P, (A)=0.5, P(B)=0.24, P(B)=0.24, and P(A and B)=0.2, find the value of P(A or B), rounding to the nearest thousandth, if necessary.
Answers
Work Shown:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.5 + 0.24 - 0.2
P(A or B) = 0.54
A parabola has x-intercepts of (2, 0) and (-4, 0) and has a leading coefficient of 1. What is the equation of the parabola in standard form? *
Answers
9514 1404 393
Answer:
y = x^2 +2x -8
Step-by-step explanation:
For x-intercepts p and q, factors of the parabola's equation are (x-p) and (x-q). Since the leading coefficient is 1, those are the only factors.
y = (x -2)(x -(-4))
y = (x -2)(x +4) = x(x +4) -2(x +4) . . . . use the distributive property
y = x^2 +4x -2x -8 . . . . use the distributive property again
y = x^2 +2x -8 . . . . . . . .equation in standard form
solve for x in the following question 2x - 3 = 1
Answers
Answer:
x = 2
Step-by-step explanation:
2x-3 = 1
use addition property of equality (add 3 to each side to keep balance)
2x = 4
use division property of equality (divide both sides by 2)
4/2 = 2
so,
x = 2
Please mark me brainliest, and I really hope you have a great day!
2x - 3 + 3 = 1 + 3
2x = 4
2x/2 = 4/2
X = 2
So, in conclusion, X is equal to 2.
Factorize 27x3 - 16y3
Answers
Answer:
27x3-16y3=
3x-4y
Step-by-step explanation:
I don't understand your question fully
I hope I helped you
GIVING BRAINLIEST!! PLZ HELP ME I HAVE TO FINISH BY SIX O CLOCK!!
This is number 155. Look at the picture below!
Answers
Cut= 1/36
So if victor rides for time t+ 1/36
Alex rides for t
D= 18 (t + 1/36) = 24 t
18 t+ 18/36 = 24 t
6 t = 1/2
T = 1/12 hour = 5 minutes
Marie and Jorge are both trying to lose weight. After 3 months they compared their weight loss. Marie’s weight went from 175 to 150. Jorge’s weight went from 190 to 180. Which statements are true regarding their weight loss? Select three options. WILL GIVE BRAINLIEST +20 POINTS
ill tell em to ya right now
Jorge’s weight change was approximately 5%.
Marie’s weight change was approximately 14%.
Marie had the greater percent change.
Jorge had the greater percent change.
Marie’s weight change was approximately 1.4%.
#edge2021
Answers
Answer:
1 ,2, and 3
Step-by-step explanation:
Jorge's weight percent decrease is (190-180)÷190, or amount of change/original amount. Simplified, 10÷190=5.2637157894...%, approximately equal to 5%. The first option is correct. Marie's percent decrease is (175-150)÷175. Simplified, that is 25÷175=14.2857142857...%, which is about 14%. The second option is correct. Clearly, we can tell that Marie had the greater percent change, about 14% to about 5%. Also clearly, Jorge did not have the greater percent change, so we can tell Option 4 is wrong. We already know that Jorge's change is about 5% and Marie's is about 14%, so they can't be about 0.5% or about 1.4%. Options 5 and 6 are incorrect. The correct answers are 1, 2, and 3.
Hope this helps you!
Find the circumference of each circle. Use 3.14 for pi.
6
=
Answers
Answer:
First Question: 18.84
Second Question: 12.56
Step-by-step explanation:
Factor.
y^2-12y+20
i need help
Answers
Answer:
(y−10)(y−2)
Step-by-step explanation:
Please help!! Tysm!!!!!!!!!!
Answers
the one with 9 squares with 2 filled in
25POINTS HELP!!!!!!!!!!!
Answers
The first number plus the second number equals 83, the first number
minus the second number equals 33. What are the two numbers?
Answers
Answer:
I hope this helps
Step-by-step explanation:
So the way to handle a problem like this is to rewrite the three numbers in terms of their relationship to one of the three numbers. Let's call the numbers x, y, and z, where x is the first number, y is the second, and z is the third.
We know x + y + z = 83.
Since the third number is twice the second, we say that z = 2y.
Since the second number is seven less than the first, we say that y = x - 7. We can rewrite this as x = y + 7.
Now all three can be written in terms of y.
x + y + z = 83
(y + 7) + y + 2y = 83
4y + 7 = 83
4y = 76
y = 19
The second number is 19. The first is 19 + 7 or 26, and the third is 2 times 19 or 38.
A check reveals that 26 + 19 + 38 = 83.
Continue the pattern by filling in the next 3 terms
-5, -2, 1,
Answers
Answer:
4, 7, 10
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = - 2 - (- 5) = 1 - (- 2) = 3
To obtain a term in the sequence add d = 3 to the previous term, then
a₄ = a₃ + 3 = 1 + 3 = 4
a₅ = a₄ + 3 = 4 + 3 = 7
a₆ = a₅ + 3 = 7 + 3 = 10
What is the y-intercept of the line represented by -2x + 3y = 12?
F -4
H 4
G 1/4
J 12
Answers
Answer:
The graph of 2x + 3y = 12 crosses the x-axis at (6, 0), so its x-intercept is 6. The graph of 2x + 3y = 12 crosses the y-axis at (0, 4), so its y-intercept is 4.
