Answer:
30 31 33 are the three integer consective
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
https://brainly.com/question/8957529
(ii) Kolyan has $9 to spend.
Work out the total amount Kolyan spends on water and biscuits as a fraction of the $9.
Give your answer in its lowest terms.
The amount spent on water and biscuits is $5.4 and $3.6, respectively
From the question, the ratio is given as:
[tex]Biscuits : Water= 3 : 2[/tex]
Represent both proportion as a fraction
[tex]Biscuits = \frac 35[/tex]
[tex]Water= \frac 25[/tex]
Kolyhan has $9.
So, the amount spent on biscuit is:
[tex]Biscuit= \frac 25 \times 9[/tex]
[tex]Biscuit= 3.6[/tex]
The amount spent on water is:
[tex]Water = 9 - 3.6[/tex]
[tex]Water = 5.4[/tex]
Hence, the amount spent on water and biscuits is $5.4 and $3.6, respectively
Read more about ratios and proportions at:
https://brainly.com/question/18170686
Graph the system of linear equations in desmos. identify the solution to the system of linear equations.
y=1/2x+5
2x+3y=-6
Answer:
Step-by-step explanation:
The solution is the point where the lines cross: (-6,2)
Youi can also solve the equations.
y=1/2x+5
2x+3y=-6
Use the first in the second equation to find x:
2x+3y=-6
2x+3[(1/2)x + 5]=-6
2x + 1.5x + 15 = -6
3.5x = -21
x = -6
Use this in either equation to find y:
y=1/2x+5
y=1/2[-6]+5
y = 2
The answer is (-6,2)
pls add the polynomials and find degree 1. p(x) = 6x² – 7x + 2 q(x) = 6x³ – 7x +15 2.h(x) = 7x³ – 6x + 1 f(x) = 7x² + 17x – 9
First let us know about Polynomial –
The degree of a polynomial is defined as the highest power on a variable in a polynomial.Types of polynomials based on the degree–
[tex]\qquad[/tex] ☀️ Constant polynomial :-
A polynomial having 0 as its degree is known as a constant polynomial.Example : 6 (6x⁰ : degree of x : 0)
[tex]\qquad[/tex]☀️ Quadratic polynomial :-
A polynomial having 2 as its degree is known as a quadratic polynomial.Example : 3x² + 7x + 6 (3x² : degree of x : 2)
[tex]\qquad[/tex]☀️ Cubic polynomial :-
A polynomial having 3 as its degree is known as a cubic polynomial.Example : 5x³ + 3x² + 7x + 6 (5x³ : degree of x : 3)
[tex]\qquad[/tex][tex] \purple{\bf \longrightarrow (1) p(x) = 6x² – 7x + 2 + q(x) = 6x³ – 7x + 15}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 6x² – 7x + 2 + (6x³ – 7x + 15)[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 6x² + 6x² – 7x – 7x + 2 + 15[/tex]
[tex]\qquad[/tex][tex]\purple{ \bf \longrightarrow 6x³ + 6x² – 14x + 17}[/tex]
The degree of the polynomial is 3.[tex]\qquad[/tex][tex]\pink{\bf \longrightarrow (2) h(x) = 7x³ – 6x + 1 + f(x) = 7x² + 17x – 9}[/tex]
[tex]\qquad[/tex][tex]\sf \longrightarrow 7x³ – 6x + 1 + (7x² + 17x – 9)[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 7x³ + 7x² – 6x + 17x + 1 – 9[/tex]
[tex]\qquad[/tex][tex]\pink{\bf\longrightarrow 7x³ + 7x² + 11x – 8}[/tex]
The degree of the polynomial is 3.1) The degree of the polynomial is 3.
2) The degree of the polynomial is 3.
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.
Gerry purchases 12 hamburgers at a fast food restaurant for $2.25 each. For half the amount of money, he could purchase 5 buffalo chicken sandwiches. What is the “half” amount?
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
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°
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 +/- = -
Help me plz I would really appreciate it!
[tex]x = \frac{7}{9} \: \: \: y = \frac{5}{6} \\ \\ - 2y + x \\ = - 2( \frac{5}{6} ) + \frac{7}{9} \\ = - \frac{5}{3} + \frac{7}{9} \\ = \frac{ - 15 + 7}{9} \\ = \frac{ - 8}{9} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
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
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.
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:
https://brainly.com/question/16045079
How can you find approximations of square roots?
Answer:
you can do a trial and improvement
Step-by-step explanation:
A two-digit integer is randomly selected. What is the probability that its digits are
different? Express your answer as a common fraction.
Answer:
9/10
Step-by-step explanation:
There are 10 possible choices for the 2nd digit : 0, 1, 2, 3, 4, 5, 6, 7, 8 , and 9.
Whatever the first digit is, there are 9 ways to make the 2nd digit different.
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
Given below, if Xy and are congruent, what is the measure of
A. 140°
B. 280°
C. 100°
D. 80°
(it’s A. 140°)
Answer:
holi , cómo estás espero que bien bueno déjame te digo que está facil soy de México pero voy a clases de inglés y ya me la hicieron esa pregunta y es la D hojala te ayude mucho
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).
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
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
Need help homework almost due
Answer:
i dont know
Step-by-step explanation:
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!
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!
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!
Solve, 7x-5y=20
-8x-3y=12
Answer:
x=0 y=-4
Step-by-step explanation:
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
2b-3(1+b)=-3(b+7) help
Hence, 'b = -9' is the answer.
Hoped this helped
[tex]BrainiacUser1357[/tex]
Your class is learning to tie knots. Each student needs a piece of rope that is 3/6 yard long how many yards of rope are needed for the 16 students in your class.
Therefore, the class will need 8 yards.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
What is the number of Santa’s reindeer (without Rudolph!) times the number of
golden rings in the song, “The Twelve Days of Christmas”?