Answer:
I think the density is 4cm.
Hope that helps you.
Step-by-step explanation:
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)
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:
https://brainly.com/question/17193351
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Wendy went to Starbucks and spent $15.75 on coffee. She had to pay 8% in sales tax. She then wanted to tip the baristas 20%. What was her total bill with tax and tip?
20.52 is the answer Sol ed
Helppppppppppp!!!!!!!!!!!
The 20th term of the number sequence is 50
Write down the 21st term of the number sequence.
I hope this help too.
Answer:-
The linear sequence 27, 25, 23, 21, 19... is an arithmetic progression with (-2) as the common difference.
The nth term of an arithmetic progression is an=a1+(n−1)da_n=a_1+(n-1)dan=a1+(n−1)d, where ana_nan is the nth term, a1a_1a1 is the first term, d is the common difference.
In our case, n=50,a1=27,d=−2n=50, a_1=27, d=-2n=50,a1=27,d=−2 , hence, we get
a50=27+49⋅(−2);a50=27−98=−71.a_{50}=27+49\cdot(-2);\\ a_{50}= 27-98=-71. a50=27+49⋅(−2);a50=27−98=−71.
The 50th term of this sequence is (-71).
helppppppppppppppppppppppppppppp
Answer:C
Step-by-step explanation:
I seraph it up
Latisha works x hours a day.
No. of hours Demetrius works = x+1 a day.
No. of working days a week = 5
No. of hours Demetrius works weekly =
= 5(x+1)
which can also be written as 5x+5
So the c option is correct.
Pls explain how to solve it!
Answer:
a = jd
Step-by-step explanation:
We want to solve for a given that a/d = j
To do so we want to isolate a (get a by itself )
We can do this by using inverse operations.
We would want to get rid of the d
A is being divided by d.
The inverse of division is multiplication so to get rid of the d we multiply a/d by d but whatever we do to one side we must do to the other so we multiply both sides by d
a/d * d = a
j * d = jd
we are then left with a = jd
And we are done!
Answer:
a = jd
Step-by-step explanation:
We have to solve the equation for a - in other words, we have to find a in terms of d and j. Another way to think about this is that we need a by itself on one side, equal to the other two values in some sort of relationship.
So, how can we accomplish this? Well, currently a is being divided by d, so we should probably multiply both sides by d to get that d away from a. The process is shown below:
[tex]\frac{a}{d} =j[/tex]
[tex]\frac{a}{d} *\frac{d}{1} =j*d[/tex]
[tex]\frac{ad}{d} =jd[/tex]
[tex]a=jd[/tex]
And look at that! We've solved for a in terms of the other two values. If you need any more help or everything I just did was confusing or overwhelming, let me know so I can clarify. :)
What is 2/5 divided by 2/3
Answer:
0.6
Step-by-step explanation:
Trust me
PLZ mark as brainliest
Which describes how triangle D was transformed to result in similar triangle D'?
A. Dilation
B. Rotation
C. Reflection
D. Translation
Answer:
C. Reflection
Step-by-step explanation:
Hope it helps!
1)
Which of the following is not a linear equation in one variable?
(a) 32+5 = 0 (b) 3(x+y) = 0 (c) 3x+5 = 0 (d) 3y+5 = 0
Answer:
letter c is the answer
Step-by-step explanation:
hope it helps you
Answer:
The answer is Option C.) 3x+5 = 0
Step-by-step explanation:
Option A, can't be the answer. It doesn't show a linear graph. Therefore it's incorrect.
Option B, can't be the answer. It doesn't show a linear graph either. This one is also incorrect.
Option C, on the other hand, is correct because it's not a linear equation.
Option D, can't be the answer. It shows a graph, but with a squiggly line. Therefore, this one is also incorrect.
Hope this helps!
Have a nice day/night/afternoon.
(Can you mark me brainliest?)
