Write the equation of the ellipse that has a center at
(-2, – 6), a vertex at (-8, – 6), and a covertex at
(-2, -3)
Answers
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]
Final answer:
The equation of the ellipse is (x+2)²/36 + (y+6)²/9 = 1, where the center is at (-2, -6), the vertex is at (-8, -6), and the covertex is at (-2, -3).
Explanation:
The equation of an ellipse with a center at (-2, -6), a vertex at (-8, -6), and a covertex at (-2, -3) can be determined using the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the distance from the center to a vertex along the major axis, and b is the distance from the center to a covertex along the minor axis. In this case, the major axis is horizontal because the vertex has the same y-coordinate as the center. Thus, a = 6 (the distance from the center to the vertex) and b = 3 (the distance from the center to the covertex).
The equation becomes: (x+2)²/6² + (y+6)²/3² = 1. Simplified, this is (x+2)²/36 + (y+6)²/9 = 1.
Related Questions
The park modeled consists of a rectangular area and 2 semicircular areas the area of the rectangle part of the park is 60000
Answers
Answer:
1,228 yards
Step-by-step explanation:
I think the photo below is your full question
And here is my answer:
Area of a rectangle = bh
60,000 = 300h
<=> h = 200
and the Circumference + 300 + 300 +πd + 300 + 300 + 3.14 x 200 + 300 + 300 = 1,228 yards
Tegan biked 5 1/3 miles today, and Jack biked 3 3/4 miles. How many times the length of Jack’s bike ride was Tegan’s bike ride?
Answers
Answer:
5 1/3= (3*5+1)/3=16/3
3 3/4=(4*3+3)/4=15/4
16/3: 15/4=16/3*4/15=64/45=1.422
Step-by-step explanation:
Answer:
1.422
Step-by-step explanation:
A shipping company charges $6 to skip a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound. Which equation represents the cost, in dollars, of shipping a package that weighs x pounds?
Answers
Step-by-step explanation:
A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound.
lets make an assumption that the total weight of the shipment is x pound and cost for shipping is y.
the shipping company charges $6 for the first pound.
Up to now the charge is y=6
After 1 pound, i.e for the remaining (x-1) pounds, they charge $2 per pound.
So, the total charge will be, y=6+2(x-1)
weight is always starting from zero as there is no negative weight.so X>0
so the equation is 6(2x-1), where X is more than 0
Answer:
Its A on edge, f(x)=6+2[x-1], the brackets are rounding up
y=-2x²
how do I find the vertex and other points to graph
Answers
Now back to the question, the vertex would be (0,0). And to find other points, you make a table.
X | Y
2 | -8
1 | -2
0 | 0
-1 | -2
2 | -8
To find the X’s you just put the numbers that are to the left and right of 0 (which is the x of the vertex). Then, you plug in those numbers into the equation and solve. You will notice a pattern with the Y’s every time you make a table for a parabola. I hope this helps :)
The glee club needs to raise money for the spring trip to Europe, so the members are assembling holiday wreaths to sell. Before lunch, they assembled 15 regular wreaths and 15 deluxe wreaths, which used a total of 135 pinecones. After lunch, they assembled 15 regular wreaths and 20 deluxe wreaths, using a total of 160 pinecones. How many pinecones are they putting on each wreath?
Answers
Answer:
5 pinecones on the deluxe wreath and 4 pinecones on the regular wreath
Step-by-step explanation:
Answer:
Regular: 4
Deluxe: 5
Step-by-step explanation:
15x + 15y = 135
15x + 20y = 160
5y = 25
y = 5
15x = 135 - 15(5)
15x = 60
x = 4
8a+ 12a - 75 - 95 – 11a
How to combine like terms
Answers
Answer:
9a -170
Step-by-step explanation:
Answer:
9a-170
Step-by-step explanation:
8a+ 12a-11a= 9a
-75-95= -170
9a-170
Call an integer $n$ oddly powerful if there exist positive integers $a$ and $b$, where $b>1$, $b$ is odd, and $a^b = n$. How many oddly powerful integers are less than $2010$?
Answers
Answer:
There are 16 oddly powerful integers less than 2010
Step-by-step explanation:
∵ b is an odd integer
∵ b > 1
∴ The first value of b is 3
∵ a is an integer
- We can use a = 1, 2, 3, ..........
