An outdoor racetrack is shaped like an ellipse. The equation of the inner lane is x^2/6241 + y^2/1296=1. Each lane is approximately 1 meter apart. Find the length and width of the second lane, as indicated in the figure. Assume that the center is located at (0,0), that the track is a horizontal ellipse, and that one meter is equivalent to one coordinate unit.

ANSWER CHOICES:

A.
length = 79 m
width = 36 m
B.
length = 81 m
width = 38 m
C.
length = 158 m
width = 72 m
D.
length = 160 m
width = 74 m

After considering the equation, inverse of y = [tex]9x^ {2}[/tex] - 4 is found as  [tex]f^{-1x}[/tex]= ±√[(x + 4)/9].

To find the inverse of the function y = [tex]9x^{2}[/tex] - 4, we can follow these steps:

x = [tex]9y^{2}[/tex] - 4

x + 4 = [tex]9y^{2}[/tex]

[tex]y^{2}[/tex] = (x + 4)/9

y = ±√[(x + 4)/9]

Note that since we are finding the inverse of a function, we need to include both the positive and negative square roots to ensure that the inverse is a function.

3. Switch the roles of x and y by replacing y with [tex]f^{-1x}[/tex] and x with f(y):

[tex]f^{-1x}[/tex] = ±√[(x + 4)/9]

Therefore, the inverse of y = 9x² - 4 is [tex]f^{-1x}[/tex] = ±√[(x + 4)/9].

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2.95 miles

The question involves radio direction finders placed at two points, A and B, which are 4.32 miles apart on an east-west line. The transmitter has bearings 10.1 degrees from A and 310.1 degrees from B. The task is to determine the distance from A.In order to determine the distance from A, the first step is to construct a diagram of the scenario to visualize the placement of the three points, A, B, and the transmitter. To do so, a coordinate system is used, with A being located at the origin (0,0).The bearing of the transmitter from A is 10.1 degrees, which can be plotted on the diagram as a straight line from the origin to an angle of 10.1 degrees to the east. Similarly, the bearing of the transmitter from B is 310.1 degrees, which can be plotted on the diagram as a straight line from point B to an angle of 49.9 degrees to the west.To determine the distance from A, the Law of Cosines can be applied, which states that c^2 = a^2 + b^2 − 2ab cos(C), where c is the unknown side, a and b are the known sides, and C is the angle opposite the unknown side. In this case, c is the distance from A, a is the distance from B, and b is the distance between A and B. The angle C is equal to the sum of the two bearings (10.1 + 49.9 = 60 degrees).Therefore, c^2 = a^2 + b^2 − 2ab cos(C) can be rewritten as:dA^2 = d^2 + 4.32^2 - 2d(4.32)cos(60)dA^2 = d^2 + 4.32^2 - 2d(4.32)(1/2)dA^2 = d^2 + 4.32^2 - 2.16dTo solve for dA, the equation can be rearranged and solved for d:0 = d^2 - 2.16d + dA^2 - 4.32^2d = 1.08 ± sqrt(1.08^2 - dA^2 + 4.32^2)The positive root of this equation can be used to determine dA:dA = 1.08 + sqrt(1.08^2 - d^2 + 4.32^2)dA = 1.08 + sqrt(1.08^2 - 4.32^2 cos^2(10.1))dA ≈ 2.95 milesTherefore, the distance from A is approximately 2.95 miles.

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Answer:

A. 6cm B. 10cm

Step-by-step explanation:

The rectangle

Lenght = 18cm and width = 2cm

Area = l x w

Area = 18 x 2 = 36

Ifna square has area of 36cm², all sides are equal

X² = 36

X = square root of 36

X = 6cm

If a square as a Perimeter as the rectangle

Perimeter = 18 +18+ 2+2 =40cm

If Perimeter of square is 40cm and all 4 sides are equal

X =40/ 4

X= 10cm

Answer:

it's D some other type of polyomial

Step-by-step explanation:

because it has more three it's a polynomials= that is many.

By answering the presented question, we may conclude that As a result, equation a milkshake costs $3.50.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.

