The vertices of an ellipse are (0,-1) and (8,-1). The endpoints of the minor axis are (4,1) and (4,-3). Write the equation of the ellipse in general form
Answer:
x^2+4y^2-8x+8y+4=0
Step-by-step explanation:
The general form of the given ellipse is x² +4y² - 8x + 8y + 4 = 0.
What is an ellipse?An ellipse can be defined as a shape that looks like an oval circle.
The equation of an ellipse is
[tex]\dfrac{\left(x - h\right)^{2}}{a^{2}} + \dfrac{\left(y - k\right)^{2}}{b^{2}} = 1[/tex]
Where (h, k) is the center a and b are the lengths of the semi-major and the semi-minor axes.
The vertices of an ellipse are (0,-1) and (8,-1).
The endpoints of the minor axis are (4,1) and (4,-3).
The following equations take into account the different properties of an ellipse:
[tex]k = -1k=−1, h^{2} = a^{2}h 2 =a 2 , \left(h - 8\right)^{2} = a^{2}[/tex]
[tex]\begin{cases} b = 2 \\ k = -1 \\ h^{2} = a^{2} \\ \left(h - 8\right)^{2} = a^{2} \end{cases}[/tex]
We get that h = 4 k = -1, a = 4, and b = 2
The standard form of the given ellipse is
[tex]\dfrac{\left(x - 4\right)^{2}}{4^{2}} + \dfrac{\left(y + 1\right)^{2}}{2^{2}} = 1[/tex]
So the general form will be as : x² +4y² - 8x + 8y + 4 = 0.
Thus, the general form of the given ellipse is x² +4y² - 8x + 8y + 4 = 0.
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Please help thank you so mich
Answer:
15w = s
Step-by-step explanation:
When you look at the graph, after one week, Michael has earned 15 dollars. So if you're trying to find the amount for w weeks, you would multiply 15 by w to get s, the amount of money in Michael's account.
Hope this helps!
Hedgehog68
Please, i need help on how to solve problems like these. I dont understand and i wasnt in class when they taught it to us. PLzzzz.Will make it the brainiest if its corrected and explaining how to solve problems like these.
Answer:
x = 20
Step-by-step explanation:
You can use Pythagorean theorem which is [tex]a^2 + b^2 = c^2[/tex]
a = 12
b = 16
and c would be x.
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
square root
c = 20 or x = 20
In order to join gymnastics after school, there is $75 on-time fee and $30 monthly fee. Which slope-intercept from equation models this situation
A. Y=30x + 20
B. Y=75x + 30
C. Y=30x + 75
D. Y= 30x
{(0, 1), (1, 4), (2, 5), (3, 7)}
not a function or function
Answer:
It's a function
Step-by-step explanation:
Emma's sister is nine years older
than Emma. Their combined ages
add up to 49. How old is Emma?
(The answer isn’t 40 bc it say that her sister is 9 years OLDER then Emma) pls help
Answer:20 I believe
Step-by-step explanation:
Answer:
yeah it should be 20 they're correct
What is the equation of the line that has a slope of 1/2 and contains the points 0,3?show work please
Answer:
Step-by-step explanation:
y - 3 = 1/2(x - 0)
y - 3 = 1/2x - 0
y = 1/2x + 3
help with these equations please!
#3, #19, and #16 please!!
Solve 4x + 8y = 16 for x.
O A. x=-8y + 4
O B. x= -2y+ 16
O C. x= -2y+ 4
D. X = 8y + 16
4x + 8y = 16
4x = 16 - 8y
4x = 4 (4 - 2y)
x = 4( 4 - 2y)/4
X = 4 - 2y
X = -2y + 4
Which ordered pair represents a reflection of the point (-3,5) across the y-axis?
Answer:
-5,6
Step-by-step explanation:
YO MOM ZZZZZZZZZZZZZZZZP
What is
y
+
3
=
7
(
x
−
2
)
y+3=7(x−2)y, plus, 3, equals, 7, left parenthesis, x, minus, 2, right parenthesis written in standard form?
Choose 1 answer:
The standard form of the given expression is 7x - y = 17
Equation of a line in standard formThe equation of line in standard form is expressed as Ax + By = C
Given the equation
y + 3 = 7(x - 2)
Expand
y + 3 = 7x - 14
y -7x = -14 - 3
-7x + y = - 17
7x - y = 17
Hence the standard form of the given expression is 7x - y = 17
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The number of patients treated in a dental office each day was recorded for 8 days. Find the mean, median, and mode for this set of numbers.
5, 25, 25, 25, 11, 20, 25, 16
a.
mean: 25, median: 22.5, mode: 19
c.
mean: 19, median: 22.5, mode: 25
b.
mean: 19, median: 25, mode: 22.5
d.
mean: 22.5, median: 19, mode: 25
Answer:
I don't understand
Step-by-step explanation:
the math team has 11 boys 10 girls and 1 coach. What is the ratio of coach to students?
Solve for a: am=n+p
Help me
Answer:
a = (n + p)/m
Step-by-step explanation:
just divide by m on both sides
hope this helped!
