An ellipse has foci located at (2,4) and (2,16) and vertices located at (2,0) and (2,20) this ellipse is vertical
Answer:
The equation of the ellipse is [tex]\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1[/tex].
Step-by-step explanation:
The statement is incomplete, the most probable outcome may be the equation of the ellipse based on information given.
The equation of an ellipse whose major axis is vertical and is centered at a point different from origin is defined by:
[tex]\frac{(x-h)^{2}}{b^{2}} + \frac{(y-h)^{2}}{a^{2}} = 1[/tex] (1)
Where:
[tex](h,k)[/tex] - Coordinates of the center of the ellipse.
[tex](x,y)[/tex] - Coordinates of a point in the line of the ellipse.
[tex]a[/tex] - Length of the major semiaxis.
[tex]b[/tex] - Length of the minor semiaxis.
The coordinates of the center of the ellipse is midpoint of the segment between vertices, which are collinear with foci:
[tex](h,k) = \frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2}(x,y)[/tex] (1)
Where [tex]V_{1} (x,y)[/tex] and [tex]V_{2} (x,y)[/tex] are the coordinates of the vertices.
If we know that [tex]V_{1} (x,y) = (2,0)[/tex] and [tex]V_{2} (x,y) = (2, 20)[/tex], then the coordinates of the center ellipse are:
[tex](h,k) = (2, 10)[/tex]
The length of the semimajor axis can be determined by using the following vectorial expression, which is equivalent to the Pythagorean Theorem:
[tex]a = \sqrt{[(h,k)-V_{1}(x,y)]\,\bullet\,[(h,k)-V_{1}(x,y)]}[/tex] (2)
If we know that [tex](h,k) = (2, 10)[/tex] and [tex]V_{1} (x,y) = (2,0)[/tex], then the length of the semimajor axis is:
[tex]a = \sqrt{(2-2)^{2}+(10-0)^{2}}[/tex]
[tex]a = 10[/tex]
And the length of the minor semiaxis is found by means of this Pythagorean identity:
[tex]b = \sqrt{a^{2}-c^{2}}[/tex] (3)
Where [tex]c[/tex] is the length between the center and any of the foci. This distance can be found by using this vectorial formula:
[tex]c = \sqrt{[(h,k)-F_{1}(x,y)]\,\bullet\,[(h,k)-F_{1}(x,y)]}[/tex] (4)
If we know that [tex](h,k) = (2, 10)[/tex] and [tex]F_{1} (x,y) = (2,4)[/tex], then the length between the center and any of the foci is:
[tex]c = \sqrt{(2-2)^{2}+(10-4)^{2}}[/tex]
[tex]c = 6[/tex]
And the length of the minor semiaxis is:
[tex]b = \sqrt{10^{2}-6^{2}}[/tex]
[tex]b = 8[/tex]
FInally, the equation of the ellipse is [tex]\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1[/tex].
In golf, each hole has a score called par, which is the
number of strokes a good golfer should take to get the
ball in the hole. Scores that are under par are repre-
sented by a negative number. The table shows the golf
scores from team members in a golf tournament. If the
team's total score is -32, what is Curran's score?
Rose -9
Garcia -15
Curran ?
Answer:
-8
Step-by-step explanation:
Let r, g and c be the scores of, respectively, Rose, Garcia and Curran.
We know that
[tex]r + g + c = - 32 \\ r = - 9 \\ g = - 15[/tex]
Thus
[tex] - 9 - 15 + c = - 32 \\ - 24 + c = - 32 \\ c = - 8[/tex]
When ringing up a customer, a cashier needs 10 seconds to process the payment as well as 5.7 seconds to scan each item being purchased. Write an equation that shows the relationship between the items being purchased, p, and the time, t.
Answer: 5.7p + 10
Step-by-step explanation:
From the question, we are given the information that when ringing up a customer, the cashier will need 10 seconds to process the payment and 5.7 seconds to scan every item that are purchased.
The equation that shows the relationship between the items being purchased, p, and the time, t will then be:
= 5.7p + 10
Denise earns $4,500 per month plus 4% commission on her sales. One month she had sales of $50,000. What were her total earnings? • a. $50,000 • b. $2,000 • c. $6,500
Answer:
$6500
Step-by-step explanation:
Given data
Monthly Earnings= $4500
Commission= 4%
Sales= $50000
Let us find the amount of the commission
=4/100*50000
=0.04*50000
= $2000
Since the monthly earning is $4500, hence the total earning is
=2000+4500
=$6500
What is the correct factorization of
x2 - 11x + 18?
Answer:
(x-2)*(x-9)
Step-by-step explanation:
hope this helps!!
Mrs. Morales wrote a test with 15 questions covering spelling and Y vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100.
Find the distance between the two points below.