∵ [tex]a^{b}=n[/tex]
∵ n < 2010
- Let a = 1, 2, ............... 12 because 12³ is greatest integer < 2010
∵ 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343,
8³ = 512, 9³ = 729, 10³ = 1000, 11³ = 1331, 12³ = 1728
∴ There are 12 oddly powerful integers with b = 3
Now the second value of b is 5
[tex]1^{5}=1[/tex] but we took 1 before so we will start with 2
∵ [tex]2^{5}=32[/tex], [tex]3^{5}=243[/tex], [tex]4^{5}=1024[/tex]
- [tex]4^{5}[/tex] is the greatest integer < 2010
∴ There are 3 oddly powerful integers with b = 5
Now the third value of b is 7
∵ [tex]2^{7}=128[/tex]
- [tex]2^{7}[/tex] is the greatest integer < 2010
∴ There is 1 oddly powerful integers with b = 7
Now the fourth value of b is 9
∵ [tex]2^{9}=512[/tex]
- [tex]2^{9}[/tex] is the greatest integer < 2010
- But we used 512 before
∴ There is no oddly powerful integers with b = 9
- 9 is the greatest value of b which makes [tex]a^{b}<2010[/tex]
∵ 12 + 3 + 1 = 16
∴ There are 16 oddly powerful integers less than 2010
3. What is the value of the x in the solution to the system of linear equations below?
y = 8x − 8
3x + 2y = −16
A x = 0
B x = 2
C x = −5
D x = −8
Answers
Answer:
B x = 2
Step-by-step explanation:
Step 1: Add -2y to both sides.
−75x+2y+−2y=−16+−2y
−75x=−2y−16
Step 2: Divide both sides by -75.
−75x /−75 = −2y−16 −/75
x= 2 /75 y+ 16 /75
Answer:
x= 2 /75 y+ 16 /75
Answer:
x=0
Step-by-step explanation:
3x+2(8x-8)=-16 plug the 1st y for the 2nd y
----------------------------------------------
3x+16x-16=-16 distribute the 2
--------------------------------------------
19x -16 = -16 combine like terms
+16 +16 add 16 both sides
--------------------------------------------
19x=0
19 19 divide 19 both sides
x=0
Hope This Helps
WILL GIVE BRAINLIEST ANSWER!
Given the parent function f(x)=|x|, which equation would occur if the function is vertically compressed by 13, shifted down 6 units, and shifted right 5?
f(x)=3|x+5|−6
f(x)=13|x−5|−6
f(x)=13|x+5|−6
f(x)=13|x−6|+5
Answers
[tex]f(x)=13|x-5|-6[/tex] is the equation represented by all the operations.
Step-by-step explanation:
The given function is
[tex]f(x)=|x|[/tex]
It is vertically compressed by a factor of 13 then the function becomes,
[tex]f(x)=13|x|[/tex]
It shifted down 6 units, then the function becomes,
[tex]\mathbf{f}(\mathbf{x})=\mathbf{1 3}|\boldsymbol{x}|-\boldsymbol{6}[/tex]
It shifted right by 5 units then the function becomes,
[tex]f(x)=13|x-5|-6[/tex]
Thus the resultant equation thus obtained is [tex]f(x)=13|x-5|-6[/tex]
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Which of the following statements is true? Select all that apply. A. The probability of the pointer landing on an even-numbered section is 66.67%. B. It is impossible that the pointer will land on 1. C. It is less likely that the pointer will land on an odd-numbered section. D. It is certain that the pointer will land on a number less than 6. E. The spinner is fair.
Answers
Answer:
A, B and C are the correct answers.
Step-by-step explanation:
Correct:
A - There are 4 even numbers all together. 2 is repeated twice, there is a 4 and a 6. 4 divided by 6 is 0.666 repeated. Multiply by 100 which gives you 66.666 repeated and then round up, so now we have 66.67%. This is the probability.
B - It’s impossible that the pointer will land on 1 because there in no 1.
C - It’s less likely because there are only two odd numbers, 3 and 5. Compare that to the 4 even numbers. 4 > 2. Therefore the odd numbers, or the two, is less likely than the even numbers, the 4.
Incorrect:
D - There is only one 6 out of 6 numbers total. So 1 out of 6. We cannot be certain, it fact, it would be said that it’s very unlikely for the pointer to land on the 6.
