For the following exercise graph the given ellipse, noting center, vertices, and foci #41
Answers
Given the equation of an ellipse: #41
[tex]x^2+8x+4y^2-40y+112=0[/tex]To find the center and the vertices, we will complete the square of (x) and (y):
[tex]\begin{gathered} x^2+8x+4(y^2-10y)=-112 \\ (x^2+8x+16)+4(y^2-10y+25)=-112+16+100 \end{gathered}[/tex]Factor for (x) and (y) then simplify:
[tex]\begin{gathered} (x+4)^2+4(y-5)^2=4\rightarrow(\div4) \\ \\ \frac{(x+4)^2}{4}+\frac{(y-5)^2}{1}=1 \end{gathered}[/tex]The general form of the ellipse will be:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Comparing the equation with the form:
[tex]\begin{gathered} (h,k)=(-4,5) \\ a=\sqrt[]{4}=2 \\ b=\sqrt[]{1}=1 \\ c=\pm\sqrt[]{a^2-b^2}=\pm\sqrt[]{4-1}=\pm\sqrt[]{3} \end{gathered}[/tex]The graph of the ellipse will be as shown in the following picture:
As shown in the figure:
The center C = (h,k) = (-4 , 5)
The vertices denoted by V = (-6, 5) and (-2, 5)
Foci denoted by F =
[tex](-4+\sqrt[]{3},5),(-4-\sqrt[]{3},5)[/tex]
Related Questions
Apollo Spas services 298 hot tubs. If each hot tub needs 175 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?
Answers
In a case whereby Apollo Spas services 298 hot tubs and each hot tub needs 175 mL of muriatic acid,number of liters of acid that are needed for all of the hot tubs is 52.15 litres.
What is unit conversion?The unit conversion can be described as the changing of bone unit to another.
We can calculate the number of liters of acid that are needed as (298 * 175)= 52150ml
This can be converted to liter by dividing 52150ml by 1000 which can be done as (52150ml/1000) = 52.15 litres of acid.
Therefore, the liters of acid are needed for all of the hot tubs can be expressed as the 52.15 litres
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Find the equation of a line parallel to 2x-2y=-4 that passes through the
point (3,9).
Answers
The line which is parallel to 2x-2y=-4 that passes through the
point (3,9) is x-y = -6.
Given that, 2x-2y = -4 passes through the point (3,9) then we have to find the equation of a line which is parallel to the given equation of line.
Let's proceed to find the equation of the line.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
Using the slope-intercept formula, the equation of the line is:
y = mx + b
where,
m = the slope of the line
b = y-intercept of the line
(x, y) represent every point on the line
x and y have to be kept as the variables while applying the above formula.
2x-2y = -4
-2y = -4-2x
y = -4/-2 - 2x/-2
y = 2+x
y = x+2
On comparing with y = mx+b
m = 1 and b = 2
As the lines are parallel then the slope of other line will also be same i.e., m = 1
The point from which it is passes is (3,9)
⇒ x₁ = 3 and y₁ = 9
y-y₁ = m(x-x₁)
⇒ y-9 = 1(x-3)
⇒ y-9 = x-3
⇒ y = x-3+9
⇒ y = x+6
⇒ x-y = -6
Therefore, the line which is parallel to 2x-2y=-4 that passes through the
point (3,9) is x-y = -6.
Hence, x-y = -6 is the required answer.
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Hayden recorded his speed while walking and determined he walked 120 feet in 30 seconds . At this rate how many feet will Hayden walk in 45 seconds
Answers
Answer:
180
Step-by-step explanation:
120ft/30sec=4sec per ft
45-30=15
4(15)=60
120+60=180
Suppose the heights of adult American males are normally distributed with a mean of 66.9 inches and a standard deviation of 4.33. What would be the upper boundary, in inches, of a symmetric, centered interval that contained all the sample averages (from samples of size 167) that are within 0.92 standard deviation units of the mean? Round to the nearest hundredth.