Answer:
Hi! The answer to your question is C. 4
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Dans mother bought a car for 15,000 five years ago. She wants to sell it to Dan based on 12% annual rate of depreciation. At this rate, how much will Dan pay for the car?
Step-by-step explanation:
= P [ 1-R/100 ] T
= 15000 [ 1-12/100] ⁵
= 15000 [100-12/100]⁵
= 15000 [0.88]⁵
= 15000 × 0.52773
= 7915.95..
i hope it's correct....
Can y’all put this from greatest to least?
-0.3
3
-0.9
2.91
-1.01
3, 2.91, -0.3, -0.9, -1.01,
8 m
10 m
What is the area of the triangle?*
Answer:
Step-by-step explanation:
Area = 1/2 (base) (height) I don't know what the numbers provided
represent in this problem. They colud be
the base and height or they could be two
of the three sides.
PLEASE HELP ME I'M CLUELESS!!
Answer:
352.7 m
Step-by-step explanation:
Distance from the cliff 2000m
Angle = 10°
How tall is the cliff?
We solve the above question using the trigonometric function of Tangent
tan θ = Opposite/Adjacent
Opposite = x
Adjacent = 2000m
θ = 10°
Hence:
tan 10 = x/2000m
Cross Multiply
x = tan 10 × 2000m
x = 352.65396142 m
Approximately = 352.7 m
The cliff is 352.7 m tall
b)
(-32)+(+17)+(+32)
Answer:
17
Step-by-step explanation:
-32 and 32 get cancel
and the answer is 17
At a school. Number of boys:number of girls=11:9. There are 124 more boys than girl. Work out the total number of students at the school
Answer:
Total students = 1240
Step-by-step explanation:
Given that,
Number of boys: number of girls=11:9
[tex]\dfrac{x}{y}=\dfrac{11}{9}\\\\9x=11y[/tex] ......(1)
There are 124 more boys than girls i.e.
x = 124+y .....(2)
Put the value of x from equation (2) in equation (1). So,
9(124+y) = 11y
1116 +9y = 11y
1116 = 2y
y = 558
Put the value of y in equation (2).
x = 124+558
x = 682
Total students = x+y
= 682+558
= 1240
So, there are 1240 students at the school.
Please help me with 1,2,3,4,5,6 please
Answer:
all of these are right angled triangle. so u can use pythagoras theorem, h²=p²+b²
longest side is called hypotenious (h)
and u can assume any of the remaining side as p and b as your choice
eg=
1) h=13
p=12
b=?
using pythagrous theroem
h²=p²+b²
13²=12²+b²
169= 144+b²
169-144=b²
25=b²
25 is the square root of 5 so
5²=b²
square root of each side will be cancelled so
b = 5
In this way u can solve your questione.....
Answer:
1.
[tex] {h}^{2} = {p }^{2} + {b}^{2} [/tex]
[tex] {13}^{2} \: = {12}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {13}^{2} - {12}^{2} [/tex]
[tex] {b }^{2} = 169 - 144[/tex]
[tex] {b}^{2} = 25/tex]
[tex]b = \sqrt{25} [/tex]
[tex]b = 5[/tex]
hope this helps you all of your question's is base on the formula given above
mark me as brainliest pls
whats is 2x2 given brainlest
Answer:
4
Step-by-step explanation:
A cheese pizza cost $5. Additional toppings cost $1.50 each. Write an equation in two variables that represents the cost of the pizza.
Answer:
Heres one
c = 5 + 1.5t
Step-by-step explanation:
Let t represent the number of toppings
and c represent the total cost of the pizza
Help I will be marking brainliest!! No links please!
A. 42,757.2
B. 4,750.8
C. 128,271.6
D. 256, 543. 2
Show work, if possible. Thanks❤️
Answer:
42,757.2
Step-by-step explanation:
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. You always multiply the numbers!
Please mark me brainliest!
Hey there, friend!
Here's my answer!
[tex] \colorbox{red}{A{ \colorbox{orange}{N{ \colorbox{yellow}{S{ \colorbox{blue}{W{ \colorbox{royalblue}{E{ \colorbox{cyan} {R{ \colorbox{purple}{S}}}}}}}}}}}}}: [/tex]
[tex] {\bold\green{Answer}} \green\implies\blue{\overbrace{\underbrace{\boxed{\bold\blue{A.\:42,757.2}}}}} [/tex]
B. 4,750.8
C. 128,271.6
D. 256, 543. 2
============================
[tex] \LARGE\bold\blue{\tt{SOLUTIONS}} [/tex]
First, multiply 37 and 42.8
[tex] {\bold\green{37 × 42.8 }} \green\implies\blue{\boxed{\bold\blue{1,583.6 }}} [/tex]
Second, multiply 1,583.6 and 27
[tex] {\bold\green{1,583.6 × 27}} \green\implies\blue{\boxed{\bold\blue{42,757.2}}} [/tex]
[tex] {\bold\green{Final\:answer}} \green\implies\blue{\overbrace{\underbrace{\boxed{\bold\blue{42,757.2}}}}} [/tex]
============================
That's my answer
Keep safe, friend
What is the length of the missing leg?45 and 36
Answer:
27
Step-by-step explanation:
If this is a right angle triangle, we will do this.
