What is the equation of the line shown in the graph?

The equation represents the graph is (y+1)² / 9 + (x+3)²/1 = 1 i.e, option(a)

Define Ellipse

In mathematics, an ellipse is the location of points in a plane so that their separation from a fixed point has a fixed ratio of "e" to their separation from a fixed line (less than 1). The conic section, which is the intersection of a cone with a plane that does not intersect the base of the cone, includes the ellipse. The eccentricity of the ellipse is symbolized by the constant ratio "e," the fixed point is known as the focus, and the fixed line is known as the directrix (d).

Standard from of the equation of an ellipse with centre (0,0) and major axis on x-axis is,

x² / a² + y² / b² = 1

Standard from of the equation of an ellipse with centre (H, K) and major axis parallel to the x-axis is,

(x - h)² / a² + (y - k)² / b² = 1

In equation,

(y+1)² / 9 + (x+3)²/1 = 1

Ellipse properties are :  (h,k) = (-3, -1) , a = 3, b = 1

b>a therefore b is semi-major axis, a is semi minor axis.

Ellipse Centre are :  (h,k) = (-3, -1) , a = 1, b = 3

Hence, the equation represents the graph is (y+1)² / 9 + (x+3)²/1 = 1 i.e, option(a).

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Answer:

Step-by-step explanation: 9x3

9x2

and 9 x 1 then when you get all of the answers but the answers  all  together now leave me alone pleaseeeeeeeeeeeeee  .

Answer: the height of this triangle is 55.4 mm

Step-by-step explanation:

[tex]\displaystyle\\Area\ of\ a\ triangle:\ A =\ \frac{ah}{2} \\\\Hence,\\[/tex]

Multiply both parts of the equation by 2:

[tex]2A=ah[/tex]

Divide both parts of the equation by a:

[tex]\displaystyle\\\frac{2A}{a} =h\\\\Thus,\ h=\frac{2A}{a} \\\\h=\frac{2(227.14)}{8.2} \\\\h=\frac{454.28}{8,2} \\\\h=55.4\ mm[/tex]

The solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a.

The solution of the equation 2x^2 + 5x + 3 = 0 can be found by using the Quadratic Formula. The Quadratic Formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a. By substituting the given coefficients a = 2, b = 5, and c = 3 into this equation, we can solve for x. First, we calculate the discriminant b^2 - 4ac, which in this case is 25 - 24 = 1. Because the discriminant is positive, the equation has two real solutions. Next, we use the Quadratic Formula to calculate the solutions. To calculate the first solution, we substitute the given coefficients into the formula and solve for x: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3 and -1/2.

Therefore, the solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2.

Discriminant: b^2 - 4ac = 25 - 24 = 1

Solution 1: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3

Solution 2: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -1/2

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The purpose of the ninth was to assert the principle that the enumerated rights are not exhaustive and final and that the listing of certain rights does not deny the existence of other rights.

The Ninth Amendment was part of the Bill of Rights added to the Constitution on December 15, 1791. It states that all rights not enshrined in the Constitution belong to the people, not to the US government. In other words, the rights of citizens are not limited to those stipulated in the Constitution. Simply put, the Ninth Amendment declares that the enumeration of certain rights in the Constitution should not be construed as withholding or disrespecting others from people. According to Judge Harry A. Blackman, Roe v. Wade (1973),

, "As we believe, this right to privacy is limited by the Fourteenth Amendment concept of restrictions on individual liberty and government action. The Ninth Amendment to the Constitution contains ample scope, including determining whether a woman should terminate a pregnancy."

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The volume of the pyramid is one-third of the product of its height and the area of its base. That is volume of the pyramid is linearly proportional to its height and the area of its base.

A pyramid is a solid with a base and rectangle face on the edge of base meeting at a vertex. Generally we consider a right pyramid.

Consider a pyramid of base area A and height h, the volume of the pyramid is one-third of the product of its height and the area of its base, that is the volume formula of pyramid is

V = A × h/ 3

That is

V ∝ A and

V ∝ h

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Answer:

m = 13

Step-by-step explanation:

(-9, -6) (-8,7)

The slope is rise/run or ( y2 - y1) / (x2 - x1)

We see the y increase by 13 and the x increase by 1, so the slope is

13/1 or 13

So, m = 13

Answer:

Right angle triangles

Step-by-step explanation:

the only type of triangles that can be solved with pythagorem theorem is right angle triangles. otherwise you would need to use a different formula

The point (2,-4), (x,y), A, and B all lie on the line. An equation relating x and y is m(x-2)=y+4.

The points (2, -4), (x, y) are lie on the line.

The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x. Slope is a ratio that includes how y changes for every unit increase of x.

The slope formula,

m[tex](x_{2}-x_{1})= y_{2}-y_{1}[/tex]

Here, [tex]x_{1} = 2, x_{2}= x, y_{1}= -4[/tex] and [tex]y_{2}= y[/tex]

Now, we have to substitute the values in the formula,

[tex]m=\frac{y-(-4)}{x-2}[/tex]

[tex]m= \frac{y+4}{x-2}[/tex]

m(x-2)= y+4

Therefore, the equation is m(x-2)=y+4.

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The area henry' rectangular kitchen island top with length 35. 5 inches and width 46. 75 inches is 1659. 625 inch².