Answers
Using the normal distribution, the upper boundary, in inches, of a symmetric and centered interval of the sample averages with n = 167 that are within 0.92 standard deviation s of the mean is of:
67.21 inches.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Considering samples of 167, with the mean and standard deviation of the population given in the problem, the parameters are given as follows:
[tex]\mu = 66.9, \sigma = 4.33, n = 167, s = \frac{4.33}{\sqrt{167}} = 0.335[/tex]
The desired height is X when Z = 0.92, because it is 0.92 standard deviations from the mean and we want the upper limit, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
0.92 = (X - 66.9)/0.335
X - 66.9 = 0.92 x 0.335
X = 67.21 inches.
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I need help on this one:)
Answers
iven: ²
equired:
xplanation:
Since the graph is translated vertically downwards by 3 units, so the function f(x) is
[tex]\begin{gathered} f(x)=h(x)-3 \\ f(x)=3x^2-6-3 \end{gathered}[/tex]Hence, the function is
[tex]f(x)=3x^2-9[/tex]inal Answer
[tex]f(x)=3x^2-9[/tex]PLEASE HELP MEEEEEEEEEE
18 Answer:
Write the verbal phrase as an algebraic expression. Use x for the
variable in your expression: Sum of 8 and a number
19 Answer:
Write the verbal phrase as an algebraic expression. Use x for the
variable in your expression: Ten less than a number
20 Answer:
Write the verbal sentence as an equation or an inequality:
The sum of three and x is ten.
21 Answer:
Write the verbal sentence as an equation or an inequality:
Four is greater than six times a number t.
22 Answer:
Write an equation or inequality to model the situation:
The distance d to school is 1 1/2 miles more than the distance p to
the park.
23 Answer:
Write an equation or inequality to model the situation:
The perimeter of a square with a side length s is greater than or equal
to seventy plus five.
Answers
Answer:
Yquandary dinglegrt
Step-by-step explanation:
go and minijrir
18) x+8 or 8+x
19) x-10
20) x+3=10
22)4>6t or 6t<4
23)4s[tex]\geq[/tex]70+5
Simplify fully 12(x - 2)² /6(x-2)(x + 5) 4
Answers
2x−4
Alternative Form
2−
x+5
14
Explanation:
Evaluate
6(x−2)(x+5)
12(x−2)
2
Multiply the terms
(x−2)(x+5)×6
12(x−2)
2
Factor the expression
(x+5)(6x−12)
(2x−4)(6x−12)
Solution
x+5
2x−4
Alternative Form
2−
x+5
14
9583cm=9hm+5dam+8m+3cm
Answers
Answer:
a=(9580c-8-9h)/5d
Step-by-step explanation:
9hm+5dam+8m+3cm=9583cm
Subtract (9hm+8m+3cm) from both sides
5dam=9580mc-8m-9mh simplify
then divide both sides by 5dm
a=(9580c-8-9h)/5d
THIS QUESTION IS VERY UNCLEAR SO I JUST SOLVED FOR A
11.7 divided by 26.2
Answers
Answer:
Step-by-step explanation:
the answer is 0.4465 or if needed to be rounded then 0.45
4va olleckpoiniDiscrete Mathematics OL v1 A - Koscianski, Megan / Chapter 2: Set TheoryRD 2. Use the accompanying Venn diagram that shows the number of elements in regions I through IV to answer the question.10MHow many elements belong to neither set A nor set B?BU Font FamilyAAIFEEOOOE•"'NE
Answers
The elements that are neither in set A nor set B are: {10}
Answer: 10
A computer repair shop charges a flat fee of $10.95 and then $24.90 per hour.
A customer paid $147.90 for computer repairs.
How many hours did the shop work on the customer's computer?
Enter your answer as a decimal in the box.
Answers
Shop work on the customer's computer for 5.5 hours.
Given,
Charge is flat fee of $ 10.95
and, then $24.50 per hour.
And, to find the number of hours if customer paid $147.90.
Now, According to the question:
Let shop work on computer for x hours .
Then, Amount paid = 10.95 + 24.90x
So, if customer paid $147.90
then, 147.90 = 10.95 + 24.90x
24.90x = 147.90 - 10.95
24.90x = 136.95
x = 136.95/ 24.90
x = 5.5
Hence, Shop work on the customer's computer for 5.5 hours.
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The Adidas Flagship Building located in Herzogenaurach is shaped like a rhombus One of the diagonals measures 255.4 meters and the other diagonal measures 203.7 meters. Find the area of the top of the building.
