Answer:
The equation of the ellipse is;
[tex]\dfrac{(x + 4)^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = 1[/tex]
Step-by-step explanation:
The parameters of the ellipse are;
The location of the center of the ellipse = (-4 0)
The coordinates of the vertex of the ellipse = (-8, 0)
The coordinates of the the co-vertex = (-4, 1)
The general form of the equation of an ellipse is presented as follows;
[tex]\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1[/tex]
The center of the above equation of an ellipse = (h, k)
The vertex of the above equation are; (h - a, k) and (h + a, k)
The co vertex of the above equation are; (h, k - b) and (h, k + b)
By comparison, we have;
h = -4, k = 0
For the vertex, we have;
When
h - a = -8
∴ -4 - a = -8
-a = -8 + 4 = -4
a = 4
When
h + a = -8
-4 + a = -8
∴ a = -4
a = 4 or -4
We note that a² = 4² = (-4)²
For the covertex, we have;
When
k - b = 1
0 - b = 1
b = -1
When k + b = 1
0 + b = 1
b = 1
∴ b = 1 or -1
b² = 1² = (-1)²
We can therefore write the equation of the ellipse as follows;
[tex]\dfrac{(x - (-4))^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = \dfrac{(x + 4)^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = 1[/tex]
Therefore;
[tex]\dfrac{(x + 4)^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = 1[/tex]
Topic : Multiple Representations of points
PLEASE HELP ME, am having a hard time with these questions
Answer:
Hmm, want piña colada and Jar Jar Binks cookies? just go to India.
Answer:
See below directions.
Step-by-step explanation:
The condition [tex]-2\pi<\theta<2\pi[/tex] means you can get to the point by rotating no more than one revolution in either the positive or negative direction.
See the attached image to see the point [tex]\left(3,\,-\frac{3\pi}{4}\right)[/tex]. Think about how you get to that point: start at the origin, go right (along the positive x-axis) 3 units, then turn in the negative direction (to your right!) through an angle of [tex]\frac{3\pi}{4}[/tex].
Now, go again, starting at the origin, only this time, go 3 units right, then turn through an angle of [tex]-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}[/tex]. In other words, you turn one whole revolution in addition to the [tex]-\frac{3\pi}{4}[/tex] angle. Your point can now be described by [tex]\left(3,\,\frac{5\pi}{4}\right)[/tex].
Another description can be found by rotating in the opposite direction, so an angle of [tex]\frac{3\pi}{4}[/tex] and backing up 3 units -- specify a "radius" of -3. The point is then [tex]\left(-3,\,\frac{3\pi}{4}\right)[/tex].
You can also try subtracting one revolution [tex](2\pi)[/tex] from the angle, but be careful not to let the angle go outside the interval [tex]-2\pi<\theta<2\pi[/tex].
The changes you can try are:
add [tex]2\pi[/tex] to the angle, leave r alone
subtract [tex]2\pi[/tex] to the angle, leave r alone
add/subtract [tex]\pi[/tex] (half a revolution) to the angle, make r the opposite.
Complete the following statement
with the correct number.
The sum of the three angles of
any triangle is [?]
Enter
Answer:
180°
Step-by-step explanation:
According to Angle sum property of a triangle , sum of all the three angles of a triangle equals to 180°
Item 8 Find the lateral surface area of the cylinder. Round your answer to the nearest tenth. in.2
Answer:
LSA = 2πrH
Step-by-step explanation:
The lateral surface area of a cylinder is given by the formula as:
LSA = 2πrH
where, r and H are radius and height of the cylinder respectively.
The volume of cylinder is πr^2H
and Total surface are of cylinder = LSA+ 2× base are
= 2πrH +2πr^2
You can substitute any values of r and H to find LSA of the cylinder
What is the salesperson's commission on a $900
sale if the commission rate is 25%?
Answer:
Amount of commission earned = $225
Step-by-step explanation:
Commission rate = 25%
Sales amount = $900
Find the amount of commission earned by the salesperson
Amount of commission earned = Commission rate × Sales amount
= 25% × $900
= 25/100 × $900
= 0.25 × $900
= $225
Amount of commission earned = $225
Find the value of x in the following equations
1. 2=64
ILL BRAINLIEST YOU
PLEASE HELP ME
EXPLANATION IF YOU CAN
Answer:
Blank 1; AB
Blank 2; AC
Blank 3; BC
Step-by-step explanation:
Mathematically, the greater the angle that faces a side of a triangle, the bigger the side length of the triangle
so what this mean is that, bigger side lengths faces bigger angles
From the list of angles we have, the side that faces vertex C is the biggest
We have this as;
AB faces C and that is the biggest
the next is the side that faces angle B; we have the length as AC
the least faces angle A ; we have the length as BC
What is the answer??
