An elliptical mirror measures 20 inches wide and 24 inches high. The ellipse is centered at (0, 60) on a coordinate plane, where units are in inches. Which equation represents the mirror?
Answers
The height and width of the outline (perimeter) of the mirror, as well as the
center in relation to the plane of the edges are given.
[tex]\displaystyle The \ mirror \ can \ be \ \mathbf{ represented} \ by \ the \ equation; \underline{\frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}[/tex]
Reasons:
Width of the elliptical mirror = 20 inches
Height of the elliptical mirror = 24 inches
Center of the ellipse = (0, 60)
The equation of an ellipse is; [tex]\displaystyle \mathbf{\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2}} = 1[/tex]
Where;
(h, k) = Coordinates of the center;
a = Semi major axis
b = Semi minor axis
In the mirror, we have;
(h, k) = (0, 60)
a = 24 ÷ 2 = 12
b = 20 ÷ 2 = 10
Which gives;
[tex]\displaystyle \frac{(x - 0)^2}{10^2} + \frac{(y - 60)^2}{12^2} = \frac{x ^2}{100} + \frac{(y - 60)^2}{144} = \mathbf{\frac{(y - 60)^2}{144} + \frac{x^2}{100}} = 1[/tex]
Therefore;
[tex]\displaystyle The \ equation \ that \ represent \ the \ mirror \ is; \underline{ \frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}[/tex]
Learn more about the equation of an ellipse here:
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Related Questions
Which of the following is a solution of 4x + 3x = 12?
(a) (4,0)
(b) (3,0)
Answers
Answer:
B
Step-by-step explanation:
Given equation is 4x+3y = 12
(3,0) is a solution because
LHS =
⇛ 4(3)+3(0)
⇛ 12+0
⇛ 12
⇛ RHS
LHS = RHS
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Which is a solution to the equation y=12-3x A.(4,3) C.(4,0) B.(-4,4) D.(0,4)....
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Mark has a certain amount budgeted for dining out each month. Last month, the difference between the amount he budgeted and the amount he actually spent on dining out was less than -20 dollars.
Which of the following best describes this situation?
A.
Mark is under his budget by less than 20 dollars.
B.
Mark is under his budget by more than 20 dollars.
C.
Mark is over his budget by less than 20 dollars.
D.
Mark is over his budget by more than 20 dollars.
Answers
how do i solve for this?
Answers
Answer:
see explanation
Step-by-step explanation:
(16)
The mid segment ZW is half the sum of the parallel bases
ZW = [tex]\frac{38+20}{2}[/tex] = [tex]\frac{58}{2}[/tex] = 29
(17)
The lower base angles are congruent , so
∠ UYX = ∠ VXY = 35°
(18)
Any lower base angle is supplementary to any upper base angle , then
∠ VUY = 180° - ∠ UYX = 180° - 35° = 145°
(19)
[tex]\frac{UV+XY}{2}[/tex] = ZW
[tex]\frac{3x-1+7x+1}{2}[/tex] = 10 ( multiply both sides by 2 to clear the fraction )
10x = 20 ( divide both sides by 10 )
x = 2
Then
XY = 7x + 1 = 7(2) + 1 = 14 + 1 = 15
(20)
The legs are congruent , so
UY = VX
5a - 6 = 3a + 2 ( subtract 3a from both sides )
2a - 6 = 2 ( add 6 to both sides )
2a = 8 ( divide both sides by 2 )
a = 4
Which statement is true about the value of 1-5/?
O It is the distance that -5 is from 0 on the number line.
O It is the distance that -5 is from 5 on the number line.
O It is less than 5.
0 It is greater than 5.
Answers
Answer:
O It is less than 5.
Step-by-Step
OK so, first u check if it has a negative. It does, so its at the left of 0. SO you know its less than.
5^2 x 5^2 20 80 625 425
Answers
Consider this diagram of quadrilateral ABCD, which is not drawn to scale.