Answers
Answer:
26012.49 m²Step-by-step explanation:
Area of the rhombus in terms of given diagonals:
A = ab/2, where A- area, a and b - diagonals.Plug in the values and calculate:
A = 255.4*203.7/2 = 26012.49Evaluate the expression when c=-3 and x=3 and x-2c
Answers
⇒Plug in places the given values in the expression x-2c and simplify
given that x=3 and c =-3
⇒[tex]=(3)-2(-3)\\=3+6\\=9[/tex]
The expression evaluated at the given variables is equal to 9.
a national caterer determined that 87% of the people who sampled their food said it was delicious. A random sample of 144 people is obtained from a population of 5,000. The 144 people are asked to sample the caterer's food. Will the distribution of p hat, the sample proportion saying that the food is delicious, be approximately normal?
Answers
The sample proportion saying that the food is delicious will be approximately normal.
In this question, we have been given that 87% of the people who sampled their food said that it was delicious
so, the Population proportion = 87%
A random sample of 144 people is obtained from a population of 5,000. The 144 people are asked to sample the caterer's food.
The sample size of 144 from 5000 will have proportion p cap which will follow a normal distribution with mean= p = 87%
and variance = npq
Since the mean of the sampling distribution of p hat, mean is 0.87 the sample proportion saying that the food is delicious will be approximately normal.
Therefore, the sample proportion saying that the food is delicious will be approximately normal.
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Please help! 8th grade pre-algebra math question
Answers
Answer:
a) 16
Step-by-step explanation:
[tex]x^{2} =(-4)^{2} =(-4)(-4)=16[/tex]
Hope this helps
Write the slope intercept form for the points through (-4,-5) and (0,2)
Answers
Answer:
y = (7/4)x + 2
Step-by-step explanation:
(-4, -5) and (0, 2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2 - (-5) 2 + 5 7
m = ------------- = ------------- = ------------- = --------
x₂ - x₁ 0 - (-4) 0 + 4 4
(it doesn't matter which points you put)
y - y₁ = m(x - x₁)
y - 2 = (7/4)(x - 0)
y - 2 = (7/4)x - 0
+2 +2
----------------------------
y = (7/4)x + 2
I hope this helps!
Y-intercept 9 and slop -2
Answers
The equation of the line that has the given features is y = -1/3x - 4
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation of the line?From the question, the given parameters are
Slope, m = -2
y-intercept, c = 9
As a general rule:
A linear equation is represented as
y = slope * x + y-intercept
This can be rewritten as
y = mx + c
Next, we substitute the known values in the above equation
So, we have the following equation
y = -2x + 9
The above equation cannot be further simplified
So, we have
y = -2x + 9
However, it can also be expressed as
y = 9 - 2x
Hence. the linear equation is y = -1/3x - 4
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Possible question
What is the equation of a linear equation that has the following features
Y-intercept 9 and slop -2
Are these right? Geometry by the way
Answers
Answer:
ABM is 60; DBC is 60; CBM is 120; HGF is 120; EFM is 120
Step-by-step explanation:
Which correctly shows the title of a movie?
"In an Old House"
In an Old House
Answers
Answer:
The answer to your question is A "In an Old House" I hope this helps
Sorry if I am wrong
Answer: It would be "In an Old House"
Step-by-step explanation:
SOMEONE HELP PLS I WILL MAKE BRAINLEIST I PROMISE ONE U AWNSER SAY PLS MARK BRANILIEST HERE MAKE IT SIMPLE OR NO BRANILEST
Answers
The addition of 45 + 90 using the greatest common factor is 45(1 + 2) = 135
How to illustrate the information?From the information, it should be noted that Claude uses the greatest common factor and the distributive property to write the sum of 45 + 90.
It should be noted that the greatest common factor between 45 and 90 is 45.
This will be illustrated as:
45 + 90 = 45(1 + 2)
= 45 + 90
= 135
Therefore, the addition is 135.
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Let t(x) = gof (x). where g (12) = 6. g(6) =-8, and f(x) = 4x - 6.
What is the value of t(3)?
Answers
The composition of functions evaluated in x = 3 is equal to -8.
t(3) = -8.
How to evaluate the composition of functions?Here we have the two functions g(x) and f(x), and the composition:
(g°f)(x) = t(x).