- ❤ 7272033Alt ❤
find the indefinite integrals
Answer:
Below in bold
Step-by-step explanation:
∫ dx / (x^2√(9-x^2))
Substitute x = 3sinu and dx = 3cosu du
then the √(9-x^2) = √( 9 - 9sin^2u) = 3 cos u and u = arcsin(x/3)
= 3 ∫(csc^2 u du )/ 27
= 1/9 ∫(csc^2 u du
= -1/9 cot u
= -√9-x^2) / 9x.
Pleasee helpp
Write at least 4 key features of the graph shown below.
Answer:
There are a few key features of a graph; though I'm not exactly sure which ones are the '4 key features'
Step-by-step explanation:
There are a few key features of a graph.
- (x and y) intercepts
- Domain
- Range
- Increasing/Decreasing
- Vertex
-Max/min
- is the graph a function?
I'm not exactly sure what the 4 main key features of a graph is; since there are many features of a graph.
But I'm guessing its the
-x and y intercept
-Max/min
-Domain
-Range
The x intercept is (-15,0)
y intercept is (0,-5)
I was never properly taught how to find the domain and range of a graph, and I can't really find much about the domain and range of graphs that have no clear end to either side (continuous line) so I'm sorry, I can't really help you on that.
Answer:
Linear graph
Slope is 1/3
The y intercept is -5
The x intercept is -15
Step-by-step explanation:
The graph is a straight line graph
Slope = ∆y/∆x
= (-5 - 0)/-15-0
= -5/-15
= 1/3
Y-intercept is the value on the y-axis when x is 0
X-intercept is the value on the x-axis when y is 0
what is 174 divided by 74
Answer:
2.35
Step-by-step explanation:
Answer:
2.35
Step-by-step explanation:
I hope this helps you!
What is the number of Santa’s reindeer (without Rudolph!) times the number of
golden rings in the song, “The Twelve Days of Christmas”?
7-3x=2x-8, How do you solved for x?
Answer:
x = 3
Step-by-step explanation:
7- 3x = 2x - 8
7 = 5x - 8 Add 3x on both sides
15 = 5x Add 8 on both sides
3 = x Divide both sides by 5
Using the formula A = l w, determine the area of a rectangle when l = 3.7 and w = 4. Group of answer choices A.) 4.1 B.) 7.7 C.) 12.7 D.) 14.8
Answer:
D 14.8
Step-by-step explanation:
A=L*W which means length times width. 3.7x4= 14.8
Solve, 7x-5y=20
-8x-3y=12
Answer:
x=0 y=-4
Step-by-step explanation:
does anyone know this answer?
Answer:
2x = 40°
3x = 60°
4x = 80°
Step-by-step explanation:
2x+3x+4x = 180°
9x = 180
x = 20
SO
2x = 2(20) = 40°
3x = 3(20) = 60°
4x = 4(20) = 80°
Classify the number -5
Integer
1. Whole Number
2. Irrational Number
3. Natural Number
Answer:
1. Whole number
Step-by-step explanation:
It's a negative number, but it is not a decimal, therefore it is a whole number.
I need help with the answer to this question.
9 - 3 divided by 1/3 + 1 = ?
Will give the ranking thing to best explanation.
(sry I don’t know the name of what the ranking is called)
19
Explanation:
9-3=6
(Check your work)
3+6=9
__________________________________
6÷1/3=18
(Check your work)
(6×3=18)
__________________________________
18+1=19
Therefore,
the answer is 19!
Tell which line contains each point for triangle ABC.
the circumcenter
the orthocenter
the centroid
the incenter
5. The line that contains the circumcenter in ΔABC is: line k.
6. The line that contains the orthocenter in ΔABC is: line m.
7. The line that contains the centroid in ΔABC is: line l.
8. The line that contains the centroid in ΔABC is: line n.
What is the Circumcenter of Triangle?Circumcenter is the point where all three perpendicular bisectors of the three sides of a triangle meet and they are of equal distance from the three vertices of the triangle.
The line that contains the circumcenter in ΔABC is: line k.What is the Orthocenter of a Triangle?Orthocenter is the point in a triangle where the three altitudes that are perpendicular to the opposite sides and connect with the vertices of the triangle intersect.