Step-by-step explanation:
The graph of 2x + 3y = 12 crosses the x-axis at (6, 0), so its x-intercept is 6. The graph of 2x + 3y = 12 crosses the y-axis at (0, 4), so its y-intercept is 4.
pls help me this was due a long time ago ❤️
Answers
Answer:
The second option
Denise makes three times as many chocolate cupcakes as vanilla. She makes three dozen strawberry cupcakes. Total cupcakes are 132, how many are chocolate?
Answers
Answer:
55
Step-by-step explanation:
Who does Plato for money ?
Answers
Answer:
what are you talking about the picture is not there
Step-by-step explanation:
Answer:
i ate plato for money if thats what your asking
Step-by-step explanation:
What is the area of the circle? *
10 ft
31.4 square feet
78.5 square feet
314 square feet
15.7 square feetT
Answers
Answer:
The answer is 314.159 which can be rounded to 314.
Explain the three different types of solutions you can get when solving a system of
equations.
Answers
Answer:
There are three possible outcomes for a system of linear equations: one unique solution, infinitely many solutions, and no solution.
Step-by-step explanation:
9514 1404 393
Answer:
no solutionsa finite non-zero number of solutionsinfinite solutionsStep-by-step explanation:
1. No Solutions
This case arises when the equations are inconsistent. No values of the variables can satisfy all of the equations. An example is ...
y = xy = x+1__
2. Finite Number of Solutions
The number of distinct solutions depends on the degree of the system and the domain being considered. For example, an n-th degree polynomial equation in one variable will always have n solutions in the domain of complex numbers. However, it may or may not have any real-number solutions. (The question here has no context, so we have to assume it is about any system of equations of any degree or nature (rational, polynomial, exponential, mixed, or other.))
__
3. Infinite solutions
An under-specified system, such as a system of 3 equations in 4 variables, may have an infinite number of solutions. In such a system, one or more of the variables may be allowed to assume any value. Systems that have dependent equations will fall into this category.
HELP I NEED HELP ASAP
Answers
Answer:
D
Step-by-step explanation:
6x^2 + 10x^2 = 16x^2
2x-x = x
-8 + 14 = 6
16x^2 + x + 6
Can someone help me with this??
Answers
Answer:
the second option, a=3 b=3 c=5
Step-by-step explanation:
first I would change them both into an improper fraction:
9/2 divided by 5/4
dividing is the same thing as mulitiplying by the reciprocal of the second number. so you would mulitply 9/2 x 4/5 = 36/10 and then you simplify back to a mixed number 3 6/10, 6/10 can be reduced so the final answer is 3 3/5.
please help!!! Im very confused, giving brainleist
Answers
Answer:
For the boys box, the answer is 8.
For the Girls top box the answer is 18.
Step-by-step explanation:
81/ 72=1.125
9/ 8=1.125
18/16=1.125
Hope this helps! :)
WILL MARK BRAINLIEST what is the standard deviation for the normal distribution shown at the right?
Answers
Answer: 916. Because if you do 856+60=916.
Step-by-step explanation: The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. Formula: and natural statistics x and x2. The dual expectation parameters for normal distribution are η1 = μ and η2 = μ2 + σ2.
I need help please please
Answers
Answer:
the right answer is three ok your welcome
Answer:
It is option 4
What is the slope of the line?help pls
Answers
Answer:
1
Step-by-step explanation:
Solve:
-1/4a - 4 = 4
Answers
Answer:
a = -12
Step-by-step explanation:
-1/4a - 4 = 4
(-1/4a / -1/4) - 4 = (4 / -1/4)
a - 4 = -16
(a - 4 + 4) = -16 + 4
a = -12
I might have made some mistake but if my memory is right this is how you solve it.
I will give brainiest to whoever answers right PLEASE
Answers
Answer: questions aren't clear
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. D
2.B
3.B
4.C
5.D
6.A
Martin is two years younger than three times his daughter Ada’s age. The sum of their ages is 54. If Ada’s age is given by a, then which equation below fully models in the information given in this problem?
A. 3a-2=54
B. a+(3a-2)=54
C. a+(2-3a)=54
D. a-(3a-2)=54
Answers
Answer:
A. 3a-2=54
Step-by-step explanation:
3 x her age - the 2 year will equal 54
cuál es el resultado de 3/5 - 1/2?
A._ 1/10
B._ 2/7
C._ 2/3
D._ 4/7
Answers
La respuesta es la C :
2/3
Amanda plans on going to the amusement park this Friday. It costs $25.00 to
enter the park, and then $1.25 for every ride that Amanda goes on. What will be
the total cost if Amanda goes on 9 rides?
Answers
Answer:
$36.25
Step-by-step explanation:
To enter the park, Amanda pays 25 dollars.
+$25
It costs 1.25 for every ride that Amanda goes on.
Since we don't know the number of rides Amanda goes on, we will add a variable to represent the number of rides.
1.25x
Then, the passage says that Amanda goes on 9 rides. So, substitute 9 for x.
Equation: 25+1.25(9)
Then solve:
$36.25