Answer:
The slopes if the two lines will be the exact same
Step-by-step explanation:
the only way for a system of equations to have indefinitely many solutions would have to be having the same equation. same equation means same slope and y intercept
Part 3: Write the equation of and graph an ellipse.
Given the foci and vertices of an ellipse, complete the following steps.
Vertices at (4, -6 +-9)
Foci at (4, -6 +-5sqrt2)
a) What is the center of the ellipse? Explain how to determine this from the given points.
b) Write the standard equation of the ellipse. (3 points
c) What are the lengths of the major and minor axes? (2 points)
Major Axis:
Minor Axis:
d) Sketch a graph of the ellipse and label the center, foci, and the major and minor axes. (4 points)
Answer:
Step-by-step explanation:
The center is halfway between vertices, at (4, -6).
It is also halfway between foci.
:::::
The vertices are vertically aligned, so the parabola is vertical.
General equation for a vertical ellipse:
(y-k)²/a² + (x-h)²/b² = 1
with
center (h,k)
vertices (h,k±a)
co-vertices (h±b,k)
foci (h,k±c), c² = a²-b²
Apply your data and solve for h, k, a, and b.
center (h,k) = (4, -6)
h = 4
k = -6
vertices (4,-6±a) = (4,-6±9)
a = 9
foci (4,-6±c) = (4,-6±5√2)
b² = a² - c² = 9² - (5√2)² = 31
b = √31
The equation becomes
(y+6)²/81 + (x-4)²/31 = 1
:::::
length of major axis = 2a = 18
length of minor axis = 2b = 2√31
The various parts of the question needs to be answered.
Center: (4,-6)
Standard equation: [tex]\dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis: 18 units
Length of minor axis: [tex]2\sqrt{31}\ \text{units}[/tex]
Graph is attached.
EllipseThe Vertices are of the form
[tex](h,k\pm a)=(4,-6\pm 9)[/tex]
This means that the ellipse is symmetrical to the y axis.
The center of an ellipse is given by [tex](h,k)[/tex]
So, here the center is [tex](4,-6)[/tex]
[tex]a=\pm 9[/tex]
The foci are of the form
[tex](h,k\pm c)=(4,-6\pm 5\sqrt{2})[/tex]
So, [tex]c=\pm 5\sqrt{2}[/tex]
[tex]b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{9^2-(5\sqrt{2})^2}\\\Rightarrow b=\pm\sqrt{31}[/tex]
The standard equation for major axis being parallel to y axis is given by
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis is
[tex]2a=2\times 9\\ =18\ \text{units}[/tex]
Length of minor axis is
[tex]2b=2\sqrt{31}\ \text{units}[/tex]
Learn more about ellipse:
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decreases slowly
decreases quickly
increases quickly
increases slowly
Answer:
increases slowly
Step-by-step explanation:
ghehjje euheje heyru
please help on this question i will give u brainliest:
Mr. Ramirez informs the students that some of the trees they plant will not survive their first year, so the class will take precautions to monitor the trees to give them the best chance of survival.
Abby does some research and finds that, on average, 3 out of every 25 trees planted will die their first year.
Answer:
smalls
Step-by-step explanation:
Which names the figure correctly?
Group of answer choices
Lines DF and BE are parallel
Lines BD and CF are perpendicular
Lines DB and AC are intersectind
Lines FC and DB are parallel
Answer:
Step-by-step explanation:
In a garden, 1/3 of the flower are yellow,1/6 of them are pink, and 1/3 of the remaining flowers are red.If there are 120 flowers, how many are red? How many are yellow? How many are pink?
Answer:
20 Red flowers
40 Yellow flowers
20 Pink flowers
Step-by-step explanation:
1/3 of 120 is 40
1/6 of 120 is 20
40+20=60
120-60=60
Remaining=60
1/3 of 60 is 20
City Hall is planning to construct a new building. The height of each triangular-shaped face on the top of the building will be 75 feet. The diagram shows all the building dimensions.
Calculate the total area of the exterior faces of the building (do not include the base area). Show your work.
Answer:
74 630 ft
Step-by-step explanation:
85×182×4+1/2×85×75×4
Graph x + 4y = 8.
identify the x intercept
step by step explanation
Answer:
(8,0)
Step-by-step explanation:
3 - n = 9
algebra what does n =
HELP PLS THIS IS FOR STATISTICS
Step-by-step explanation:
P(A) = . 6
P(B) = . 3
P(A or B)
= P(A) + P(B)
= . 6 + .3
= . 9
Hope it will help :)❤❤
WILL MARK BRAINLELIST HELPPPP ME
Answer:
17
Step-by-step explanation:
180 - 5 - 5 = 170 : 2 = 85 : 5 = 17
9
A group of friends went to lunch. Their original bill cost $50.00, but they had a coupon for 20% off their meal. Find the discounted price (before tax and tip).
Answer: $
A sales tax of 7% was added. What was the total amount including sales tax?
Answer: $
The group chose to tip 20%. What is the total amount that their bill cost including tax and tip?