4x + 2y = 23.50 (equation 1) (equation 1)

8x + 6y = 56.50 (equation 2) (equation 2)

By dividing both sides by 2, we can simplify equation 2:

4x + 3y = 28.25 (equation 3) (equation 3)

We now have two equations and two unknowns. We can find x by deleting y:

4x + 2y = 23.50

4x + 3y = 28.25

We obtain the following when we subtract the first equation from the second:

y = 4.75

To solve for x, we may now plug y = 4.75 into equation 1 or equation 3. Let's look at equation 1:

4x + 2y = 23.50

When we substitute y = 4.75, we get:

4x + 2(4.75) = 23.50

Simplifying:

4x + 9.50 = 23.50

Taking 9.50 off both sides:

4x = 14

Divide all sides by four:

x = 3.50

As a result, a milkshake costs $3.50.

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When the triangle ABC is similar to triangle DEF see in above figure. The measure of side length DE, is equals to the 53.1 .

Similar triangles are the triangles that looks similar to each other but their sizes may or may not be exactly the same. Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio (corresponding sides). We have, triangle ABC and triangle DEF. From the above figure, in ∆ABC,

length of side BC = 8

length of side AB = 13.7

In ∆DEF, length of side, EF = 31

We have to measure the length of side DE. Now, it is specific that triangle ABC is similar to triangle DEF. Using the definition of similar triangles, ratio of corresponding sides of ∆ABC and ∆DEF are in the same ratio. That is, BC/EF = AB/DE

=> 8/31 = 13.7/DE

Cross multiplication

=> DE × 8 = 31× 13.7

=> DE = 31×13.7/8

=> DE = 53.0875

Hence, required rounded side length,DE is 53.1..

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Complete question:

Triangle ABC is similar to Triangle DEF ( see the above figure). Find the measure of side DE. Round Your answer to the nearest tenth if necessary.

Answer:

(-7.5, -2.5)

Step-by-step explanation:

We take

- 12 - 3 / 2 = -15/2 = -7.5

-1 - 4 / 2 = -5/2 = -2.5

So, the midpoint is (-7.5, -2.5)

a.) Jill has 6 pence less than jack, therefore Jill has x-6 pences.

b.) If one box weighs 60grams, b number of boxes will weigh 60*b grams.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The fact that the set of solutions to such an equation forms a straight line in the plane is where the word "linear" originates.

The three forms of linear equations are

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If Jack has x pence, then Jill has 6 pence less than Jack, which means Jill has (x - 6) pence.

Therefore, in terms of x, the number of pence that Jill has is (x - 6).

If one box weighs 60 stams, then the weight of b boxes can be expressed as:

Weight of b boxes =[tex] 60 × b[/tex]

Therefore, in terms of b, the weight of b boxes is 60b stams.

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In this scenario, the two variables being considered are time and parking fee. Time represents the amount of time Alayna parks her car, while the parking fee represents the cost incurred for parking her car for that duration.

The independent variable in this case is time, as it is the variable being manipulated or changed by Alayna, and the dependent variable is the parking fee, as it is dependent on the amount of time Alayna parks her car.

To create a graph for this data, the time should be plotted on the x-axis (horizontal axis) and the parking fee should be plotted on the y-axis (vertical axis). This is because time is the input variable, and parking fee is the output variable, meaning that it is determined by the time value.

In conclusion, time is the independent variable and should be placed on the x-axis, while parking fee is the dependent variable and should be placed on the y-axis to create a graph that illustrates the relationship between these two variables.

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Answer:330%

Step-by-step explanation:

20-------100%

66-------x%

x=100*66/20=330%

Answer:

3

Step-by-step explanation:

To find the absolute deviation, we need to find the difference between each data point and the mean of the data set, take the absolute value of each difference, and then calculate the average of those absolute differences.

First, let's find the mean of the data set:

(10 + 2 + 6 + 12 + 6 + 10 + 4 + 12) / 8 = 8

The mean is 8.

Next, we find the difference between each data point and the mean:

|10 - 8| = 2

|2 - 8| = 6

|6 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|10 - 8| = 2

|4 - 8| = 4

|12 - 8| = 4

Now we take the average of those absolute differences:

(2 + 6 + 2 + 4 + 2 + 2 + 4 + 4) / 8 = 3

The absolute deviation of the data set is 3.

