Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark

quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1

Answers

Answer 1

The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

The vertices of the ellipse = (1, 0) and (11, 0)

Eccentricity of ellipse = 3/5

We have equations:

[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]

[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]

[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]

From the fourth equation:

The vertices of the ellipse:

(1, 0) and (11, 0)

The eccentricity:

c²  = a² - b²

c² = 25-16

c = 3

e = c/a = 3/5

Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

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Which Of The Following Is The Standard Equation Of The Ellipse With Vertices At (1, 0) And (11, 0) And

Related Questions

Factor the binomial 9t to second power,-4 =

Answers

Using subtraction of perfect squares, it is found that the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

What is the subtraction of perfect squares factoring?

It is given as follows:

a^2 - b^2 = (a - b)(a + b)

In this problem, the binomial is given as follows:

9t² - 4.

Hence:

a² = 9t² -> a = 3t.b² = 4 -> b = 2.

Hence the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

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If the factors of quadratic function f are (x-7) and (x+3) what are the zeros of function g?

Answers

If the factors of quadratic function f are (x – 7) and (x + 3). The solution of the quadratic function f will be the negative 3 and 7.

What is a factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the factors of quadratic function f are (x – 7) and (x + 3).

Then the zeroes of function f will be

(x – 7)(x + 3) = 0

                x = 7, -3

Then the solution of the quadratic function f will be the negative 3 and 7.

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[tex] \displaystyle \sum_{n = 1}^{ \infty } {4}^{ - n} [/tex]
evaluation of the sum above ​

Answers

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]

The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.

To find the first term in the series, substitute n = 1 into the expression:

[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]

The common ratio of the geometric series can be found by dividing one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]

As | r | <  1  the series is convergent.

When a series is convergent, we can find its sum to infinity (the limit of the series).

Sum to infinity formula:

[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]

where:

a is the first term in the seriesr is the common ratio

Substitute the found values of a and r into the formula:

[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]

Therefore:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]

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Which expression is equivalent to this polynomial?
x2+12
OA. (X +2v3i)(c – 2v3i)
OB. (x+6i)(x - 6i)
OC. (x + 2√3)²
OD. (x + 2√3)(x − 2√3)

Answers

x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).

What are Polynomials?

Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.

The given expression is x² + 12.

We have the identity (a + b) (a - b) = a² - b²

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²

                                = x² - (2² × √3² × i²)

We know that i² = -1, where i is the imaginary number in complex numbers

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)

                                = x² + 12

Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.

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f(x)=1/x at x=1 find slope of tangent

Answers

Answer:

f'(1)=-1

Step-by-step explanation:

You can just find the derivative using the power rule for d/dx (x^-1)=-1x^-2=-1/x^2 then find f'(1)=-1.

I used the limit definition of the derivative to find the slope in the picture attached

The parabolas y = -x² and y= -x² - 4x + 6 are graphed below. What are the y-values of the solutions to this system of equations?

y= 1,9
y= 1,6
y= -0,6
y= -3,1

Answers

Answer:

y = 1, 9.

Step-by-step explanation:

They are the y values of the points of intersection of the 2 parabolas.

y = 1, 9.

The graphs below have the same shapes. What is the equation for the red graph?

Answers

The equation for the red graph is f(x) = -x².

How to depict the equation?

From the information given, g(x) = 4 - x².

The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:

(x, y) = (x, y -4).

The equation of the function will be:

f(x) = g(x) - 4

f(x) = (4 - x²) - 4

f(x) = -x²

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What is the equation of the parabola? (3 points)

A) y = -1/8x^2 +5

B) y = 1/8x^2 +5

C) y = 1/8x^2 - 5

D) y = -1/8x^2 -5

Answers

Answer:

A.

Step-by-step explanation:

The parabola opens down, so the "a" value (the number in front of x^2) must be negative. The y-intercept is (0, 5) so the constant must be positive 5.



6 out of 11 players played well on the baseball team. What percent is it?

Answers

It would be 54.5% or 55%. If you divide 6/11 you get .545 so you move the decimal place 2 to the left and that’s how you get the percentage.

Answer: 54%

Step-by-step explanation:

You will need to divide these numbers.

[tex]6/11=0.54[/tex]

After you divide that, simplify that to a percentage by multiplying it by 100.

[tex]0.54 *100=54%[/tex]%

I hope this helps!!

A teacher asked her students how many pets they own. Here
are the results:
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8
On a piece of paper, draw a dot plot to represent the data.
Then determine which answer choice matches the dot plot
you drew.

Answers

Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

What is a dot plot?

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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Which expression is equivalent to √48x5, if x> 0?
A. 12x³√3x
B. 4x³√3
C. 4x²√3x
D. 12x²√

Answers

Answer:

C. 4x²√(3x)

Step-by-step explanation:

if x > 0

[tex]\sqrt{48x^{5}} =\sqrt{48} \times \sqrt{x^{5}}[/tex]

          [tex]=\sqrt{16\times 3} \times \sqrt{x^{4}\times x}[/tex]

          [tex]=\sqrt{16} \times \sqrt{3} \times \sqrt{x^{4}} \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times \sqrt{\left( x^{2}\right)^{2} } \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times x^{2}\times \sqrt{x}[/tex]

          [tex]=4\times x^{2} \times \sqrt{3} \times \sqrt{x}[/tex]

          [tex]=4\times x^{2}\times \sqrt{3x}[/tex]

Find BC.
plssss helpp!!!

Answers

Answer:

BC is 22.5 mi

Step-by-step explanation:

Using the pythagorean theorem formula. c² = a² + b²

BC² = AB² + AC²

BC² = 19² + 12²

BC² = 361 + 144

BC² = 505

BC² = 505

BC = 22.5

Therefore BC is 22.5 mi

Y-6.37x=-3 which of the following function notation corresponds to the equation below

Answers

Wheres the other part of the question

Solve for y.
frankly im confusion
a:4.53
b.4
c.7.47
c.8

Answers

Answer:

8

Step-by-step explanation:

Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.

