What are the coordinates of the focus of the conic section shown below?
x^2+6x-4y+5=0
Answers
Answer:
The coordinates of the focus are [tex](-3,0)[/tex]
Step-by-step explanation:
The general equation for any conic section is [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] where [tex]A[/tex], [tex]B[/tex], [tex]C[/tex], [tex]D[/tex], [tex]E[/tex], and [tex]F[/tex] are constantsIf [tex]B^2-4AC<0[/tex], the conic section is either a circle or ellipseIf [tex]B^2-4AC=0[/tex], the conic section is a parabolaIf [tex]B^2-4AC>0[/tex], the conic section is a hyperbolaSince [tex]B^2-4AC=0^2-4(1)(0)=0[/tex], the conic section is a parabola.
The standard form equation for a parabola is [tex](x-h)^2=4p(y-k)[/tex]Vertex is [tex](h,k)[/tex]Focus is [tex](h,k+p)[/tex]Directrix is [tex]y=k-p[/tex]Vertical axis is at the line [tex]x=h[/tex][tex]p\neq 0[/tex]Convert general form into standard form by completing the square:
[tex]x^2+6x-4y+5=0[/tex]
[tex]x^2+6x+5=4y[/tex]
[tex]x^2+6x+9=4y+4[/tex]
[tex](x+3)^2=4(y+1)[/tex]
Now that the equation is in the form of [tex](x-h)^2=4p(y-k)[/tex], we can see that [tex]h=-3[/tex] and [tex]k=-1[/tex] which tells us that the vertex is at [tex](-3,-1)[/tex]. To determine the coordinates of the focus, we need to solve the equation [tex]4p=4[/tex] and plug the value of [tex]p=1[/tex] into [tex](h,k+p)[/tex] to get [tex](-3,-1+1)[/tex] which is [tex](-3,0)[/tex].
In conclusion, the coordinates of the focus for the conic section are [tex](-3,0)[/tex].
Related Questions
PLEASE HELP ME SOLVE THIS!!!
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Answer:
c. m < 13
Step-by-step explanation:
13 - 7 is equal to 6 so m must be less than 13 to be less than 6.
according to Ms. Duckett, what is important to remember about finances?
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Answer:
Being financially literate helps a person to distinguish between financial decisions that will be beneficial, and that will be detrimental to their financial future. Having a plan for your finances will help you meet your short and long-term needs, without going beyond your income
Step-by-step explanation:
Ppbags where here
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Answer:
y=4x-3
Step-by-step explanation:
Answer:
DO i care... no ask your dam teacher won der why u aint pass
Step-by-step explanation:
help with this please i dont understand?
Answers
a) Evaluate the given function at each value of x. We have f(x) = 2x + 3.
• If x = -2, then
f(-2) = 2 (-2) + 3 = -4 + 3 = -1
• If x = -1, then
f(-1) = 2 (-1) + 3 = -2 + 3 = 1
• If x = 0, then
f(0) = 2 (0) + 3 = 0 + 3 = 3
and so on.
b) Kind of a silly question. Of course f(x) is a function, the instructions for part (a) say so!
But the real reason f(x) is indeed a function is that no single value of x returns more than one value of f(x).
Need help asap! I would appreciate it soo much if your answered.
Answers
Answer:
Step-by-step explanation:
The point of closest approach is on a line perpendicular to the zip line
perpendicular lines have negative reciprocal slopes, so the perpendicular line has slope (8/3)
y = (8/3)x + b
adding our known point (3, 16)
16 = (8/3)3 + b
b = 8
y = (8/3)x + 8
now find where the two lines intersect by solving two equations with two unknowns
y = (-3/8)x + 8
as the two lines have a common y intercept of 8, that is the common point
(0, 8)
The distance from (0, 8) to (3, 16) is
d = √((3 - 0)² + (16 - 8)²) = √73 = 8.5440037453...
d = 8.5 ft
Solids X and Y are similar.
X has volume 64 cm3
Y has volume 343 cm3
The surface area of X is 176 cm2
Work out the surface area of Y.
Answers
Answer:
i think surface area of Y is 539 cm²
if the length of a cuboid is 60cm and width 40cm and its surface area is 14800cm² find its height
Please Guyz I Want Full Solved Not Just Answer Please
Answers
Answer:
50 cm
Step-by-step explanation:
let x be the heigth we are looking for.
Each rectangle that covers the cuboid is the product of two dimensions [tex](60\cdot40;\ 60x;\ 40x)[/tex]
Since it's a cuboid, we assume opposite sides are equal.