The line that contains the orthocenter in ΔABC is: line m.What is the Centroid of a Triangle?The centroid of a triangle is a the point of intersection where all three medians of a triangle. Medians of a triangle connects the vertices to the midpoints of the opposite sides of a triangle.
The line that contains the centroid in ΔABC is: line l.What is the Incenter of a Triangle?The incenter of a triangle is the point in a triangle where all three angle bisectors of the vertices of a triangle.
The line that contains the centroid in ΔABC is: line n.Learn more about centers of a triangle on:
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What is an equation of a line that passes through the point
(0,3) and is perpendicular to the line whose equation is
y = 2x - 1?
-
Answer: y = -(1/2)x + 3
Step-by-step explanation:
y = 2x - 1
This is in the format of y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
Perpendicular lines have a slope that is the negative inverse of the reference line. The slope of this reference line is 2, so the slope of a perpendicular kline will be -(1/2).
This yields the equation y = -(1/2)x + b
To find the value of b, we can use the given point, (0,3) and use these values of x and y to solve for b:
y = -(1/2)x + b
3 = -(1/2)(0) + b
b = 3
The equation of a line perpendicular to y = 2x - 1 and goes through point (0,3) is:
y = -(1/2)x + 3
A teacher wants to give each student 2 pencils. A store is selling pencils in boxes of 24. If the teacher has a total of 125 students, how many boxes of pencils should he buy?
Answer:
10.41
Step-by-step explanation:
hehe
Answer:
11
Step-by-step explanation:
Total number of pencils needed = 125 × 2 = 250
Total number of boxes = [tex]\frac{250}{24}[/tex] = 10.416
the teacher need to buy 11 boxes
The letter in front of a number, showing multiplication.
A.) Combining like terms
B.) Coefficient
C.) Distributive property
D.) Like terms
4. The original price of a pair of shoes is $80 and they are on sale for $48. What is the percent of discount?
O A 32%
O B. 40%
OC. 60%
O D. 66.7%
Answer:
c
Step-by-step explanation:
80 × percent = 48
percent = 48/80
= 0.6
= 60%
By which angle measures can the regular pentagon be rotated so it maps onto itself?
Select each correct answer.
72°
90°
135°
144°
216°
300°
Answer:
hi there the answer is 72
Step-by-step explanation:
sorry but my work is on a piece of paper in front of me
To map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.
What is a regular polygon?A polygon is a geometric form with a limited number of sides that exists in two dimensions. On the sides or edges of polygons, single-direction segments are joined end to end to form a closed shape. Vertices or corners are the points at which two line segments converge to form an angle.
It is given that:
There are five sides to the pentagon.
We are known that the typical pentagon has five vertices and interior angles of 72 degrees each. Rotational symmetry is also present in a regular pentagon.
Angles are 72°,144°,216°, and 288°
Thus, to map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.
Learn more about the regular polygon here:
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How can you find approximations of square roots?
Answer:
you can do a trial and improvement
Step-by-step explanation:
Need help homework almost due
Answer:
i dont know
Step-by-step explanation:
select all values equal to -4/5
Answer:
C and E
Step-by-step explanation:
the position of the minus either up or down affects both the numerator and denominator.
but if both number have minus the minus cancels each other
Answer:
B, C, E
Step-by-step explanation:
A is -/- and therefore +
B is - -/- = -+ = -
C is -/+ = -
D is - -/+ = -- = +
E is +/- = -
On Tuesday, it snowed 15 inches in 6 hours. On Friday, it snowed 30 inches in 8 hours. On which day did it snow at a greater rate each hour? How much more per hour? please answer asap
Answer: Friday, 1.25 more per hour
Step-by-step explanation: if we take the inches it snowed and divide it by the hours, we get the rate of snowfall for one hour. 15/6=2.5 and 30/8=3.75
To get how much more we take the bigger snowfall per hour minus the smaller snowfall per hour 3.75-2.5=1.25
A two-digit number is such that the sum of its digits is 12 and the ones digit is twice its tens digit. Find the number.
Answer:
48
Step-by-step explanation:
4 plus 8 is 12 and the ones digit is double the tens digit