Answer: .41+.34=.75
Step-by-step explanation:
7 times as much as 1/3 and 4/5
Answer:
3.13333333333
Step-by-step explanation:
It is a recurring so u could write it as 3.13 with a dot on top of the last three hope it helps :D
Determine the value of x.
Question 9 options:
A)
2
B)
2
C)
D)
4
Answer:
2√2 = x
Step-by-step explanation:
x
---- = sin 45 degrees, or
4
x 1
----- = -----
4 √2
this results in x = 4 / √2 = 4√2/2 = 2√2 = x
The value of the variable 'x' will be 2√2 units. Then the correct option is C.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
The triangle is an isosceles right-angle triangle. Then by the Pythagoras theorem, we have
4² = x² + x²
2x² = 16
x² = 8
x = 2√2
The value of the variable 'x' will be 2√2 units. Then the correct option is C.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
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Please Answer This Question!
Answer: x=25
Step-by-step explanation: equation comes out to
4x+80=180
4x=100
x=25
Answer:
x=25
Step-by-step explanation:
x+30+x+40+2x+10=180
Add the X up together and the other number which will be
4x+80=180
subtract 80 from both sides
4x=100
divide 4 from both sides
x=25
Mr. Meyer is planning a sixth-grade field trip to Washington DC. He divides his students evenly between 9 chaperones will lead a group of 8 students. If S represents the total number of students going on the field trip with equation models the problem?
A. 8s = 9
Or
B. s/9 =8
I think there is 72 students because there is 9 chaperones with groups of 8 so that is 9x8 which is 72
Hope this helps answer some questions that you may have had.
Find the area of the figure. The area is square inches.
please help!
Answer:
154 inchs
Step-by-step explanation:
22 * 14 divided by 2
write in standard rorma
y =2/3x-6
Answer:
-2/3x+y=6
Step-by-step explanation:
Standard form is just x+y=n, so all that we have to do it get that x over by subtraction.
M
135°
Angle JKL is a straight angle.
The measure of angle JKM is 135º.
The measure of angle MKL is xº.
What is the value of x
Answer: 45
Step-by-step explanation:
Hello there!
So this problem looks a lot more complex than it really is. First, we need to know that a straight line is 180 degrees. Since both of these angles must add up to 180, we just subtract 135 from 180. We then get 45.
Hope this helped! :D
Sorry if any information was incorrect or if i didn’t understand what you were asking. Just comment and I will reply back ready to help!
Jessica has 24 marbles and Jenny has 33 how many more marbles does jessica have than Jenny
The volume of a cube is 124 cubic inches.
What is the side length of the cube?
Answer:
4.987 in
Step-by-step explanation:
Volume of a cube= (where x= side)
x³
we know that
124=x³
∛124=x
x=4.986630952 which rounds to
4.987
Answer: a≈4.99in
Step-by-step explanation:
Using the formula
V=a³
Solving for a
a=V <To Power> ⅓ = 124⅓ ≈ 4.98663in
Let's compare two different raffles to see which ticket you should buy? A. Raffle 1: 800 raffle tickets are sold $2.00 each. There is one gran prize for $450 and two consolation prizes of $100 each that will be awarded. What is the expected value of one ticket? B. Raffle 2: 350 raffle tickets are sold for $2.00 each. There is one grand prize of $150 and three consolation prizes of $50 each. What is the expected value of one ticket?
Answer:
(a) The expected value is: $0.40625
(b) The expected value is: $0.4286
Step-by-step explanation:
Solving (a): Raffle 1
Given
[tex]Tickets=800[/tex]
[tex]Value = \$2[/tex] per ticket
[tex]Grand\ Prize = \$450[/tex] ---- for 1
[tex]Consolation = \$100[/tex] --- for 2
Required
The expected value of each ticket
First, calculate the total amount of the 800 tickets
[tex]Amount = Tickets * Value[/tex]
[tex]A_1 = 800 * \$2[/tex]
[tex]A_1 = \$1600[/tex]
Next, calculate the total amount of the prizes
[tex]Amount = Tickets * Value[/tex]
[tex]A_2 = \$450 * 1 +\$100 * 2[/tex]
[tex]A_2 = \$450 +\$200[/tex]
[tex]A_2 = \$650[/tex]
The expected value E(x) of 1 ticket is calculated as:
[tex]E(x) = \frac{A_2}{A_1}[/tex]
[tex]E(x) = \frac{\$650}{\$1600}[/tex]
[tex]E(x) = \$0.40625[/tex]
Solving (b): Raffle 2
Given
[tex]Tickets=350[/tex]
[tex]Value = \$2[/tex] per ticket
[tex]Grand\ Prize = \$150[/tex] ---- for 1
[tex]Consolation = \$50[/tex] --- for 3
Required
The expected value of each ticket
First, calculate the total amount of the 800 tickets
[tex]Amount = Tickets * Value[/tex]
[tex]A_1 = 350 * \$2[/tex]
[tex]A_1 = \$700[/tex]
Next, calculate the total amount of the prizes
[tex]Amount = Tickets * Value[/tex]
[tex]A_2 = \$150 * 1 +\$50 * 3[/tex]
[tex]A_2 = \$150 +\$150[/tex]
[tex]A_2 = \$300[/tex]
The expected value E(x) of 1 ticket is calculated as:
[tex]E(x) = \frac{A_2}{A_1}[/tex]
[tex]E(x) = \frac{\$300}{\$700}[/tex]
[tex]E(x) = \$0.4286[/tex]
What is the velocity of a plane that traveled 4828 kilometers west from New York to California in 4 hours
pls help answer in under 2 mins plssss
Answer:
Step-by-step explanation:
Solve for one variable and substitute the value in to another equation.