Please help me
Will mark as brilliant<3
Answer:
day on will be 5 day two will be 8 day 5 is 17 day 7 is 23
Step-by-step explanation:
tell weather each equation has one solution , zero solution or infinte solutions really easy : )
Answer:
several different solutions,
what is the coefficient of -2x+8=10
Step-by-step explanation:
Let's solve your equation step-by-step.
−2x+8=10
Step 1: Subtract 8 from both sides.
−2x+8−8=10−8
−2x=2
Step 2: Divide both sides by -2.
−2x−2=2−2
x=−1
Answer:
Answer:
-2
Step-by-step explanation:
The coefficient of an equation or expression is any constant that precedes a variable. So, in this case, the only variable is x, so the coefficient is the preceding number, -2.
need help ASAP ,
-40 points
Answer:
A
Step-by-step explanation:
MK and KM are the same line segment
and JKM and LMK share two angles K and M as well as the side of MK or KM making it a Side.Angle.Side
I can’t understand what the question is asking me pls help
Answer: 3/4
Step-by-step explanation:
28 members in all - 12 boys = 16 girls
12/16 = 3/4
What's the answer to this?
Answer:
3 the answer is 3
Step-by-step explanation:
Identify the domain of the function.
Answer:
Step-by-step explanation:
domain represents the numbers at the x endpoints of a graph.
on the graph we see that on the left, the line ends when x is -4
on the right, the line ends when x is 4
the domain is
-4, 4
but notice how on the left there is an open circle
this will be written with a parentheses
( -4, 4
and notice how on the right there is a closed circle
this will be written with a bracket
(-4, 4]
so the answer is C
Audrey bought a refrigerator for $266 that was originally priced at $665. What percentage is the discount?
Answer:
40.6%
Step-by-step explanation:
discount percentage:
x/y*100
266/655 *100 which is 40.6%
Hope this helps plz hit the crown :D
Katie can buy 2 lb of apples for $7. What is the unit rate for the apples?
Answer:
$3.50 per lb of apples
Step-by-step explanation:
7/2 = 3.5
Coach Burns charted the change in his runners’ 5K times from the first race of the year to the second race of the year. Which student improved the most by decreasing the time needed to run the race? PLEASE HELP IM ON A EXAM!!!
Answer:
student a
Step-by-step explanation:
i just took the exam
Seven less than 4 times the square of a number is 18. Find the two numbers.
The two numbers of seven less than 4 times the square of a number is 18 are -5/2 and 5/2
Let the unknown number be "x"
The square of an unknown number is expressed as x²4 times the square of a number is 4x²Seven less than 4 times the square of a number is 4x² - 7If the resulting expression is 18, this will be expressed as 4x² - 7 = 18
Solving the resulting expression
[tex]4x^2-7=18\\4x^2= 18+7\\4x^2=25\\x^2=\frac{25}{4}\\x=\pm \frac{5}{2}[/tex]
Hence the two numbers of seven less than 4 times the square of a number is 18 are -5/2 and 5/2
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can someone solve 8x + 38 = - 3 ( - 6 - 4x) STEP BY STEP PLEASE
Answer:
x = 5
Step-by-step explanation:
[tex]8x+38=-3(-6-4x)\\\\8x+38=18+12x\\\\8x+38-38=18-38+12x\\\\8x=12x-20\\\\8x-12x=12x-12x-20\\\\-4x=-20\\\\\frac{-4x=-20}{-4}\\\\\boxed{x=5}[/tex]
Hope this helps!
SOMEONE PLEASE ANSWER
the equation is 7x-3 over 9 > 8-2x
Answer:
solving the inequality we get [tex]\mathbf{x\geq 3}[/tex]
The graph is attached below.
Option C is correct option.
Step-by-step explanation:
We need to solve the inequality [tex]\frac{7x-3}{9}\geq 8-2x[/tex]
First we will solve the inequality to find value of x
Solving:
[tex]\frac{7x-3}{9}\geq 8-2x[/tex]
Step 1: Multiply both sides by 9
[tex]9(\frac{7x-3}{9})\geq 9(8-2x)\\7x-3\geq 72-18x[/tex]
Step 2: Adding 3 on both sides
[tex]7x-3+3\geq 72-18x+3\\7x\geq 75x-18x[/tex]
Step 3: Add 18x on both sides
[tex]7x+18x\geq 75-+18x\\25x\geq 75[/tex]
Step 4: Divide both sides by 25
[tex]\frac{25x}{25}\geq \frac{75}{25}\\x\geq 3[/tex]
So, solving the inequality we get [tex]\mathbf{x\geq 3}[/tex]
The graph is attached below.
Option C is correct option.
please help?
Find measure of angle C
Answer:
82
Step-by-step explanation:
Im pretty sure the answer is 82 as it's a striaght line and all you have to do is subtract 180-98
Please help i will mark braniliest and 30 points
If you solve the inequalty 2x < 14, the solution set is x < 7. Graph x < 7 on a number line. Which one of the listed values of x is included in x < 7
A) x=8
B) x = 7
C) x = 12
D) x= -8
Answer:
D) x = -8
Step-by-step explanation:
All the values less than 7 are included in the number line. The graph on number line is shown in figure attached. In the options given, all values in Option A, B and C are greater than 7 so these cannot be included.