Answers
Answers: Choice B and Choice D.
[tex]\angle ABE \cong \angle CDE[/tex] and [tex]\overline{AE} \cong \overline{CE}[/tex]
=====================================================
Explanation:
The tickmarks tell us which segments are congruent to one another. The segments with single tickmarks show that AE and CE are the same length. So this is why [tex]\overline{AE} \cong \overline{CE}[/tex]
---------------
The two triangles AEB and CED can be proven congruent through the use of the SAS theorem. From there, use CPCTC to conclude that the corresponding angles ABE and CDE are the same measure i.e. [tex]\angle ABE \cong \angle CDE[/tex]. They are alternate interior angles which helps lead to side AB being parallel to CD.
Answer:
B & D or <ABE=<CDE, AE=CE
Step-by-step explanation:
I got it right on khan
Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point. You must show all your work
3x + y = -2
y = 2x +3
Answers
The substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
A system of linear equation is a group of one or more linear equations which can be solved by using a simultaneous equation or elimination method.
From the information given;
3x + y = -2 ----- (1)
y = 2x +3 ----- (2)
By using substitution method, we will replace the value of equation (2) into equation (1), by doing so, we have:
3x + (2x + 3) = -2
3x + 2x + 3 = -2
5x + 3 = -2
5x = -2 - 3
5x = - 5
x = -5/5
x = -1
From equation (2), let's replace the value of x = - 1 into equation (2);
y = 2x + 3
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
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Find the Value for X,Y and z using Gauss-Jordan Inversion method
2X+3Y=4
X+2Y=2
Answers
Answer:
x = 2 y = 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
product of (x+2y^2)(2x-2y^2)
Answers
Answer:
Step-by-step explanation:
(x + 2y²)(2x - 2y²)
FOIL
First
x(2x) = 2x²
Outside
x(-2y²) = - 2xy²
Inside
2y²(2x) = 4xy²
Last
2y²(-2y²) = - 4y⁴
combine like terms
2x² + 2xy² - 4y⁴
Answer:
-4y^4 + 2xy^2 + 2x^2
Step-by-step explanation:
(x + 2y^2) (2x - 2y^2)
x(2x) + x(-2y^2) = 2x^2 - 2xy^2
2y^2(2x) + 2y^2(2y^2) = 2xy^2 + 4y^4
2x^2 - 2xy^2 + 4xy^2 - 4y^4
2x^2 + 2xy^2 - 4y^2
or
-4y^4 + 2xy^2 + 2x^2
A courtyard has the shape of a rectangle 45 ft and 28 ft wide. How long is a sidewalk from one corner diagonally to the opposite corner?
56 ft
47 ft
50 ft
53 ft
Answers
Answer:
53
Step-by-step explanation:
We use the pythagorean theorem, a^2 + b^2 = c^2. We can fill a and b for 45 and 28. 45^2 is 2025, and 28^2 is 784. Adding them up gives us 2809. The square root of 2809 is 53.
Solve for x (13x + 2) (5x - 7) (3x - 4)
Thank you
Answers
[tex]\huge \bf༆ Answer ༄[/tex]
As we know, sum of interior angles of a triangle is 180°
that is ~
[tex] \sf13x + 2 + 5x - 7 + 3x - 4 = 180[/tex][tex] \sf21x - 9 = 180 [/tex][tex] \sf21x = 180 + 9[/tex][tex] \sf x = \dfrac{189}{21} [/tex][tex] \sf x = 9 \degree[/tex]
Hence, value of x is 9°
Answer:
x = 9Step-by-step explanation:
Sum of interior angles is 180:
(13x + 2) + (5x - 7) + (3x - 4) = 18021x - 9 = 18021x = 189x = 189/21x = 9Is 7,301,771 divisible by 6?
Answers
[tex]\huge\boxed{Hi\: there!}[/tex]
[tex]\huge\mathfrak{Question:}[/tex]
Is 7,301,771 divisible by 6?