This is equal to:
t(x) = g(f(x))
Then:
t(3) = g( f(3) )
Evaluating f(x) in 3 we get:
f(3) = 4*3- 6 = 12 - 6 = 6
Then:
t(3) = g( f(3)) =g(6)
And we know that g(6) = -8, then:
t(3) = -8.
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write 1062 correct to the nearest thousand
Answers
Answer:
1062 would be 1000 because if you are rounding anything less than 5 is 0 and everything behind it is 0
Please help I’ll mark you as brainliest if correct!
Answers
a) quotient = 23 and remainder = 14
b) quotient = 28 and remainder = 12.
c) quotient = 20 and remainder = 10.
a) Here in the first question we have to divide 405 by 17.
405 is not completely divisible by 17.
So when we divide 405 by 17 we get 23 as quotient and 14 as remainder.
we can cross check this by the formula;
Dividend= Divisor × Quotient + Remainder.
So in here the dividend is 405 and the divisor is 17 which when multiplied by the quotient 23 and added by the remainder that is 14 gives us 405.
Thus quotient = 23 and remainder = 14
b) Here dividend = 656 and divisor = 23
Thus when we divide 656 by 23 we get:
we get quotient as 28 and remainder as 12.
c) Given dividend is 1990 and divisor is 98.
Thus we divide 1990 by 98 we get:
Quotient = 20 and remainder = 10.
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Solve for x.
4(3x - 5) = 6x-2
Answers
Answer:
x = 3
Pls, choose me as brainliest!
Which of the following is the same as the equation x + 5y = 4x - 3y ?
a) 3x = 2y b) 3x=8y c) 5x = 2y (d) 6x=y
Answers
Answer:
b
Step-by-step explanation:
x + 5y = 4x - 3y ( subtract 4x from both sides )
- 3x + 5y = - 3y ( subtract 5y from both sides )
- 3x = - 8y ( multiply both sides by - 1 )
3x = 8y → b
Please help I’ll mark you as brainliest if correct!!
Answers
Set A ={q, g, c, z, b}
What is a Venn diagram?
A Venn diagram is a popular diagram type for displaying the logical relationship between sets. Venn diagrams display all potential relationships between the sets by having all of the curves overlap in every way.Simple closed curves depicted on a plane are used in Venn diagrams to illustrate sets. These curves resemble circles or ellipses quite frequently.What is a roaster form?
Roster notation is a straightforward way to represent a set in mathematical form. Within the curly brackets of the roster form, the components of a set are listed in a row. If the set has more than one element, a comma is used to denote the separation of every pair of elements in a roster notation. Because the enumeration is done one by one, the roster form is also known as an enumeration notation.For example : A ={q, g, c, z, b}To learn more about Venn diagrams, refer:
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(-1, 2), slope = 2 slope intercept form
Answers
Answer:
Slope-intercept form is given as y = mx + c where m is the slope and c is the y-intercept.
Since slope = 2, equation is y = 2x + c.
Substitute (-1,2) into the equation to find c.
2 = 2(-1) + c
c = 4
Hence, equation is y = 2x + 4
2(3/4L-1) + 2(18) = 2L + 2(12)
Answers
2(3/4L-1) + 2(18) = 2L + 2(12)
Distribute
3/2 L -2 +36 = 2L +24
Subtract 3/2 L from each side
-3/2 L-3/2L
-2+36 = 4/2L-3/2L +24
34 = 1/2L +24
Subtract 24 from each side
34-24 = 1/2 L +24-24
10 = 1/2L
Multiply each side by 2
10*2 =1/2L * 2
20 = L
Which equation represents the graphed function?
a. y=-3x + 3
b. y = 3x3
c. y = 3x -
d.y=-x+3
Answers
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
Answer:
A: Reflection over the y-axis
B: Translation 3 right
C: Translation 4 down
D: Reflection over the x-axis
Step-by-step explanation:
A: This is a reflection over the y axis because we can tell it has been flipped to the other side, vertically.
B: Count the spaces between the two 'P's, getting 3 to the right. This is not a reflection because it is facing the same way.
C: Count the spaces between the two 'P's, getting 4 down. Again, this is not a reflection because it is facing the same way.
D. This is a reflection over the x axis because we can tell it has been flipped to the other side, horizontally.
Hope it helps!