A system of equations is made up of an ellipse and a hyperbola.
Part A: Create the equation of an ellipse centered at the origin, with a vertical major axis of 8 units and a minor axis of 6 units. Show your work. (3 points)
Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (–4, 0), and asymptotes of y equals plus or minus seven fourths x period Show your work. (4 points)
Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points)
Answers
The equation of the ellipse and the equation of the hyperbola can be
derived from the given information and the general form of the equations.
[tex]Part \, A: The \ equation \ of \ the \ ellipse \ is; \displaystyle \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1[/tex]
[tex]Part \, B: The \ equation \ of \ the \ hyperbola \ is; \displaystyle \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1[/tex]
Part C: The domain of the ellipse is; [-3, 3]
The domain of the hyperbola is; (-∞, -4]
The domains of the ellipse and the hyperbola do not intersect, therefore, the system of equation has no solution.Reasons:
Part A: The center of the ellipse = At the origin;
The vertical major axis = 8 units
The minor axis = 6 units
The general equation for an ellipse is presented as follows;
[tex]\displaystyle \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]
Where;
[tex]\displaystyle a = The \ \mathbf{ semi \ major \ axis} = \frac{8}{2} = 4[/tex]
[tex]\displaystyle b = The \ semi \ \mathbf{ minor} \ axis = \frac{6}{2} = 3[/tex]
The equation of the ellipse is therefore;
[tex]\displaystyle \underline{\frac{x^2}{3^2} + \frac{y^2}{4^2} = 1}[/tex]Part B: center of the hyperbola = The origin
The transverse axis = Horizontal
The vertex of the hyperbola = (-4, 0)
[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{ \pm\frac{7}{4} \cdot x}[/tex]
The general equation of an hyperbola is presented as follows;
[tex]\displaystyle \mathbf{\frac{x^2}{a^2} - \frac{y^2}{b^2}} = 1[/tex]
[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{\pm\frac{b}{a} \cdot x}[/tex]
The vertices = (a, 0), (-a, 0)
Therefore, by comparison, we have;
a = -4
b = -7
Which gives the equation of the hyperbola as follows;
[tex]\displaystyle \underline{ \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1}[/tex]The above equation can be written as follows;
[tex]\displaystyle \frac{x^2}{(4)^2} - \frac{y^2}{(7)^2} = 1[/tex]
Part C: Given that both equations are equal, we have;
The covertices of the ellipse are; (-3, 0) and (3, 0)
The domain of the ellipse = [-3, 3]
The domain of the hyperbola = x < The negative vertex
∴ The domain of the hyperbola = x < -4 = (-∞, -4]
The above domain of the ellipse does not extend to the hyperbola, therefore there is no solution to the system.Learn more about ellipse and hyperbola here:
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Related Questions
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Is it 95 If it is give me brainliess
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How can you tell that x and y are NOT directly proportional? A) x is 0 when y is 0. B) y is getting farther away from x. C) x is increasing by the same amount. D) y is increasing by different amounts.
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Answer:
y = 5x +7
Step-by-step explanation:
Using the hint, we have ...
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Which statement is true when looking at a black ball?
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Answer:
Only the primary color wavelengths are being absorbed by the ball.
Answer:Which statement is true when looking at a black ball?
Group of answer choices
Only the primary color wavelengths are being reflected by the ball.
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
11) y = -1x - 2
12) y = -(3/2)x + 3
13) y = 3x - 2
14) y = (3/4)x + 1
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16) y = -(2/5)x
17) y = 7x + 2
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Attached graph for 19 and 20
when the perimeter of a regular polygon is divided by 5 the lenght of a side is 25 cm what is the perimeter
Answers
Answer:
125 cmStep-by-step explanation:
when the perimeter of a regular polygon is divided by 5 the lenght of a side is 25 cm what is the perimeter?
A Regular polygon is a polygon with all sides of equal length
so
25 * 5 = 125 cm
after riding a bike 9 miles,Alex’s total time was 40 1/2 minutes. Find his time per mile.
Answers
if x is the midpoint of AB, then AX=XB?