[tex]\huge\mathfrak{Answer:}[/tex]
No.
Remember, divisible by means the given number can be divided by a number without a remainder.
If we divide 7,301,771 by 6, we will get a remainder.
[tex]\huge\boxed{Therefore,\: 7,301,771 \: isn't \: divisible\: by 6.}[/tex]
[tex]\huge\mathfrak{Good\: luck!}\\\huge\bold {~CheerfulTeen}[/tex]
Simplify 1/3 (5x-8)+2/3x
Answers
Answer:
7x-8
3
Step-by-step explanation:
Answer:
2 1/3x - 2 2/3
Step-by-step explanation:
1/3 x 5
1/3 x -8
and add 2/3x to the mix
so
1 2/3x - 2 2/3x + 2/3x = 2 1/3x - 2 2/3
square root of the quantity x minus 3 end quantity plus 5 equals x
Answers
Answer:
x =1 if understood it correctly
Step-by-step explanation:
What’s the 16th term for 32,27,22,17
Answers
Answer:
-43
Step-by-step explanation:
By staring at it for a while you can tell that you're losing 5 every step. You can write the succession as [tex]a_n = 32-5n[/tex] (please notice the first terms starts when [tex]n=0[/tex], not 1!). The 16th term happens at [tex]n=15[/tex]:
[tex]a_1_5=32-5(15) = -43[/tex]
whats -6-10k if k=-1
Answers
Answer:
The answer would be 4
Step-by-step explanation:
Calculate it
Answer:
4 is the answer.
Step-by-step explanation:
-6 - 10k
=> -6 - 10(-1)
=> -6 + 10
=> 4
Therefore, 4 is the answer.
Hoped this helped.
Find the values of x and y
Answers
Answer:
x = 25, y = 19
Step-by-step explanation:
The external angle is supplementary to the adjacent internal angle.
2x +130 = 180
2x = 50 . . . . . . . subtract 130
x = 25 . . . . . . . divide by 2
__
The external angle is equal to the sum of the remote internal angles.
130 = 54 +4y
76 = 4y . . . . . . . subtract 54
19 = y . . . . . . . divide by 4
the hoover dam is 725 feet tall. how long would it take an object to fall from the top to the base of the dam? round the answer to two decimal places
Answers
Answer:
45.05 seconds
Step-by-step explanation:
Use the formula: d = v[tex]i[/tex] t + [tex]\frac{1}{2}[/tex] a[tex]t^{2}[/tex]
d = distance v[tex]i[/tex] = initial velocity (m/s)
t = time (s) a = acceleration (m/[tex]s^{2}[/tex])
m is meters and s is seconds. They are units of measurement so leave them be.
Assuming the object is simply dropped, the initial velocity is 0 since the object was not moving before it was dropped.
The distance is 725 feet, which is 220.98 meters.
The acceleration is 9.81m/[tex]s^{2}[/tex] since that is the acceleration of Earth's gravity, aka free fall.
Time is what we are trying to find so just leave it as the variable t.
So plug the values into the equation:
220.98m = (0)(t) + [tex]\frac{1}{2}[/tex] (9.81m/[tex]s^{2}[/tex])(t)
220.98m = (4.905m/[tex]s^{2}[/tex])(t)
45.0519877676s = t
t = 45.05s
Remember to pay attention to units because your answer will be wrong otherwise
Evaluate the expression
“-8.56x + 31.7 for x= 75.6”
A. -615.436
B. 614.436
C. 615.436
D. -614.436
Answers
Answer:
Substitute
Step-by-step explanation:
x=75.6
-8.56(75.6) + 31.7=-615.436
Answer: -615.436
What is the number that is greater than 0.13 but smaller than 0.131
Answers
Answer:
any number between the two
for example: 0.1309, 0.1308, 0.1301, etc.