So each rectangle is counted twice:
[tex]Area=2(60\cdot40+60x+40x)=14800[/tex]
Now, we just isolate x:
[tex]60\cdot40+60x+40x=7400\\2400+100x=7400\\100x=5000[/tex]
Answer:50 cm
Why does a rectangle with different side lengths have only 2 lines of symmetry?
A.
all four angles are congruent, and all four sides are congruent
B.
all four angles are congruent, and opposite sides are congruent for a horizontal and diagonal line of reflection
C.
all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection
D.
all four angles are congruent, and opposite sides are congruent for two diagonal lines of reflection that cut through different angles
Answers
Answer:
C. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection
Step-by-step explanation:
A. isn't correct because all four sides aren't congruent, only the pair of opposite sides are congruent. Sense only opposite side are congruent you can only reflect the opposite sides onto each other and not diagonally meaning B. and D. are incorrect leaving C. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection as the correct answer
What is the probability of getting an odd number on the first roll and less than 3 on the second roll? * choise 1/6 3/6 2/6 3/5
Answers
The probability of getting an odd number on the first roll and less than 3 on the second roll is 1/6.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability of getting an odd number on the first roll is 3/6
since there are three odd numbers (1, 3, 5) out of six possible outcomes (1, 2, 3, 4, 5, 6).
The probability of getting less than 3 on the second roll is 2/6, since there are two possible outcomes (1, 2) out of six.
To find the probability of both events happening, we multiply the probabilities:
P(odd on first roll and less than 3 on second roll) = P(odd on first roll) × P(less than 3 on second roll)
= (3/6)× (2/6)
= 1/6
Therefore, the probability of getting an odd number on the first roll and less than 3 on the second roll is 1/6.
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90 is 95% of what number?
Answers
Answer:
94.74
Step-by-step explanation:
Hope this helps!
Answer:
94.74
Step-by-step explanation:
The population of a slowly growing bacterial colony after t hours is given by
p(t) = 4t² + 27t + 150. Find the growth rate after 2 hours.
bacteria/hour
Submit Question
Answers
A function is an expression that defines a relationship between an independent variable and a dependent variable.
The number of bacteria colonies after 2 hours is 220.
What is a function?It is an expression that defines a relationship between an independent variable and a dependent variable.
We have,
P(t) = 4t² + 27t + 150
Where t = time
P(t) = population of a slowly growing bacteria colony after a particular time
The growth rate after 2 hours:
P(2) = 4 x (2)² + 27 x 2 + 150
P (2) = 16 + 54 + 150
P (2) = 220
Thus the number of bacteria colonies after 2 hours is 220.
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write a quadratic equation in standard form.
1. -6 and 4 are solutions
2. 2 and 5 are solutions
1 and 2 are two different problems
Answers
Answer:
1. x^2 +2x -24 = 0
2. x^2 -7x +10 = 0
Step-by-step explanation:
If you look at the factored and expanded forms of a quadratic with solutions p and q, you see ...
(x -p)(x -q) = x^2 -(p+q) +pq
The x-term coefficient is the opposite of the sum of solutions.
The constant is the product of solutions.
This knowledge lets you write down the standard form equation with no particular effort.
1. x^2 +2x -24 = 0
2. x^2 -7x +10 = 0
solve for x??????????
Answers
Answer:
x=4
Step-by-step explanation:
you take both equations, and make them equal to each other. so....
5x-6=3x+2 subtract 3x from both sides
2x-6=2 then add 6 to the other side.
2x=8 then divide 8 by 2.
X=8
Choose all the numbers that make the comparison true.
42 > __
A, 22
B, 64
C, 41
D,40
E, 40
Answers
Answer:
22, 40, 40, and 41
Step-by-step explanation:
happy to help have a nice day
Please help with this question please and thank you
Answers
Answer:
I need help with this too!!!
Step-by-step explanation:
Answer:
what does it mean?
Step-by-step explanation:
I do not understand.
1) 0.52 + 1.6 + 8.26 =
2) 1.4 + 5.98 + 9 + 0.39 =
3) 4.45 + 7 + 0.049 =
4) 12.54 – 1. 054 =
5) 0. 685 – 0. 5903 =
6) (34. 89) (0.875) =
7) (840) (0.625) =
8) 28.5 ÷ 0.87 =
9) 104 ÷ 6.4 =
Answers
Step-by-step explanation:
1 10.38
2 16.77
3 11.499
4 11.486
5 0.0947
6 30.52875
7 525
8 32.57862069
9 16.5625
=
Given f(x) = -3x – 2 and g(x) = -2x - 4, find h(x) = g(x) – f(x).
