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The equation of ellipse with foci (-6,-1) and (-6,-7), and co-vertices (-2,-4) and (-10,-4) is [tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]

What is equation of an ellipse?

The standard equation of an ellipse centered at (h, k) with a major axis parallel to the x-axis is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

where the coordinates of the vertex are (h±a, 0), coordinates of co-vertex are (h, k ± b) and the coordinates of foci are (h±c, k), where a² = c² + b².

According to the given question:

Given foci of the ellipse :

(-6, -1) and (-6, -7)

Co-vertices of the ellipse :

(-2, -4) and (-10, -4)

From the given foci and vertices ,

c = -1 - (-7) /2 = 3

b = -2 - (-10) /2 = 4

c² = a² + b²

∴ a² = 3 x 3 + 4 x 4 = 25

( h, k) = (-6 - 6 /2 , -1 - 7 / 2) = (-6, -4)

Equation of the ellipse is given by:

(x - h)²/ a² + (y - k)²/b² =1

(x - (-6))²/ 25 + (y - (-4))²/16 = 1

[tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]

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Answer:

y = 2/3x - 2

Step-by-step explanation:

To Literally Solve for y, we must first isolate it. This means putting it and its coefficient on the own side of the equation.

If you add, multiply, divide, subtract, put something to the power/root both sides of an equation, the final result will stay the same.

4x - 6y = 12

Subtract 4x on both sides.

4x - 4x -6y = 12 - 4x

Simplify.

-6y = 12 - 4x

Divide both sides by -6.

y = -2 + 2/3x

Adjusted the equation for clarity.

y = 2/3x - 2

Answer:

The graph of x - y = 4 is D.

Step-by-step explanation:

substituting a random value for either x or y will give you a value for the other unknown

that's to say,if x is 2 ,then y will be -2

More pairs of coordinates then are got using the same method

these are plotted and a graph similar to the one in D is got.

As the given polynomial -8y has only 1 term in is and hence it is classified as a monomial.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The quantity of terms allows for the classification (naming) of polynomials.

A polynomial may contain exponents, constants, and variables, but it never divides by a variable.

They may also contain one or more terms, but not an infinite quantity.

The degree can also be used to categorize polynomials (the largest exponent of the variable).

An expression with only one term is called a monomial.

The sole term in an expression needs to be non-zero in order for it to be a monomial.

Therefore, as the given polynomial -8y has only 1 term in is and hence it is classified as a monomial.

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Answer:

I think it's 0.5%

Step-by-step explanation:

16/32 x 100% = 0.5%

Answer:

13

Step-by-step explanation:

You take the number of miles from weeks 5-8 and add them up. 2+3+4+4=13

Answer:

3,4

Step-by-step explanation:

use section formula,as it divides in 1 :1

7+x/2 =5 so x is 3

The letters of the points that satisfy the inequalities are  points A, D, E, I

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The given parameters are:

y<-[tex]\frac{1}{2}x +2[/tex]   and

2x+y≤8

If we plot the graphs of the first inequality,

we notice that the coordinates of the origin are (0,0) then we have

Rearrange the inequality

[tex]y > -\frac{1}{2} x=2[/tex]

At origin y=0, x=0

[tex]0+\frac{1}{2}(0) > 2[/tex]

⇒ 0+0<2                (false)

Therefore the origin is not included

In the second inequality

2x+y≤8

Coordinates of the origin are (0,0)

2(0)+(0)≤8

0+0≤8             (False)

Therefore the origin is not included.

In conclusion the points that satisfy the inequalities are points A,D,E,I

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Answer:

43 p

Step-by-step explanation:

total cost = 10 - 4.84 = 10.00 - 4.84 = £5.16

b + t = 5.16

t = 11b

b + 11b = 5.16

12b = 5.16

12 / 12 b = 5.16/12

b = £0.43

Answer:

? = 180

Step-by-step explanation:

For this we have to calculate 50% of 7,000 which is 3,500

What does a math percent mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula for percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

first we have to calculate 70% of 10,000 which is 7,000

Then now we have to calculate 50% of 7,000 which is 3,500

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Entonces, la distancia entre los puntos A y B es de aproximadamente 15.

Generalmente, Para encontrar la distancia entre los puntos A y B, puedes utilizar la fórmula de la distancia euclidiana:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

En este caso, la distancia sería:

d = √((3 - (-6))² + (-7 - 5)²)

The square root of ((3 - (-6))² + (-7 - 5)²) is equal to:

=√((3 - (-6))² + (-7 - 5)²)

= √((9)² + (-7 - 5)²)

= √(81 + 144)

= √225

d ≈15

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Encontró la pregunta completa

El punto A está en (-6,5) y el punto B está en (3,-7). ¿Cuál es la distancia entre los puntos

Based on the definition of an equilateral triangle, the measure of angle KML is: d 60.

An equilateral triangle can be described as a triangle that has three sides that are equal and also equal interior angles that measures 60 degrees each.

The image shows that the three sides of triangle KML are marked equally by three strokes. This shows that the three sides of triangle KML are congruent to each other. Since they are congruent, they have equal length.

Therefore, triangle KML is an equilateral triangle that has interior angles that measures 60 degrees.

Angle KML is an interior angle of the equilateral triangle, therefore:

The measure of angle KML is: d. 60 degrees.

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Answer: log81 = 1/4

Step-by-step explanation:

Log81^3

81^x = 3

The common base is 3, so

(3^4)^x=3

3^4x = 3^1

4x = 1

x= 1/4

Answer:

16.5

Step-by-step explanation:

8.25+8.25=16.5

The pound as a unit of mass , 14 x (1ounce)= 14 ounce.