Answer: $
add 10 to p translate into algebraic expression (plss help me)
Answer:
10+p
Step-by-step explanation:
that's pretty much it
(1 p 18. Demarcus drew a pair of complementary angles. He drew one angle that had a measure of 48º. What was the measure of the other angle he drew? 42° 48° O 132° O 138°
Answer: 42
Step-by-step explanation:
Complementary angles are angles in which the sums equal 90.
90 - 48 = 42.
Will give you points and BRAINLY
Step-by-step explanation:
[tex]f(\pi) = - 3 \\ f( \frac{\pi}{2} ) = 0 \\ f( - \frac{3\pi}{2} ) = 0 \\ \: \: = 3 \cos(theta) [/tex]
Ibrahim filled a bucket with 5 7/8 gallons of water. Later, he poured out 4 5/8 gallons of the water. How much water is left in the bucket?
Answer:
1 2/8 gallons are left
Step-by-step explanation:
5 7/8 - 4 5/8= 1 2/8
please help!
Which transformation could NOT be used to prove that two circles are congruent to one another?
a dilation with a scale factor of 2
a dilation with a scale factor of 1
a reflection
a rotation
A transformation which can not be used to prove that two circles are congruent to one another is: A. a dilation with a scale factor of 2.
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is dilation?Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
In this context, we can reasonably infer and logically deduce that a dilation with a scale factor of 2 would change the size of the two circle and as such making them incongruent.
In conclusion, a dilation with a scale factor of 1, reflection and rotation can be used to congruency in two circles.
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Here is an expression: 3+ t2 1 Evaluate the expression when t is 2
Step-by-step explanation:
it would be 45 if you add it as 21 but you didn't put another symbol hope I can help :)
Can someone write down the answers pls!!!!!!!!!!
Step-by-step explanation:
6b x>=1
6c y>7
7a x>3
7b -2<=2x<6
-1<=x<3
answer:-1,0,1,2,3
a. vertical angles
b. complementary angle
c. supplementary angle
d. none of the above
Answer:
C) supplementary angles
Step-by-step explanation:
C) supplementary angles
They add up to 180.
Francisco took $20.00 to the mall. He found a DVD he wanted on sale for 18.50. The sales tax rate in his state is 8%. DOe he have enough money to buy the DVD, including tax?
A. No he need an addional $1.48
B. Yes, and he has $0.02 left over.
C. No, he need an additional $13.30.
D. Yes, and he has $1.50 left over.
In ΔDEF, the measure of ∠F=90°, FD = 33 feet, and DE = 92 feet. Find the measure of ∠D to the nearest tenth of a degree.
Answer:
69
Step-by-step explanation:
i don't know
A single six-sided die is rolled. Find the probability of rolling a seven.
Answer: there is no probability to roling a 7
Step-by-step explanation: there are only 6 sides to the die that is rolled
Please helppp ASAPPP will mark brainliest
a) SR
b) QR
c) RW and RV
RT and RS
RU and RQ
What is the slope-intercept equation for the line below?
5
(4,3)
(0, 1)
5
O A. y=2x+1
B. y=-3x+1
O C. y=-2x+1
O D. y = 2x+1
Answer:
is there a pic you could provide?
Step-by-step explanation:
The slope-intercept equation for the line is,
⇒ y = 1/2x + 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (4, 3) and (0, 1).
Now,
Since, The equation of line passes through the points (4, 3) and (0, 1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 3) / (0 - 4)
m = - 2 / - 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - 3 = 1/2 (x - 4)
⇒ y - 3 = 1/2x -2
⇒ y = 1/2x + 1
Therefore, The slope-intercept equation for the line is,
⇒ y = 1/2x + 1
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Which statement, if true, would help prove that quadrilateral
FGHJ is inscribed in Circle O and why?
Answer:
i believe its a
Step-by-step explanation:
.........
Figure A is a scale image of Figure B. Figure A: 7.2 , 4. Figure B: 3 , x. What is the value of x
Answer: 5.4
Step-by-step explanation:
Answer:
5.2
Step-by-step explanation:
Re-order the premises in each of the arguments to show that the conclusion follows as a valid consequence from the premises. It may be helpful to rewrite the statements in if-then form and replace some statements by their contrapositives. Exercises are adapted from Symbolic Logic by Lewis Carroll.
1. When I work a logic example without grumbling, you may be sure it is one I understand.
2. The arguments in these examples are not arranged in regular order like the ones I am used to.
3. No easy examples make my head ache.
4. I cant understand examples if the arguments are not arranged in regular order like the ones I am used to.
5. I never grumble at an example unless it gives me a headache. These examples are not easy.
Answer:
Step-by-step explanation:
1. If I do not grumble while doing the logic exam, then it is because I understand the questions.
2. If the arguments are not arranged in regular order, then I will not be used to these examples.
3. If my headaches, then it is probably because it is not an easy example.
4. If the arguments are not arranged in regular order like I am used to, then I will not be able to understand them.
5. If the example is not easy and I am grumbling, then it is because it is giving me a headache.
Science (from the Latin word Scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE
Answer:
?
Step-by-step explanation:
What are you even asking-
3) Find AB
B
30°
28
59
A) 24
B) 20
C)27
D) 25
The sum of a number and twice a second number is 29. The second number is ten less than three times the first number. What are the two numbers?
Also, write the two equations.
the sum of a number and twice a second number