Answers
Answer:
h(x) = x - 2
Step-by-step explanation:
h(x) = -2x - 4 -(-3x - 2)
-2x - 4 + 3x + 2
x - 2
A notecard is 3 inches by 4 inches. How
long is its diagonal
Answers
Answer:
7. Is answer
Step-by-step explanation:
Because 3+4=7
This morning, Raina's car had 23.21 gallons of fuel. Now, 1.5 gallons are left. How much fuel did Raina use?
Answers
Let x represent number of gallons of fuel used
23.21 gallons = x gallons + 1.5 gallons
x = 21.6 gallons were used
The circle graph summarizes the results of a
survey of 2800 Internet users who make
purchases online. Use this graph to answer the
following question
Online Spending per Month
$0-$15 22.5%
$15-S185 59.1%
Over 185 18.4%
Find the ratio of number of respondents who
spend $0-$15 online to number of respondents
who spend $15_$185 online. Write the ratio as a
fraction with whole numbers in the numerator
and denominator.
Answers
which among the following
Answers
We have:
[tex]1-\frac{1}{3} >0[/tex] ; [tex]1- \frac{11}{17}>0[/tex] ; [tex]1-\frac{132}{157}>0[/tex] ⇒ right
[tex]\frac{-1}{7}, \frac{-51}{107},\frac{-347}{949} <0[/tex] ⇒ wrong
[tex]\frac{7}{5}, \frac{131}{47} ,\frac{945}{711} >1[/tex] ⇒ wrong
ANSWER: [tex]\frac{1}{3} ,\frac{11}{17} ,\frac{132}{157}[/tex]
ok done. Thank to me :>
In the month of January, a certain restaurant claimed it sold 9,000 burgers and expects sales to grow at a rate of
4.8% per month over the next year. Which formula will determine the number of burgers the restaurant expects to sell
this year?
Answers
Answer:
11∑N=1 9000 (1.048)^n
Step-by-step explanation:
First month = a = 9,000burgers
Common ratio = r = 1 + 0.48 = 1.048
Total number of months = n = 11; from February to December.
Formula to determine the number of burgers the restaurant expects to sell this year:
= 11∑N=1 9000 (1.048^n)
Answer:
a
Step-by-step explanation:
£2000 is invested in a bank with 3% interest per annum. work out the amount of money in the account after 2 years
Answers
Answer:
The interest is: $120.00 +2000
Step-by-step explanation:
please help ASAP! i have been struggling on this question and need help!
Answers
Answer:
841.53
Step-by-step explanation:
equation for annual intrest is
[tex]I*y^x=f[/tex]
where I is your initial amount, y is equal to [tex]1+(interest /100)[/tex]
and x is equal to the amount of years you're looking for, with f being the final balance
so for this questions, the equation is as follows
[tex]600*(1+7/100)^5=f\\600*1.07^5=f\\600*1.40255=f\\841.53=f\\[/tex]
plz help me to answer
Answers
Answer:
H=2 r=1
Step-by-step explanation:
P= 2h+4r + πr = π+8
h= π+8- πr -4r/2
(pls give brainliest if helps!)
At the beginning of a basketball season, the Panthers won 20 games out of 80 games. At this rate, how many games will they win in a normal 100-game season?
games
Answers
The answer is 25
-7f+6=116+3f
help me plss
Answers
Explanation: Know ur algebra lol
subtract 6 from both sides of the equation and simplify and your answer should be f = 55 over 2
Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths of the missing sides of figure B
A 4 sided polygon, labeled A, with sides labeled as follows: left, 15, top, 12, right, 18, bottom, 20. A smaller, 4 sided polygon, labeled b, oriented the same way, has left side labeled: 3.
Answers
Answer:
Left 3, top 2.4, right 3.6, bottom 4. Scale factor 5
Step-by-step explanation:
Determine the slope from the given graph below:
A ⇹ The slope is -7
B ⇹ The slope is−16
C ⇹ The slope is 6
D ⇹ The slope is -6
Answers
Step-by-step explanation:
although there is no graph visible here, I suspect this is the same question as I just answered twice already.
the slope is -6.
D is the right answer.
A recipe for a loaf of bread requires 2/3 cup of flour. How many cups of flour would it take to make 15 loaves of bread?
Answers
Answer:
10
Step-by-step explanation:
1 loaf if bread= 2/3 cup
15 loaves of bread= 2/3 × 15
= 10