Step-by-step explanation:
hope this helped :)
Step-by-step explanation:
0.1308, 0.1309, 0.1301
need help with math probelem i will give you 5 stars and a good rating
Answers
Answer:
8 feet
Step-by-step explanation:
12 x 2 =24
40 - 24 = 16
16 /2 = 8
Hope it helps :)
Find NMC triangle's perimeter if BO:BK=1:3 and ABC triangle's perimeter is 96
Answers
Answer:
80
Step-by-step explanation:
If we assume the triangles are similar and are isosceles, and that BK is an altitude, then we can work the problem.
Triangle OKN will be similar to triangle BKA, so ...
AN : AK = BO : BK = 1 : 3
Then ...
AN : AK : KC = 1 : 3 : 3
In terms of ratio units, ...
AN = 1
AC = 3+3 = 6
NC = 6-1 = 5
This means NC : AC = 5 : 6. The triangle perimeters will have the same ratio.
perimeter(NMC) = 5/6·perimeter(ABC) = 5/6·96
perimeter(NMC) = 80
Sara earns a basic salary of 14250 every month with an additional 12% commission on her sales. If Sara sold items worth AED 22264 last month, what was her total pay?
a. AED 16921.68
b. AED 24935.68
c. AED 1710
d. AED 2671.68
Answers
Answer:
A
Step-by-step explanation:
Commission: 22264*0.12=2671.68
Total pay: 14250+2671.68=16921.68
The total pay of Sara after adding the commission is: Option A: AED 16921.68
How to find the net income?Sara's total pay consists of her basic salary plus the commission on her sales.
Basic salary = AED 14250
Commission on sales = 12% of AED 22264
Commission = 0.12 * 22264
Now, calculate the commission:
Commission = 0.12 * 22264 = AED 2671.68
Total pay = Basic salary + Commission
Total pay = 14250 + 2671.68 = AED 16921.68
So, Sara's total pay is AED 16921.68
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#SPJ3
Help help help help help help math math
Answers
Answer:
4x+14 = 2(2x+7}
12x+6=6{2x+1}
I’m confused with this question I need helppp please
Answers
It's the first one
I hope this help :)
Answer:
B. I and II
More Information:Function :
A special relationship where each input has a single output.
whats -3u + 5 if u=2
Answers
Answer:
-1
Step-by-step explanation:
-3(2) = -6 + 5 = -1
Answer:
-1
Step-by-step explanation:
-3u + 5 =?
when u=2
= -3(2) + 5
= -6 + 5
= -1
Three more than the product of 24 and Matt's height
Answers
Answer:
24m + 3 or (24 × m) + 3
Step-by-step explanation:
product = multiplying
matts height = variable
more than = addition
add together and that's your algebraic expression hope this helps :)
How do you do it i am very confused/ i just need the answer lol
Answers
Answer:
No question!
Step-by-step explanation:
Hi! Could you please insert a question so I could answer for you?
I would love to help!
graph A represents the function f(x)=^3 graph B and C are transformations of graph A
Answers
Answer:
A3
Step-by-step explanatio
Every Thursday, Matt and Dave's Video Venture has “roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an
amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a
second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a
second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total
amount paid for these second movies will exceed $15.00?
I saw other questions for this but why is the standard deviation 0.15*sqrt of 30 and not 0.15*30 because I thought this is a linear transformation
Answers
Using the normal distribution, it is found that there is a 0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard error is [tex]s = \sigma\sqrt{n}[/tex]In this problem:
Mean of $0.47, standard deviation $0.15, hence [tex]\mu = 0.47, \sigma = 0.15[/tex]30 instances, hence [tex]n\mu = 30(0.47) = 14.1, s = 0.15\sqrt{30} = 0.8216[/tex]The probability is 1 subtracted by the p-value of Z when X = 15, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Considering the n instances:
[tex]Z = \frac{X - n\mu}{s}[/tex]
[tex]Z = \frac{15 - 14.1}{0.8216}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
1 - 0.8643 = 0.1357.
0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.
A similar problem is given at https://brainly.com/question/25769446