Answer:

Below

Step-by-step explanation:

Correct price would be   $24  +    .25 * 24    = $30

 the manage posted the markup as the selling price ( 25% of 24 = $ 6)

The number of fruits that Mrs Ong bought is 40.

The fraction of the fruits that are pears are 1/4.

The expression that represents the number of oranges is: 1/2f - 3

Where f is the number of fruits

The expression that represents the number of pears is: (1/2 x 1/2)f - 2

1/4f - 2

The expression that represents the number of apples is: 1/2[1 - (1/2 + 1/4)]f - 1

1/8f - 1

Fraction of mangoes remaining = 1 - (1/4 + 1/2 + 1/8)

1 - 7/8 = 1/8

Number of fruits bought altogether = 1/8f = 5

f = 5 x 8 = 40

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On solving the question we have that Therefore, the correct answer is: function  As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.

Mathematicians investigate numbers and their variants, equations and related structures, shapes and their locations, and prospective locations for these things. The term "function" refers to the relationship between a group of inputs, each with its own output. A function is a relationship of inputs and outputs in which each input results in a single, distinct output. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four basic types of accessible functions.

Based on the graph, the function approaches a horizontal line at y = -3 as x approaches negative infinity, and also approaches the same horizontal line at y = -3 as x approaches positive infinity. Therefore, we can say that:

As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.

Therefore, the correct answer is:

As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.

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Answer: To write an equivalent logarithmic equation to e^8.2 = 10x, we use the fact that log base 10 is the inverse of exponential base 10. Therefore, we have:

log(10)(e^8.2) = log(10)(10x)

Using the property of logarithms that says log base a of a^b is equal to b, we get:

8.2 = log(10)(10x)

Using the fact that log base 10 is commonly written as just "log," we can simplify this to:

8.2 = log(10x)

This is the equivalent logarithmic equation.

To write an equivalent exponential equation to In0.0002 = x, we use the fact that In is the inverse of e^x. Therefore, we have:

e^(In0.0002) = e^x

Using the property of logarithms that says e^ln(a) = a, we get:

0.0002 = e^x

This is the equivalent exponential equation.

To write an equivalent exponential equation to In(4x) = 9.6, we use the fact that In is the inverse of e^x. Therefore, we have:

e^(In(4x)) = e^9.6

Using the property of logarithms that says e^ln(a) = a, we get:

4x = e^9.6

Dividing both sides by 4, we get:

x = (1/4)e^9.6

This is the equivalent exponential equation.

Step-by-step explanation:

The amount saved in one month, we need to divide this amount by 12 as he saves on a monthly basis. This gives us a total of R14 160 saved each month. Dumisani saves (42 480 x 5) / 12 = R14 160

Dumisani earns R42 480 per month. He decides to split his earnings in the ratio 7:5. This means that 7 parts of his income will be allocated to his expenses and 5 parts will be allocated to his savings. To calculate the amount saved, we need to first multiply 42 480 by 5 to find out the total amount allocated to savings. This is equal to 212 400. To find the amount saved in one month, we need to divide this amount by 12 as he saves on a monthly basis. This gives us a total of R14 160 saved each month.

Total allocated to savings = 42 480 x 5 = 212 400

Amount saved per month = 212 400 / 12 = R14 160

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Answer: a)0

Step-by-step explanation:

side "a" need to be longer than the height so that the tringle can exist and the height is longer than the side so the tringle cannot exist

height:

[tex]sin42=\frac{x}{8}[/tex]

[tex]x=8sin(42)\\x=5.3[/tex]

for the tringle to exist

height< side "a"

5.3> 3

so,

there is no tringle that exist

The equatiοn that represents the area = 5.5x + 11. Optiοn C is the cοrrect οptiοn.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.

Given that the width οf tulips and lilies in a field 5. 5 meters.

The length οf the field οf tulips is 2 meters.

The length οf the field οf lilies is x meters.

The tοtal length οf the field is (x+2) meters.

The area οf a rectangle is the prοduct οf length and width.