Answers
Answer:
Yes
Step-by-step explanation:
AX is equal to XB
Gloria likes to knit scarves to give as gifts to her friends and family. She can knit 1 over 4. of a scarf in 3 over 4. of an hour. If she continues to knit at the same rate, how many hours will it take her to knit 1 scarf?
Answers
Answer:
I don't know
Step-by-step explanation:
Gloria will knit 1 scarf in 3 hours.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Gloria likes to knit scarves to give as gifts to her friends and family.
She can knit 1 over 4 of a scarf in 3 over 4 of an hour.
Simplifying,
She can knit 1/4 of a scarf in 3/4 of an hour.
To find the time:
1/4 of a scarf in 3/4 of an hour.
Multiply by 4,
4 x 1/4 of a scarf in 4 x 3/4 of an hour.
1 scarf in 3 hours.
Therefore, she will take 3 hours to knit 1 scarf.
To learn more about the multiplication;
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question 4. Write an equation of the line that passes through (1, 2) and (3,-2).
Answer in slope-intercept form
O
Answers
Answer:
y=-2x+4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-2-2)/(3-1)
m=-4/(2)
m=-4/2
m=-2
y-y1=m(x-x1)
y-2=-2(x-1)
y-2=-2x+2
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y=-2x+4
Please mark me as Brainliest if you're satisfied with the answer.
Write an Equation in Slope Intercept form for the line described:
passes through (2.5, 0) and (0, 5)
Answers
Answer:
y=-2x+5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-0)/(0-2.5)
m=5/-2.5
m=-2
y-y1=m(x-x1)
y-0=-2(x-2.5)
y=-2(x-2.5)
y=-2x+5
Please mark me as Brainliest if you're satisfied with the answer.
Make y the subject of the formula
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Answers
Answer:
[tex]\displaystyle \large{y=\frac{18+4h}{5} }\\[/tex]
Alternatively, you can use [tex]\displaystyle \large{y=\frac{18}{5}+\frac{4h}{5} }\\[/tex] as an answer.
Step-by-step explanation:
To make y as the subject of equation, we have to find a way to isolate y-variable.
First, add 4h both sides of equation which we obtain:
[tex]\displaystyle \large{5y-4h+4h=18+4h} \\\displaystyle \large{5y=18+4h}[/tex]
Next, we divide both sides by 5 so we can finally have y-isolated equation and thus it becomes the new subject of equation.
[tex]\displaystyle \large{\frac{5y}{5} =\frac{18+4h}{5} }\\\displaystyle \large{y=\frac{18+4h}{5} }[/tex]
Thus the answer is y = (18+4h)/5
Alternatively for solution, you can separate the fraction which we obtain a valid alternative solution.
[tex]\displaystyle \large{y =\frac{18}{5} +\frac{4h}{5} }\\[/tex]
Either one of these solutions work.
_______________
Let me know in the comment if you have any questions.
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Answers
Answer:
2 2/5
Step-by-step explanation:
3y=6
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Answers
But I think the slope is 0
Please correct me if I’m wrong.
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Answers
The sum of the angles of any triangle is 180°.
75° + 75° + m<BAC = 180°
m<BAC = 180° - (75° + 75°) = 30°
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Answers
Answer:
1759.6
Step-by-step explanation:
8.3 multiplied by 212 i think
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B
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0 0
Answers
Answer:
D
Step-by-step explanation:
Given Δ ABC is similar to Δ DEF then the ratios of corresponding sides are in proportion, that is
[tex]\frac{EF}{BC}[/tex] = [tex]\frac{DE}{AB}[/tex] , substitute values
[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{30}[/tex] ( cross- multiply )
30x = 5 × 42 = 210 ( divide both sides by 30 )
x = 7
The ratio remains same
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{30}{42}[/tex]
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{15}{21}[/tex]
[tex]\\ \sf\dashrightarrow 15x=105[/tex]
[tex]\\ \sf\dashrightarrow x=7[/tex]
he A water pail in your backyard has a small hole in it. You notice that it has drained a total of 1.5 liters in 4 days. What is the average change in water volume each day?