Applying this, we'll be obtaining the equation that of:

[tex]116=15y-4[/tex]

We now simply solve for y.

[tex]120=15y\\y=8[/tex]

Therefore, y is equal to 8.

This can be checked by plugging it into the equation:

[tex]15(8)-4[/tex]

[tex]120-4[/tex]

[tex]116[/tex]

And look at that, we got 116 for our answer, exactly the same as the other angle.

Any questions feel free to ask :)

the answer to this is answer C:8.

What is 2(x+3) / 4(x+1)

Answers

Answer:

x² + 4x + 3

---------------

       2

---- => fraction line

What is 3/4 divided by 1/2

Answers

Answer:
Fraction: 3/2
Decimal: 1.5

Answer:

1 1/2

Step-by-step explanation:

Convert both fractions into decimals

⇒ 3/4 (0.75) and 1/2 (0.50)

Divide the decimals:

⇒0.75 ÷ 0.50

Find the quotient

⇒ 1.5

Convert the quotient to a fraction

⇒ 1 1/2

Terms:

Operations with fractions

please help with this problem
thanks so much

Answers

Answer:

5/17

Step-by-step explanation:

If we do the multiplication first, we get:

[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]

If we do the division next, we get:

[tex]\frac{4+1}{13+4} = 5/17[/tex]

Can anyone please help me with this question?

Karl receives his first mark of the year in his law course. He scores 94th percentile. What is his mark!?

Answers

Answer:

Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.

So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.

Find the equation of a line that passes through the point (-2,1) and has a gradient of -3.
Leave your answer in the form
y
=
m
x
+
c

Answers

A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

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PWhat are the x- and y-intercepts of the line y = 4x + 12?
A. x-intercept = 3; y-intercept = -12
B. x-intercept = -3; y-intercept = 12
C. x-intercept = -12; y-intercept = 3
D. x-intercept = 12; y-intercept = -3
PLEASE HELP

Answers

Answer:

B

Step-by-step explanation:

when x is 0 y=4(0)+12 y=12

y is 0 y=4(-3) +12 = 12=12

3. What are the roots of the polynomial y = x³ - 8?

Answers

Step-by-step explanation:

x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.

[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

Cube root of x^3 is x.

Cube root of 8 is 2

So

a=x

b= 2.

[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]

Set these equations equal to zero

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

[tex] {x}^{2} - 2x + 4 = 0[/tex]

If we do the discriminant, we get a negative answer so we would have two imaginary solutions,

Thus the only real root is 2.

If you want imaginary solutions, apply the quadratic formula.

[tex]1 + i \sqrt{ 3 } [/tex]

and

[tex]1 - i \sqrt{3} [/tex]

A student wants to simulate 37 ​birthdays, but she does not have a calculator or software program​ available, so she makes up 37 numbers between 1 and 365. Is it okay to conduct the simulation this​ way? Why or why​ not?

Answers

It is not okay to conduct the simulation because people generally favor some numbers.

How to illustrate the information?

From the information given, the student wants to simulate 37 birthdays, but she does not have a calculator or software program available.

In this case, it's not okay to conduct the simulation because people generally favor some numbers.

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Question is attached………

Answers

Answer:

d. 11:15

Step-by-step explanation:

1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;

2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;

3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.

4) finally, the both officers are in the required location at 11:15.

If xy=3 yz=6 zx=2 find x+y+z​

Answers

Answer: 1+3+2=6
Explanation: 1x3=3
3x2=6
2x1=2

What should be added to -2 1/9 to get 11

Answers

Answer:

u should add 118/9

Step-by-step explanation:

please mark me as brainlest

The following lots of Commodity Z were available for sale during the year. Beginning inventory 9 units at $50 First purchase 16 units at $50 Second purchase 21 units at $59 Third purchase 16 units at $62 The firm uses the periodic system, and there are 23 units of the commodity on hand at the end of the year. What is the ending inventory balance at the end of the year according to the FIFO method?

Answers

According to the FIFO method, the ending inventory balance for Commodity Z is $1,405

How much inventory is left under FIFO?

FIFO means that earlier inventory is sold first and later inventory would be the last goods left.

Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:

= (16 x 62) + (7 x 59)

= 992 + 413

= $1,405

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The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?

Answers

Answer:

212520 different committees

Step-by-step explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps

Answer:

To whom it may concern the answer to this problem would be 212,520.

Step-by-step explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]

Remember that the 19! cancel each other out. Hope this helps!

Question 9
Write the equation of the line passing through (3,-17) parallel to 8x - 7y=87

Answers

Rewriting the equation of the given line in slope-intercept form,

[tex]8x-7y=87\\\\-7y=-8x+87\\\\7y=8x-87\\\\y=\frac{8}{7}x-\frac{87}{7}[/tex]

The slope of the given line is thus 8/7, and since parallel lines have the same slope, the slope of the line we want to find is also 8/7.

Substituting into point-slope form,

[tex]y+17=\frac{8}{7}(x-3)\\\\y+17=\frac{8}{7}x-\frac{24}[7}\\\\\boxed{y=\frac{8}{7}x-\frac{143}{7}}[/tex]

If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5

Answers

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Given functions:f(x) = x + 8g(x) = -4x - 3Solution:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

[tex]\rule[225]{225}{2}[/tex]

Please answer all three questions Pleaseeeeee tysmm <3

Answers

Answer: 2 3/4 > 2.68 is correct (only)

Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68

The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.

Sqrt(63) = 7.93, and 7.93 > 8.11 is false.

Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2

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