A recipe for homemade clay calls for 6 cups of water for every 12 cups. How many cups of water are needed when 4 cups of flour are used ?
Answer:
2 cups of clay
Step-by-step explanation:
Given data
we are given that 6 cups of water for every 12 cups of clay
i.e
12 cups of clay require 6 cups of water
4 cups of clay will require x cups of water
cross multiply
12x= 4*6
12x= 24
divide both sides by 12
x= 24/12
x= 2cups
Hence 4 cups of water will require 2 cups of clay
Cloe Dow purchased a hot tub for $5,000. She made a 50 percent down
payment and financed the remainder. What amount did she finance?
Answer:
She financed $2500
Step-by-step explanation:
If you multiply $5000 by 50% you will be $2500. This would be the amount she financed. Hope this helps
Market price of an article is 30% above its purchase price.If the shopkeeper sold it by allowing 15% discount,then (i) Calculate the market price and profit amount if the shopkeeper paid 2500 for the article.
solution by step:
The market price and profit amount if the shopkeeper paid 2500 for the article will be 3250 and 11.05%.
What exactly is profit?Profit is made when the money generated from a commercial operation exceeds the expenses, charges, and taxes associated with operating the activity in question.
Given data;
Purchase price = 2500
Given condition;
The markup is 30% more than the purchasing price.
Mark Price is found as;
[tex]\rm MP = \frac{130}{100}\times 2500 \\\\ MP =130\times 25\\\\ MP=3250[/tex]
The marked price of an article will be 3250.
Since we are aware that discounts usually apply to mark prices, a 15 percent discount is now being offered;
[tex]\rm \frac{85}{100}\times 3250 = 2762.5 RS[/tex]
The profit in the article is found as;
Profit = 2762.5-2500
Profit = 226.25 RS
Now profit % is found as;
[tex]\% profit = \frac{276.25}{2500}\times 100 \\\\ \% profit = 11.05 \%[/tex];
Hence, the market price and profit amount, if the shopkeeper paid 2500 for the article, will be 3250 and 11.05%.
To learn more about the profit refer to the link;
https://brainly.com/question/15036999
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Item 5 is unpinned. Click to pin.
Using the trend line equation, what is the predicted approximate value of y when x= 4.5?
5.12
3.98
3.47
2.75
Answer:
I think the answer is 3.47
Three consecutive integers have a sum of 87. Find the integers.
Answer:
28, 29, and 30
Step-by-step explanation:
There's probably better ways but you can estimate by knowing 30*3=90 so it should be somewhere pretty close to 30. Guess and check with basic calculations to get 28, 29, and 30.
x + 6 = 4
what is x ??
Answer:
x= (-2)
Step-by-step explanation:
brainliest?
How much money does an Construction worker get in hour?
Answer:
$18
Step-by-step explanation:
Classify the pair of angles.
34°
O complementary
O supplementary
o vertical
Find the value of x.
x=
Answer:
supplementary
x = 146 degrees
Step-by-step explanation:
Answer:
supplementary
Step-by-step explanation:
Please help me??? like im in serious need of help!
Answer:
16 square miles
Step-by-step explanation:
Hope this helped <3
Help! Please anyone. I need help!
Answer:
Isn't it supposed to put where the number/symbol is.....
Step-by-step explanation:
3. Find the surface area of the square pyramid.
Answer:
answer: 105
Step-by-step explanation:
For triangle area you just have to do base × height ÷ 2 So we will do 8 × 5 = 40 then divide by 40 by 2 so 40 ÷ 2 = 20 now we have 1 triangles area we can find the rest because each of these triangles are equal so 20 × 4 = 80 now we just have to do the square so thats easily just base × height so 5 × 5 = 25 now we just add 80 and 25 so 80 + 25 = 105 so 105 is our surface area!