An elliptical-shaped path surrounds a garden, modeled by quantity x minus 22 end quantity squared over 225 plus quantity y minus 26 end quantity squared over 324 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?

Answer:

I don't understand what you mean

Answer:

x = 8, y = 4

This can also be written as an ordered pair: (8, 4)

Step-by-step explanation:

First, set up a system of equations:

x + y = 12, $2x + $6y = $40

The first equation shows that there are a total of 12 tickets, and the other shows that the total of money for all the tickets adds to $40.

Then, solve by elimination by subtracting twice the first equation from the second to isolate y:

  2x + 6y = 40

- (2x + 2y = 24)

  0   + 4y = 16

And now we can solve for y:

4y = 16

y = 4

Then, put this back into the original equation to solve for x:

x + y = 12

x + 4 = 12

x = 8

Answer:

[tex]7 {x}^{2} + 49 = 0 \\ 7( {x}^{2} + 7) = 0 \\ \frac{7( ({x}^{2} + 7) }{7} = \frac{0}{7} \\ {x}^{2} + 7 = 0 \\ {x}^{2} = - 7[/tex]

NOTE THERE IS NO SOLUTION FOR THE GIVEN EQUATION SINCE THE SQUARE OF ANY NUMBER CANNOT GIVE A NEGATIVE NUMBER.

THE SQUARE OF ANY NUMBER WHETHER IT'S POSITIVE OR NEGATIVE ALWAYS GIVES A POSITIVE NUMBER.

GOODLUCK!!

Popular Problems Algebra Solve for h A=1/2h(b+B)

A = 1/2h (b+B)

h=2Ab+B

Explanation

Popular Problems Algebra Solve for h A=1/2h(b+B)

A= 1/2 h(b+B)

Rewrite the equation as

1/2⋅(h(b+B))=A.

1/2⋅(h(b+B))=A

Multiply both sides of the equation by 2.

2(1/2⋅(h(b+B)))=2A

hb+hB=2A

Factor h out of hb+hB.

h(b+B)=2A

Divide each term in h(b+B)=2A by b+B and simplify.

h=2Ab+B

How is algebra solved?

A General Rule for Equation Solving

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( \frac{{x}^{2} - 4x + 5) }{2 \sqrt{x} } )}{x } [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ {x}^{2} - 4x + 5 }{ \sqrt{x} } [/tex]

We know, division rule of differentiation :

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{u}{v} [/tex]

then,

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{v\frac{du}{dx} - u \frac{dv}{dx} }{(v) {}^{2} } [/tex]

So, let's do the same in given equation :

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} \frac{d}{dx}(x {}^{2} - 4x + 5) - ( {x}^{2} - 4x + 5) \frac{d}{dx}( \sqrt{x} ) }{( \sqrt{x} ) {}^{2} } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( {x}^{2} - 4x + 5) \frac{1}{2 \sqrt{x} } }{x } [/tex]

[ This is the required Answer, but you can simplify it however you want according to the choices given ]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{x \bigg( \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } \bigg)}{x } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{(2x - 4)}{ \sqrt{ x}} - \frac{( {x}^{2} - 4x + 5) }{2 \sqrt{x {}^{3} } }[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

 y = - 4x + - 8 is equation of slope-intercept form.

What is in slope-intercept form?

the equation of slope - intercept form

                               y = mx + c

( -1 , -4 ) is point shown in graph

            slope = -y/x

                     = - ( -4)/-1  = 4/-1 = -4

             - 4 = -4 * - 1 + c

            - 4 = 4 + c

            c = - 4 - 4 = - 8

put value of c in the equation of slope - intercept form

             y = - 4x + - 8

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The coordinates of the point of intersection are (-6, -7)

The graph represents the given parameter

On the graph, we can see that there are two lines with the following properties:

The above properties means that:

From the graph, we can see that the lines A and the other line meet at a point

The point where these lines meet is referred to as the point of intersection

The coordinates of this point are (-6, -7)

Hence, the coordinates of the point where line a & tne line that has an undefined slope intersect are (-6, -7)

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Answer:

y = 25x + 865

so the monthly rent in 2021 is 1,140

do you need an explanation or is this fine?

ANSWER

EXPLANATION

First, we have to draw horizontal lines at the minimum and maximum heights. These are 10 feet and 210 feet, respectively.

Then, we calculate the midline,

And we have to draw this line too.

As mentioned, the period is the time it takes to do one revolution, which this wheel makes in 90 seconds. Thus, the period is 90 seconds and the first cycle starts at t = 0 and ends at t = 90 s,

Then, we know that the graph is sinusoidal, so we have to draw the first cycle - note that if the period is 90 s, the graph must intersect the midline at 45 seconds,

And finally, draw another cycle just like the first one.

The pairs of whole numbers which have 40 as a sum is 21

What is Whole numbers ?

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.