Answers
Answer:
0.375 liters per day
Step-by-step explanation:
1.5 / 4 = 0.375 liters per day
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Answer:
V = 14130 inches cubed
Step-by-step explanation:
the volume formula for a sphere is [tex]V=\frac{4}{3} \pi r^{3}[/tex]. To solve plug in the values for each part of the equation. Pi will equal 3.14, and r will equal 15.
Determine whether the lines 3x+2y=6 and 4y=-6x-12 are parallel, intersect, or coincide
Answers
Answer:
parallel
Step-by-step explanation:
3x + 2y = 6 can be written as y = -3/2x +3
4y = -6x -12 can be written as y= -3/2x-3
same slope different y intercept so parallel
Your little brother wants hot chocolate ot be 150 degrees, but you accidentally heated the water to 175 degrees. If after 5 minutes the temperature is 165 and the temperature in your house is 70 degrees, how long will your little brother have to wait to drink his hot chocolate?
Answers
Answer:
12.5 minutes
Step-by-step explanation:
it takes 5 minutes to cool 10 degrees
after ten minutes it would be 20 degrees less
then after 2.5 minutes it would be 5 degrees less
so it would take you 12.5 minutes to get 25 degrees less
We know that in 5 minutes, the temperature of the hot chocolate decreased by 10 degrees. We also know that the temperature is fixed at 70 degrees. Now, using the info given, let's solve!
=> 5 minutes = 10 degrees decrease=> 1 minute = 2 degrees decrease=> 1 minute x 12.5 = 2 x 12.5 degrees decrease=> 12.5 minutes = 25 degrees decreaseConclusion:Therefore, my little brother will have to wait for 12.5 minutes to drink his hot chocolate.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
A regular polygon has 15 sides find the size of each of its interior angles
Answers
Answer:
156°
Step-by-step explanation:
A regular polygon has 15 sides find the size of each of its interior angles
Pentadecagon
The formula for calculating the sum of interior angles is ( n − 2 ) × 180° where is the number of sides. All the interior angles in a regular polygon are equal.
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13 × 180 =
2340
we divide by the number of sides2340 : 15 =
156° is your answer
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Answer:
The solution is in the photo
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Which of the following is a solution of x2 + 2x + 4?
Answers
Answer:8x
Step-by-step explanation:
2++2=4 add x up 4 = 8x
Do you mean 2x for the first term or x^2? If the first term is 2X then the solution would be 4x+4. If the first term is not 2x but x^2 instead, then there is no solution for it
A cylinder has a height of 4 centimeters. Its volume is 12.56 cubic centimeters. What is the radius of the cylinder?
Answers
Step-by-step explanation:
hope it will help you...
Answer:
radius of cylinder = 1 cm
Step-by-step explanation:
Start with the formula for the volume of a cylinder: V = (pi)r²h, where r is the radius and h is the height. We want to solve this for the radius, r.
Dividing both sides of the Volume formula (above) by (pi)h, we get:
V
r² = -----------
(pi)h
If we now substitute 12.56 cc for V, 3.14 for pi and 4 cm for h, we get:
V 12.56 cc
r² = ---------- = ----------------- = 1 cm²
(pi)h 3.14(4 cm)
Taking the square root of both sides, we get r = 1 cm
6x6x6x8x8x8
write the following using index form
ps. I wrote 6^3 X 8^3 and it wasn't right.....where did i go wrong??
Answers
Answer:
Step-by-step explanation:
Maybe without the x or use a * instead, like:
6^38^3
or 6^3*8^3
Or maybe read the question again because your answer should be right, if not contact the administrator of the website because sometimes bugs like that can happen.
On a field trip, there were 5 girls for every 8 boys how many girls attended the 130-student field trip?
Answers
Answer:
5 / 13 is the fraction of girls on the field trip
5/13 * 130 = 50 girls on the trip
Or 10 groups of 13 and each group of 13 had 5 girls giving a total of
5 * 10 = 50 girls
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