The area οf the field is 5.5(x+2) square meters

The distributive prοperty:

Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.

Apply the distributive prοperty:

= (5.5 × x) + (5.5×2)

= 5.5x + 11

The equatiοn is Area = 5.5x + 11

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Jules' scatter plot will help her to visualize the relationship between the number of years of education and the annual income of the respondents.

A scatter plot is a graph that consists of points plotted in two dimensions in which the position of each point is determined by the value of two variables. In Jules' case, the two variables are the number of years of education and the annual income of each respondent. The plot allows her to visualize the relationship between the two variables.

To plot the points, Jules would have to calculate the coordinates for each respondent. For example, if a respondent said that they have 12 years of education and an annual income of $60,000, Jules would calculate the coordinates for this point as (12, 60000). She would then plot the point at (12, 60000) on the graph. She would repeat this process for each respondent in the survey.

The scatter plot will show Jules how the number of years of education is related to the annual income. She will be able to see if there is a correlation between the two variables, and if there is a pattern of how the two variables are related. This will allow her to make conclusions about the relationship between the two variables.

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Answer:

The answer is A) All four sides are equal. The simplest radical form for each side is √40.

Step-by-step explanation:

If X is plotted on 6 on the y-axis, then X is located at the point (2, 6), since W is plotted on 2 on the x-axis, W is located at the point (2, 2).

Since we know that XW is one side of the square, we can find the other three vertices of the square using the fact that all sides of a square are equal in length and perpendicular to each other.

To find the third vertex, we can use the fact that Z is plotted at (4, -2) and is perpendicular to XW. Since XW has a length of 4 (the difference in y-coordinates between X and W), we know that the length of ZY must also be 4. To find the coordinates of Y, we can move 4 units up from the y-coordinate of Z (which is -2), giving us a y-coordinate of 2. Since ZY is perpendicular to XW, we know that the x-coordinate of Y must be the same as the x-coordinate of Z (which is 4). Therefore, the coordinates of Y are (4, 2).

To find the fourth vertex, we can use the fact that all sides of the square are equal in length. Since XW has a length of 4, we know that ZY must also have a length of 4. Therefore, the fourth vertex must be located 4 units to the right of Y and 4 units up from X. This gives us a fourth vertex with coordinates of (6, 6).

Therefore, the vertices of the square are W(2, 2), X(2, 6), Y(4, 2), and Z(4, -2).

To check that the sides of the square are perpendicular to each other, we can calculate the slopes of the sides.

The slope of XW is:

m_XW = (6 - 2) / (2 - 2) = undefined

The slope of ZY is:

m_ZY = (2 - (-2)) / (4 - 4) = undefined

Since both slopes are undefined (the lines are vertical), the sides are perpendicular to each other.

To check that the sides of the square are equal in length, we can use the distance formula:

XW = sqrt((6 - 2)^2 + (2 - 2)^2) = sqrt(16) = 4

ZY = sqrt((2 - (-2))^2 + (4 - 4)^2) = sqrt(16) = 4

Since both sides have the same length of 4, all sides of the square are equal in length.

Therefore, the answer is option A) All four sides are equal. The simplest radical form for each side is √40.

Hope this helped, if it's wrong I'm sorry! If you need more help, ask me! :]

68% of buyers paid between $21,000 and $23,000 for the car.The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution

The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution. The rule states that 68% of observations fall within one standard deviation of the mean, 95% of observations fall within two standard deviations of the mean, and 99.7% of observations fall within three standard deviations of the mean. In this case, the mean price paid is $23,000 and the standard deviation is $2000. Therefore, the range of prices between $21,000 and $23,000 is one standard deviation from the mean, and 68% of buyers paid between $21,000 and $23,000.Mathematically, this can be expressed as P(21,000<X<23,000) = P(μ- σ < X < μ + σ) = 0.68, where μ is the mean and σ is the standard deviation. By substituting the given values of μ and σ, this equation simplifies to P(21,000<X<23,000) = P(23,000 - 2000 < X < 23,000 + 2000) = 0.68. Therefore,68% of buyers paid between $21,000 and $23,000 for the car.

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On this map, City C and City D are 2.1 feet apart. There are 700 kilometers between city C and city D.