45^2 - 36^2 =
√729 = 27
Therefore, the missing leg = 27
Hope that helps!
Jillian wants to download a new ringtone to her cell phone. There are 954 music tones, 158 voice tones, and 63 sound effects to choose from. How many possible choices does Jillian have for her ringtone?
A.
221
B.
1,175
C.
9,496,116
D.
3,165,372
Answer:
B
Step-by-step explanation:
Just take all three numbers (954, 158, 63) then add them all up.
What is the median of the data set?
32, 37, 38, 40, 50, 52, 55, 57
A. 23
B. 40
C. 57
D. 45
Answer:
D. 45
Step-by-step explanation:
(40+50)/2 = 45
sadly my answer has deleted here
Between which two consecutive integers is each number located on a number line?
Answer:
< 0.99 <
Answer:
[tex]0 < 0.99 < 1[/tex]
Step-by-step explanation:
Given
[tex]Number = 0.99[/tex]
Required
Determine the interval which it belongs
The given number is less than 1
i.e.
[tex]0.99 < 1[/tex]
And it is greater than 0.
[tex]0.99 > 0[/tex]
So, the number is located between 0 and 1
i.e.
[tex]0 < 0.99 < 1[/tex]
how do I find the area of this shape. Please help I need to turn this in today
Answer:
A = 70 units²
Step-by-step explanation:
Since all 4 sides are congruent then figure is a rhombus
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals )
Here d₁ = 7 + 7 = 14 and d₂ = 5 + 5 = 10 , then
A = [tex]\frac{1}{2}[/tex] × 14 × 10 = 7 × 10 = 70 units²
Find the angle of the sector given the radius and the area of the sector.
Radius = 12 ft
Area of sector is 339.3 ft2
Answer:
270 degrees
Step-by-step explanation:
[tex]Area \: of \: the \: sector \\ \\ = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ 339.3 = \frac{ \theta}{360 \degree} \times 3.14 {(12)}^{2} \\ \\ 339.3 = \frac{ \theta}{360 \degree} \times 3.14 \times 144 \\ \\ \theta = \frac{339.3 \times 360 \degree}{3.14 \times 144} \\ \\ \theta = \frac{122,148\degree}{452.16} \\ \\ \theta= 270.143312 \degree \\ \\ \theta \approx \: 270\degree[/tex]
What is BC?
Pleaseee help I have no idea what I’m doing!!
Answer:
U GOT TO KNOW THE ANGLE
Step-by-step explanation:
Answer:
BC= 35
Step-by-step explanation:
trigonometry is used as its a right angle triangle, use the formula : a² + b² = c²
Both plant and animal cells have vacuoles, which is a large sac that holds food, water and waste. True True False
Answer:
True. It is true.
Answer:
True
Step-by-step explanation:
They both have vacuoles but the vacuoles are much larger in plant cells than animal cells.
HELP ME WITH 9, 11, 12
Answer:
Question 9
Name the ordered pairs in the table: 3, 4, 5, 6, 7
Ordered pairs: (1,3), (2,4), (3,5), (4,6), (5,7)
Graph the equation: the attachment
Step-by-step explanation:
I don't know how to do questions 11 and 12.
Also sorry if these aren't correct.
PLEASE HELP ASAP PLZ
also plz don’t answer if ur gonna put down random things
THIS IS MY 5TH ATTEMP PLZ NO BOTS
Answer:
dont listen to person above me . it's a scam
Can someone please tell me the formula volume of a rectangular pyramid? Plz
Find the values of x and y. Write your answers in simplest form.
Answer:
y=7
Step-by-step explanation:
x=3
please help me get the answer i’ll give you a thanks and 10 points pls
Answer:
678.4 cm^2
Step-by-step explanation:
total surface area of prism is equal to ph+2B where p represents the perimeter of the base, h the height of the prism and B the area of the base.
Firstly, we calculate the perimeter of the base. This is equal to 10 + 14 + 10 + 14, or 48.
Secondly, we must calculate the height of the prism, which is shown as 8.3.
Lastly, we must calculate the area of the base, which is 10 * 14, or 140.
We can now substitute these values into the formula, ph + 2B to find the total surface area of the prism:
ph + 2B,
(48)(8.3) + 2(140),
398.4 + 280,
678.4
This means that the total surface area of this prism is 678.4 cm^2