E - The spinner is most certainly not fair. The spinner has one of each number except for the 2. There are double twos. On a normal spinner you would see a number 1 replace on of the 2. This ways the spinner will be 1 through 6.
If it makes any of you more confident in this answer, my assessment also had this question and I got it correct by answering with A, B and C.
Final answer:
The probability of the pointer landing on an even-numbered section is 33.33%. The pointer can't land on 1. The spinner is not fair.
Explanation:
To find the probabilities in this scenario, we need to analyze the spinner. The spinner has 6 equal sections, numbered 2, 2, 3, 4, 5, and 6. There are:
2 even-numbered sections (2 and 4)3 odd-numbered sections (2, 3, and 5)1 section with a number less than 6 (4)Based on this analysis, we can determine the following statements:
Statement A is false: The probability of the pointer landing on an even-numbered section is 33.33% (2 out of 6 possibilities).Statement B is true: The pointer can't land on 1 because it is not one of the numbered sections on the spinner.Statement C is false: The probability of the pointer landing on an odd-numbered section is 50% (3 out of 6 possibilities), which is the same as the probability of landing on an even-numbered section.Statement D is true: The pointer will certainly land on a number less than 6 because all the numbered sections on the spinner are less than 6.Statement E is false: The spinner is not fair because the probabilities of landing on different sections are not equal.Your bill at a restaurant is $4.65, and you decide to tip the waitress 90e. Because
you have only 20e in nickels, you give her six dollar bills and ask for change. The
waitress has only two quarters in change. Without changing your plans, how do
you solve this problem?
Answers
Answer: I will give her $6.05 and collect the $0.5 in her possession
Step-by-step explanation:
Before proceeding, we need to know the quantity or equivalent of some of the things mentioned.
a.Nickel:- a nickel is 5¢, this means that the 20¢ in nickels that you had in your possession while in the restaurant is equal to (20/5) 4 nickel coins.
b. Two quarters :- Just as the name implies; 2 quarters of a dollar is [(1/4) + (1/4)] of 1 dollar = 50 cent.
We need to calculate the entire amount that needs to be given to the waitress. Since your bill after eating at the restaurant is $4.65 and the intended tip is 90¢, the sum that should be offered to her =
$4.65 + $0.90
= $5.55 (five dollars : fifty five cent).
According to the question, you have only 20 cents in nickels, so although you have five dollar bills to give the waitress, 55¢ is not available. Again, if you offer her six dollar bills, she wouldn't be able to give you a change of 45¢ ($6.00 - $5.55) because she only has 2 quarters of a dollar (50¢).
Now, since you are in possession of 20¢ in nickels, the best way to tackle the situation is to demand the two quarters that she has while handing out the 6 dollar bills and 1 nickel (5¢) to her. So, you should simply offer her $6.05 while you collect $0.50 from her in return)
Recall that the total amount that must be given to her (bill + tip) = $5.55
Then subtracting 50¢ from $6.50¢ will give:
$6.05 - $0.50
= $5.55
Therefore you have given her exactly $5.55¢ if you offer her six dollars five cent and collect fifty cents in return.
Use △ABC, in which AB=37, AC=35, and BC=12, to answer the question.
what is the ratio for tan B?
(NEED HELP ASAP! HAVE TO FINISH TODAY!!!
Sorry If I am Annoying PLEASE DONT TAKE THIS DOWN I DONT WANNA FAIL D:)
Answers
Answer:
tan B = [tex]\frac{35}{12}[/tex]
Step-by-step explanation:
tan B = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{35}{12}[/tex]
help porfavor, please
Answers
Answer:
Option A, (-7, -3)
Step-by-step explanation:
The answer is: Option A, (-7, -3)
need help asap!!!!!
Answers
Answer:
The correct answer is A.
Solve the equation. Explain how you found your answer.
8y + 2y = 2y + 40
Answers
Answer:
y = 5
Step-by-step explanation:
Subtract 2y from either side. It'll cancel out both of them. Then the equation is 8y = 40.
Divide both sides by 8 and you get y=5
Pretty sure that's right. I have a dad who has a math degree so I think it would be right because he helps me every time.
Step-by-step explanation:
As shown first you combine like terms then you subtract 2y from both sides to get 40 by it self then you divide 8 by 40 to get y by itself hope this helps this answer is 100% correct and i was glad to help please give brainliest!
[tex]8y+2y=2y+40\\10y=2y+40\\ -2y -2y\\8y=40\\y=5[/tex]
What is the volume of this sphere?