For finding the term we use Arithmetic Progression which is :

a(n) = a + (n - 1)d

where,

a(n)  = the nᵗʰ term in the sequence

a = the first term in the sequence

d = the common difference between terms

Given,

The first term a₁ = 0

The common difference d = 1 (from 1 - 0, 2 - 1, etc.)

The last term aₙ = 20

Putting the values in the formula we get,

20 = 0 + (n - 1)1

20 = 0 + n- 1

20 + 1 = n

21 = n

Hence, there are 21 pairs of whole numbers that have a sum of 40

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The solution of given inequality 3-|4-n| >1 is 2<n<6.So option D is correct.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

The given inequality is 3 - |4-n| > 1

Since |4-n| is the absolute value

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

So ( 4-n ) may be negative or positive.

For positive value of ( 4-n )

3-( 4-n ) > 1

3-4+n>1

n>2

For negative value of (4-x)

3+( 4-n )>1

3 + 4-n >1

7 - n > 1

-n> 1 -7

-n > -6

n < 6

Hence, 2 < n < 6 i.e. option D is the solution to the inequality 3-|4-n| >1.

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Answer: d

Step-by-step explanation:

The value of x is given by 6 units and the value of TV is given by 7 units.

A circle may be defined as a closed loop which has a fixed point around which the loop is made called the center and the fixed distance from the center of the circle to its periphery is known as the radius of the circle. We are given a circle with center at Z. In the circle QR and ST are the chords such that QR = ST = 14 that is both are of equal length, and we know that equal chords are at equal distance from the center. Therefore,

VZ = UZ

23 = 3x + 5

18 = 3x

=> x = 18/3

=> x = 6 units.

Now, we also know that perpendicular drawn from center of the circle to the chord bisects the chord. Thus,

TV = (1/2)×ST

TV = (1/2)×14

TV = 7 units.

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Given:

Diagram is given.

Measure of X and Y forms a linear pair of supplementary.

Answer: y=(x-3)^2 -14

Step-by-step explanation:

use the formula (b/2)^2 to create a new term to complete the square

Explanation

We are given the following equation:

We are required to determine the solution of the given equation.

This is achieved thus:

The only solution to this equation involves complex numbers. So, there is no real solution.

Hence, the answer is:

the value of  P(E and F) is equal to 0.175 when E and F are independent events with P(E) = 0.25 and P(F) = 0.7.

We are given the two events:

E and F

We are also given that these events are independent events and:

P (E) = 0.25

P (F) = 0.7

We need to find:

P (E and F)

We know, that when two events are independent events that is they don't relate to each other, then P(E and F) is given by:

P(E and F) = P (E) × P (F)

P(E and F) = 0.25 × 0.7

P(E and F) = 0.175

Therefore, we get that, the value of  P(E and F) is equal to 0.175 when E and F are independent events with P(E) = 0.25 and P(F) = 0.7.

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1. The pairs of measurements that could have the dimensions of Rectangle B include:

A. 6cm by 1.5cm

D. 18cm by 4.5cm

E. 80cm by 20cm

2. Rectangle A is a scaled copy of rectangle B as the scale factor is 3:2.

Rectangle C isn't a scales factor of rectangle B since they have different ratio.

1. It should be noted that from the information, Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A.

Therefore, it should be noted that the ratio will be:

= 12 / 3

= 4 / 1

= 4:1

Therefore, the values that will give same ratio will be:

6cm by 1.5cm = 6/1.5 = 4:1

18cm by 4.5cm = 18/4.5 = 4:1

80cm by 20cm = 80/20 = 4:1

In conclusion, the correct options are A, D, and E.

2. Rectangle A is 12 long and 8 wide. The ratio will be:

= 12/8 = 3/2 = 3:2.

Rectangle B is 15 long and 10 wide. The ratio will be:

= 15/10 = 3/2 = 3:2

Rectangle C is 30 long and 15 wide. The ratio will be:

= 30/15 = 2:1

Therefore, rectangle A and B have same scale.

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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all pairs of measurements that could have the dimensions of Rectangle B.

A. 6cm by 1.5cm

B. 10cm by 2cm

C. 13cm by 4cm

D. 18cm by 4.5cm

E. 80cm by 20cm

According to the exterior angle theorem, an external angle's measure is equal to the sum of its remote interior angle's two measurements. The opposite interior angles are another name for the remote interior angles. Where can I determine a triangle's outer angle? In a triangle, how can I determine the interior and outside angles?

Take the total of two interior angles of a triangle that are known and deduct it from 180 to find the internal angle of the triangle.

Simple addition of the triangle's two opposite internal angles will yield the triangle's external angle. 180° minus the inside angle equals each exterior angle. Using this formula requires the knowledge of the corresponding internal angle. Exterior angle = Total.

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The rule of probability is

Since the die has 6 numbers, then

The total = 6

Since there are 5 numbers without 3, then

A = 5

Substitute them in the rule above

The answer is 5/6

Let's analyze the example of the ratio of 9 to 15.