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplying, division, exponents, and so forth.

City A and City B are separated by 500 kilometers. On a particular wall map, this distance is denoted by a length of 1.5 feet.

Hence:

Scale = 1.5 feet represents 500 miles

City C and City D are 2.1 feet apart on this map.

Therefore: Actual distance = 2.1 feet x  (500 miles / 1.5 feet) = 700 miles.

The actual distance between city C and D is 700 miles

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Answer: Let the probability that hunter P hits the target be denoted by "p", and the probability that hunter Q hits the target be denoted by "q".

(a) The probability that they both miss the target is given by:

(1-p)*(1-q)

(b) If the target is hit, then there are three possible outcomes:

(i) Only hunter P hits it: The probability of this event is given by:

p*(1-q)

(ii) Only hunter Q hits it: The probability of this event is given by:

(1-p)*q

(iii) Both hunters hit the target: The probability of this event is given by:

p*q

Note that the sum of the probabilities in (i), (ii), and (iii) is equal to 1, since one of these three events must occur if the target is hit.

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Answer: Can you please show a pic to help me figure it out

Step-by-step explanation:

According to the question the Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.

Coconut is a tropical fruit that grows on palm trees. It is a large, egg-shaped drupe with a hard outer shell and a white fleshy inner layer. The flesh of the coconut is rich in vitamins, minerals, and fiber, and it is also a source of healthy fats. Coconut can be eaten fresh, dried, or even in the form of coconut milk or oil.

First, we will calculate the total number of fruits Kate had at her stall. To do this, we need to solve for x in the equation [tex]$\frac{3}{4}x + \frac{1}{3}(\frac{3}{4}x - x) + (\frac{3}{4}x - \frac{1}{3}(\frac{3}{4}x - x)) = x$.[/tex]
Solving for x, we get [tex]$x = \frac{8}{7}$.[/tex]
Therefore, Kate had [tex]$\frac{8}{7}$[/tex]fruits at her stall.
Next, we need to calculate the number of coconuts she had at first. We know that she sold 1/4 of the fruits, or [tex]$\frac{2}{7}$[/tex] of the fruits. We also know that the ratio of mangosteens sold to apples sold to coconuts sold was 3:5:3.
Therefore, the number of coconuts sold was [tex]$\frac{2}{7} \times \frac{3}{13} = \frac{6}{91}$[/tex].
The total amount earned from the coconuts sold was [tex]$\frac{6}{91} \times 4.50 = \frac{27}{91}$[/tex].
Subtracting this from the total amount earned, 198, we get [tex]$198 - \frac{27}{91} = \frac{171}{91}$[/tex].
This is the amount earned from the mangosteens and apples sold. The amount earned from each mangosteen sold was 1.50, and the amount earned from each Fuji apple sold was 3.00.
Therefore, to get the total amount earned from mangosteens and apples, we need to solve for x in the equation [tex]$\frac{2}{7} \times x + \frac{2}{7} \times 3x = \frac{171}{91}$[/tex].
Solving for x, we get [tex]$x = \frac{171}{171}$[/tex].
This means that the total number of mangosteens and apples sold was $\frac{171}{171}$. Since the ratio of mangosteens sold to apples sold was 3:5, the number of mangosteens sold was [tex]$\frac{3}{8}$[/tex] and the number of apples sold was $\frac{5}{8}$.
Therefore, the number of coconuts at first was [tex]$\frac{8}{7} - \frac{3}{8} - \frac{5}{8} = \frac{4}{7}$[/tex].
Therefore, Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.

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The next four terms of the given recursive sequence using the formula are 3, 9, 21, 45

To find the first four terms of the sequence, we can use the recursive formula given:

First term a1 = 3

For the second, third and fourth term, we will substitute the preceding value to have:

a2 = 2a1 + 3 = 2(3) + 3 = 9

a3 = 2a2 + 3 = 2(9) + 3 = 21

a4 = 2a3 + 3 = 2(21) + 3 = 45

Therefore, the first four terms of the sequence are: 3, 9, 21, 45.

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Answer:

4c) the answer is :-3y=-6

divide by -3 and your ans is y=2