12pi cm^3
36pi cm^3
288pi cm^3
864pi cm^3
Answers
Answer:
Option 3
Step-by-step explanation:
Volume of a sphere:
(4/3)×pi×r³
(4/3)pi × 6³
288pi cm³
What does the transformation from f to g represent?
F(x)= √x and g(x)=6 √x
Answers
Answer:
You have to have x to answer this question
Step-by-step explanation:
A 45 foot ladder is used to clean the
gutters at your house. How far away from
the house should you put the ladder in
order for it to reach the 40 foot high
gutter? Round your answer to the nearest
tenth.
5 feet.
Answers
Answer:
20.62
Step-by-step explanation:
In this instance, we are going to use the pythagorean theorem.
The height of the gutter will be a leg of the triangle, and the ladder will be the hypotenuse. The formula is
[tex]a^{2} + {b}^{2} = {c}^{2} [/tex]
While A and B are legs and C is the hypotenuse. We are trying to find B, the distance from the house.
So plug A and C in:
[tex] {40}^{2} + {b}^{2} = {45}^{2} [/tex]
Now figure it out: first you square 40 and 45:
[tex]1600 + {b}^{2} = 2025[/tex]
Isolate the B term: subtract 1600 from both sides
[tex] {b}^{2} = 425[/tex]
Now take the square root of both sides to find B
[tex]b = 20.62[/tex]
And that's your answer
Answer:
20.6 feet
Step-by-step explanation:
The Pythagorean theorem can tell you the distance from the house the base of the ladder may be for it to reach 40 feet up. If that distance is represented by x, then it tells you ...
45^2 = x^2 + 40^2
x = √(2025 -1600) = √425
x ≈ 20.6
The ladder will reach to 40 feet high when the base is 20.6 feet from the house.
_____
Comment on ladder distance
The ladder safety association recommends an angle with the ground of about 75°. That corresponds to a distance from the house of about 10 feet. If the ladder is 20 feet away, it will barely reach the gutter, so placing it at that distance would probably not be safe.
An appropriate answer to this question is "10 feet", not based on math, but based on safety. At that distance the end of the ladder will extend about 3.7 feet beyond the gutter.
Whats the product of 2/3 × 36
Answers
Answer:
24 :)
Step-by-step explanation:
2 / 3 x 36 = ?
First of all, note that 36 is the same as 36/1 since 36 divided by 1 is 36. Therefore, start by setting up the problem like this:
36 / 1 x 2 / 3
Multiply the numerators together (36 x 2 = 72) and multiply the denominators together (1 x 3 = 3) and make it into one fraction like so:
72 / 3
The greatest common factor of 72 and 3 is 3. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get:
24 / 1
Convert the improper fraction above to a whole number to get the answer:
24
Hope this helps :)
y=x+2 2x-y=-4 Solve the systems of equations
Answers
Answer:
Step-by-step explanation:
Given that,
y=x+2 equation 1
2x-y=-4 equation 2
This is a simultaneous equation.
Substitute equation 1 into equation 2
2x-y=-4. Since y=x+2
2x-(x+2) = -4
2x-x-2 = -4
x-2 = -4
x = -4+2
x = -2
Also from equation 1
y=x+2
Since x=-2
y=-2+2
y=0
Then, solution (x, y) = (-2,0)
Answer: x = -2, y = 0
Step-by-step explanation:
[tex]y=x+2\\2x-y=-4[/tex]
Substitute y = x+2 in [tex]2x-y=-4[/tex]
Then we get, [tex]2x-(x+2)=-4[/tex]
[tex]2x-x-2=-4\\x-2=-4\\x=-4+2\\x=-2[/tex]
Then substitute x = -2 in any equations, just only one equation. For me, I'd substitute x = -2 in y = x+2
[tex]y=-2+2y=0[/tex]
So the answer is x = -2 and y = 0
Evaluate 4+2(7) help me
Answers
Answer:
18
Step-by-step explanation:
4 + 2(7)
This equation can be rewritten like this: 4 + 2 x 7
According to the order of operations, multiplication comes before addition.
So, we can go ahead and multiply 2 and 7 out:
4 + 2 * 7
4 + (2 * 7)
4 + (14)
Then, our second step is to add.
4 + 14 = 18
So, 4 + 2(7) = 18.
18 is your answer.