This ratio helps us to compare those two numbers. We can express it in different ways:

Answer:

24 ajsndkalxndma skwma wjlslaos ndnajala

I believe that Americans have just the right amount of freedom.

The First Amendment protects our freedom of speech and association, so the government cannot stop us from writing or speaking what we choose. We also have the right to create clubs and groups and participate in protests and rallies.

As long as you don't "materially and substantially" interrupt classrooms or other school activities, you have the right to voice your ideas. School administrators can disperse you if you stage a demonstration on the steps of the building and block the entrance. Additionally, they may be able to prevent you from using words that they deem to be "vulgar or indecent."

The above shows that despite the right of freedom, it's important to checkmate what people do.

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The approximate percentage of buyers who paid between $1925 and $2075 is; 68%

The approximate percentage of buyers who paid between $1925 and $2000 is; 34%

We are given;

Mean = $2000

Standard Deviation = $75

1) We want to find the approximate percentage of buyers who paid between $1925 and $2075

The formula that is used to calculate the z-score of a a normal distribution is;

z = (x' - μ)/σ

where;

z is z-score

x' is sample mean

μ is population mean

σ is standard deviation

For a payment of 1925;

z = (1925 - 2000)/75 = -1

For a payment of2075;

z = (1925 - 2000)/75 = 1

Thus, this is 1 standard deviation from the mean.

Thus, this is a percentage of 68%

2) We want to find the approximate percentage of buyers who paid between $1925 and $2000?

For a payment of 1925;

z = (1925 - 2000)/75 = -1

For a payment of 2000;

z = (2000 - 2000)/75 = 0

This translates to a percentage of (1/2) * 68% = 34%

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Missing options are;

1) What is the approximate percentage of buyers who paid between $1925 and $2075?

2) What is the approximate percentage of buyers who paid between $1925 and $2000?

Answer:

average rate of change = 23

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 4, 9 ] , then

f(b) = f(9) = 212 ← from ordered pair in table

f(a) = f(4) = 97 ← from ordered pair in table , then

average rate of change = [tex]\frac{212-97}{9-4}[/tex] = [tex]\frac{115}{5}[/tex] = 23

Brian likes the feeling of owning his own car. He takes good care of it and doesn't like changing cars often is whom a car loan would be a better option than a car lease and is denoted as option B.

This is referred to as the total money borrowed which is used in the purchase of a car while on the other hand car lease involves the vehicle being made available to be driven for  certain period of time or limit.

Since Brian likes the feeling of owning his own car and doesn't change cars often, then the car loan is best for him as it becomes his after the money or amount to be repaid is completed.

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Step-by-step explanation:

substitute with 10 in the equation

The vertices after dilation are (12, 12), (18, 21), and (24, 0)

The vertices of the triangle are given as

(4, 4), (6, 7), and (8, 0)

The scale factor of dilation is given as 3

This means that

k = 3

The vertices of the new triangle are calculated as

Vertices = scale factor * Old vertices

So, we have

[(4, 4), (6, 7), and (8, 0)] * 3

Evaluate

(12, 12), (18, 21), and (24, 0)

Hence, the vertices of the new triangle are (12, 12), (18, 21), and (24, 0)

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y = -2x + 12 is the linear equation of the line that passes through the coordinates of points (1, 10) and (2, 8).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

The slope of a line is expressed as change in y over change in x.

Slope m = (y₂-y₁)/(x₂-x₁)

Given the data in the question;

Point 1 ( 1, 10 )

Point 2 ( 2, 8 )

First, we determine the slope of the line.

Slope m = (y₂-y₁)/(x₂-x₁)

Slope m = ( 8 - 10 )/( 2 - 1 )

Slope m = (-2)/( 1 )

Slope m = -2

Now, determine the y-intercept b, by substituting the slope and the coordinates of one point into the equation of line formula.

y = mx + b

10 = -2(1) + b

Solve for b

10 = -2 + b

b = 10 + 2

b = 12

Now that we have the slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = -2(x) + 12

y = -2x + 12

Therefore, the equation of the line that goes through the given points is y = -2x + 12.

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By using trigonometric relations for right triangles, we will see that the height of the tower is 81.92 meters.

First, we know that a pole with a height of 3.3m casts a shadow of 1.48m. We can see the height of the pole and the length of the shadow as the legs of a right triangle, with that, we can get the angle at which the sun hits the pole (this angle is such that the height will be the adjacent cathetus).

Using the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

We can get:

a = Atan( (opposite cathetus)/(adjacent cathetus))

With taht we can find the angle, where:

opposite cathetus = 1.48m

adjacent cathetus) = 3.3m

Then:

a = Atan(1.48/3.3) = 24.16°

For the tower that angle will be the same one, and again, the height is the adjacent cathetus and the shadow the opposite cathetus, so we can write the same equation than before:

tan(24.16°) = shadow/height.

Solving that for the height we get:

height = shadow/tan(24.16°) = 36.75m/tan(24.16°)  = 81.92m

The height of the tower is 81.92 meters.

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