The British imperial and American customary systems of measurement both utilize the pound as a unit of mass. The international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms and is divided into 16 avoirdupois ounces, is the definition that is currently most frequently used.

The avoirdupois pound is represented by the worldwide standard symbol, lbm (for the majority of pound definitions), (mostly in the U.S.),  and  (particularly for the apothecaries' pound).

The currency came from the Roman libra (hence the abbreviation "lb"). The Dutch term pond, the Swedish word pund, and the German word pfund are all cognates of the English word pound.

Older and no longer in use, these units (replaced by the metric system).

Hence, 14 x (1ounce)= 14 ounce.

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The KN is 21.4 rounded to the nearest tenth.

The orthocenter of a triangle is the place where the perpendicular drawn from the vertices to the opposing sides of the triangle intersect each other. The orthocenter for a triangle with an acute angle is located within the triangle. The orthocenter for a triangle with an acute angle is outside the triangle.

Now we need to find the slope of JL.

From that we have to find the slope of the perpendicular line through B.

Slope of JL=  (y₂ - y₁) / (x₂ - x₁)

J (7, 8) and L (5, 2)

here x₁=  7,y₁  = 8, x₂ = 5 and y₂ = 2

=  -6 / -2

= 3

Slope of the altitude KM  =  -1/ slope of JL = -1/3

Equation of the altitude KM : (y - y₁)  =  m (x -x₁)

Here K(1,2);

(y - 2)  =  -1/3 (x -1)

(y - 2)  =  -x/3 +1/3

Now we need to find the slope of JK.

From that we have to find the slope of the perpendicular line through D.

Slope of KL=  (y₂ - y₁) / (x₂ - x₁)

J(7,8) and K(1,2)

here x₁=  7,y₁  = 8, x₂ = 1 and y₂ = 2

 = 1

Slope of the altitude JO  =  -1/ slope of JL

                                         = -1

Equation of the altitude JO : (y - y₁)  =  m (x -x₁):

 (y - 8)  =  -1 (x - 7)

Solving the equation, x = 21 and y = -6

So the orthocenter N is (21 , -6)

Now the distance of KN is = √(21 - 1)² + (-6 -2)²

                                             =√464

                                             = 21.5

Therefore, the KN is 21.5 rounded to the nearest tenth.

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Answer:6.3

Step-by-step explanation:

I got it correct on my test

The required length of AE will be 14 units on the given rhombus.

We know that all sides of a rhombus are equal, then note that AD equals DC, that is;

4x + 2 = 7x - 13

2 + 13 = 7x - 4x

15 = 3x

Divide both sides of the equation by 3

5 = x

If AD = 4x + 2, then when x  = 5

AD = 4(5) + 2

AD = 20 + 2

AD = 22

So, triangle ADE may now be separated, with AD measuring 22 units and ED measuring 17 units (midpoint between points B and D). Line AE may be determined using Pythagoras' theorem, which states:

AC² = AB² + BC²

Where AC is the hypotenuse, and AB and BC are the two other sides

Substituting for values as given in the question, we now have;

AD² = ED² + AE²

22² = 17² + AE²

484 = 289 + AE²

484 - 289 = AE²

195 = AE²

√195 = AE

13.96 = AE

So, length AE ≈ 14 units (to the nearest whole number)

Thus, the required length of AE will be 14 units on the given rhombus.

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Answer:

x = 0 and y = 2

Step-by-step explanation:

5x + 3y = 6

-5x - 3y = -6

Adding the equations gives 0 = 0, so the equations are equivalent.

x = 0 and y = 2

The outside temperature t when Josefina ate breakfast was 55F.

What are equations?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

According to the given question:

Let the temperature outside at the time of breakfast be t.

Temperature dropped by 20F by the time for dinner.

So the temperature at the time of breakfast was t - 20

Now, when she ate dinner the temperature was 35F

So the equation for outside temperature t when Josefina ate breakfast is

t - 20 = 35

Solving to get t that is temperature in the morning

t = 35 + 20

t = 55F

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can you send a picture of the question?

For the given similar triangle the value of x will be 9 inches.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Since the two triangles are similar,

Suppose the unknown side is x,

Since the ratio of the sides of the similar triangles is equal the obtained expression is,

8/6=12/x

x=12×6 / 8

x=9 inches

Thus, for the given similar triangle the value of x will be 9 inches.

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Answer:

15

Step-by-step explanation:

The slope of the line passing through the points  (-9, 6) and (-3, 9) is (1/2).

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is

y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

Given, A line passes through the points (-9, 6) and (-3, 9).

∴ Slope(m) of the line is = (9 - 6)/(- 3 + 9) = 3/6 = 1/2.

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Answer:

A. [tex]y=11x[/tex]

Step-by-step explanation:

The graph is linear, meaning it follows the formula [tex]y=mx+b[/tex], where y and x are variables, m is the constant rate that the graph increases by, and b is the y-intercept. The graph is increasing at a rate of 55 calories burned per 5 minutes spent skateboarding, which simplifies to 11 calories per 1 minute, so m is 11. The graph's y-intercept is 0 because it runs through the origin, and there's no point in writing "11x + 0" so it's just "y = 11x"

Answer:

C

Step-by-step explanation:

4x + 3y = 24

3y = -4x + 24

y = -3/4x + 8

May I please have brainliest? It will really help me get to the next level! Thank you!

Answer:

Y= -4/3x + 8

Step-by-step explanation:

4x + 3y = 24

-4x             -4x

3y = -4x + 24

/3      /3     /3

Y = -4/3x + 8

Answer: 80

Step-by-step explanation:

The owners will need 80 racks to hold all 7,200 comic books. (7,200 / 90 = 80)

Answer:

Step-by-step explanation:

o.67891