Please mark as Brainliest! :)
Answer:18
Step-by-step explanation:do parentheses. 4x7=14+4=18
If 4+2=26,8+1= 79 and 6+5=111 then what is 7+3
Answers
The answer is 70.
Explanation:The given pattern seems to follow the rule of multiplying the first number by the sum of its digits and adding the result to the second number:
For example:
4 + 2 = (4 x (4+2)) = 26
8 + 1 = (8 x (8+1)) = 79
6 + 5 = (6 x (6+5)) = 111
Therefore, for 7 + 3:
7 + 3 = (7 x (7+3)) = 70
Without multiplying, tell which is greater: 4/5 x 45 or 2/3 x 45. Explain.
Answers
Answer: It is 4/5 x 45
Step-by-step explanation: Hope i helped please mark brainliest!
I know there is suppose to be no multiplying but if you mulitply in your head 4/5 x 45 is 36 and 2/3 x 45 is 30
therefore, 4/5 x 45 is greater!
also, if not multiplying 0.8(5/4) is greater than 0.667(2/3). Therefore, 4/5 is greater than 2/3.
Without multiplying, 4/5 x 45 is greater than 2/3 x 45 because the fraction 4/5 is greater than 2/3 when both are compared using a common denominator.
Explanation:To answer which is greater without multiplying, we can look at the fraction multiples of 45 in the problems 4/5 x 45 and 2/3 x 45. Since both expressions involve the same whole number (45), we can compare the fractions 4/5 and 2/3 to determine which product is greater. By converting the fractions to have a common denominator, we can see that 4/5 is equivalent to 24/30, and 2/3 is equivalent to 20/30. Therefore, 4/5 is greater than 2/3, meaning that 4/5 x 45 is greater than 2/3 x 45.
Danielle has 3/5kg of beads. She shares the beads evenly between 5 friends.
How many Kilograms does each friend receive?
Answers
Answer:
0.12
Step-by-step explanation:
3/5=0.6
0.6/5=0.12
Find the equation of the line that is perpendicular to y = 2x + 4 and passes though the point (2, –2).
Answers
Answer:
the point is 3 i think
Step-by-step explanation:
Answer:
B y=-1/2x -1
Step-by-step explanation:
Evaluate Žy - 3+ when y = 4 and z=3
Answers
Answer:
9
Step-by-step explanation:
if
Žy - 3 when y = 4 and z=3
then,
4*3-3
=9
The values in the table represent a linear function. How does the value of y change in relation to a change in the value of x? A) for every change in x by 4, y changes by 3 B) for every change in x by 3, y changes by 4 C) for every change in x by −4, y changes by 3 D) for every change in x by −3, y changes by 4
Answers
Answer:
C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
-5 + (5 + 3)
In the box below, show each step in simplifying the expression and explain which property you used in each step.
Answers
Answer:3
Step-by-step explanation: So if we start by breaking it down -5+ (5+3) we do the parentheses first (5+3) which equals 8. Then we are left with (-5)+8 and it would equal 3.
Final answer:
The expression -5 + (5 + 3) simplifies to 3 by first evaluating the expression inside the parentheses to 8, and then subtracting 5 from 8 to get the final result.
Explanation:
The given expression is -5 + (5 + 3). To simplify this expression, we can use the Associative Property of addition, which allows us to change the grouping of the numbers. We will also use the properties of addition and subtraction. Here is the step-by-step process:
First, simplify the expression inside the parentheses: 5 + 3. This equals 8.Now, the expression is -5 + 8. According to the rule for adding two numbers with opposite signs, subtract the smaller number from the larger number and keep the sign of the larger number. Thus, 8 - 5 equals 3.Since 8 is larger than 5 and has a positive sign, the final answer is +3 or simply 3.Therefore, the simplified expression is 3.
I need some help! Evaluate the expression: -11²
Answers
Answer: -121
Step-by-step explanation:
What is the surface area of the breadbox
to the nearest square inch? Check your
answer for reasonableness.
Answers
Answer:
Step-by-step explanation:
surface area of two sides=2[(8×8)+π×8²/4]
=2[64+16π]
=128+32π
surface area of curved surface=2πrh/4
surface along length=base (16×16)+2×(16×8)+2×π×8/4 ×16
=256+256+64π
=512+64π
Total surface area=128+32π+512+64π
=640+96π
≈640+302
≈942 in²