The word "area" means an open area. A shape's area is calculated using its length and width. Length is one-dimensional and measured in units such as feet (ft), yards (yd), and inches (in). Area is defined as the total space occupied by a planar (2-D) surface or shape of an object. It is measured in units such as square feet (ft²) and square inches (in²)

Let " l " be length of rectangular island top and "w" be width of it.

We have , l = 35.5 inches , w = 46.75 inches

We have to calculate the area if henry' rectangular kitchen iland top.

let "A" be area of rectangular island top .

As discuss above, Required Area , A = l × w

=> A = 35.5 inches × 46.75 inches

=> A = 1659.625 inch²

Hence, required area is 1659.625 square inches.

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To find the median of a set of numbers, we need to first put the numbers in order from least to greatest. In this case, the ages of the Carnegie children are 3, 9, 18, and 24 years old. Since there are 4 numbers in this set, the median is the average of the middle two numbers, which are 9 and 18. The median of the ages of the Carnegie children is (9 + 18) / 2 = 27 / 2 = 13.5 years old.

To find the mean of a set of numbers, we need to add the numbers together and then divide the sum by the number of numbers in the set. In this case, the sum of the ages of the Carnegie children is 3 + 9 + 18 + 24 = 54 years old. Since there are 4 children, the mean age is 54 years / 4 children = 13.5 years old. Therefore, the mean of the ages of the Carnegie children is 13.5 years old.

Answer:

Median: 13.5

Mean: 13.5

Step-by-step explanation:

To get the median, take the middle value. Since there are two middle values, add them together and divide them by two.

To get the mean, add all the values together and divide the sum by the number of values. In this instance, mean and median are the same.

Answer:

C. Substitution

Step-by-step explanation:

Substitution is the final answer to an equation. So, the answer is C

Answer: C. Substitution

Answer:

No correlation

Step-by-step explanation: If the graph  shows a positive correlation, the correlation would be linear, if its showing a negative correlation , then the correlation would also be linear, but going in a downward slope

Arithmetic mean of the data set 4, 5, 0, 10, 8 and 3  is '5'

As per the question the given data set is :

4 , 5 , 0 , 10 , 8 and 3

Number of observations in given data set are '6'

We have to determine the value of arithmetic mean of the data

Arithmetic Mean is simply the mean or average for a set of data or a collection of numbers.

Arithmetic mean is defined as the ratio of sum of all observations in given data set to the total number of values.

Arithmetic mean ( AM ) formula is

AM = (sum of all observations in given data set) ÷ (total number of observations)

Sum of all observations in given data set :

= 4 + 5 + 0 + 10 + 8 + 3

= 30

Arithmetic mean :

[tex]=\frac{30}{6}[/tex]

= 5

Therefore arithmetic mean of the given data set 4, 5, 0, 10, 8 and 3  is 5.

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Answer: false

Step-by-step explanation:

The nature of roots of the given quadratic equation is "real and unequal".

Nature of Roots:

Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.

Depending on the value of the discriminant, we discuss the following cases for the nature of the root:

Case 1: D = 0

If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.

Case 3: D < 0

If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.

Case 4: Perfect Square with D > 0

If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.

Case 5: D > 0 and Not Perfect Square

If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.

According to the Question:

The given quadratic equation:

9x²-6x-2 = 0

Here, a = 9, b = - 6 and c = -2

To Find: the nature of roots of the given quadratic equation.

∴ Discriminant, D = b²-4ac

= (-6)² - 4×9×(-2)

= 36 -36(-2)

= 36 + 72

=108

Since,

D = 108 > 0, the roots are real and unequal.

Hence, the nature of roots of the given quadratic equation is "real and unequal".

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The median when the mean is 48 and the mode is 15 is 37.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

For instance, what is the median of our data set if we know that we have a mean of 10 and a mode of 4?

Since the Mean - Mode is 3, we may state that 10 - 4 equals 3. (10 – Median).

According to some algebra, the median of our data is 8 because 2 = (10 - Median).

So, the values are:
Mean = 48

Mode = 15

Formula: Mean – Mode = 3(Mean – Median)

Now, calculate the median using the formula as follows:

48 – 15 = 3(48– Median)

33 = 144 - 3Median

3Median = 144 - 33

3Median = 111

Median = 111/3

Median = 37

Therefore, the median when the mean is 48 and the mode is 15 is 37.

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A data set's mean can be estimated by dividing the sum of all the data points by the total number of data points in the data set.

How is the mean method calculated?

It is calculated by merely dividing the total number of values in a data collection by the sum of all the values in the data set. Both raw data and data that have been combined in a frequency table may be used in the calculation.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                 Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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The roots of the graph of f(x) = (x+4)⁶(x+7)⁵ crosses the x axis at  x = -7 .

The Roots of the Graph of the equation is defined as the point at which the curve crosses the x axis , and also the roots satisfy the equation .

the function is given as : f(x) = (x+4)⁶(x+7)⁵ ;

let the function be denoted by y = f(x) .

If the graph crosses  x - axis , then the value of y is 0 .

that means ; (x+4)⁶(x+7)⁵ = 0   ;

which implies that , (x + 4) = 0   (x + 7) = 0 ,

simplifying ,

we get ; x = -4 and x = -7 .

we know that if the power of function is even the function bounces from the x axis ,

and if the power of function is odd the function crosses the x axis ,

Therefore , the graph crosses the x axis at  x = -7 .

The given question is incomplete , the complete question is

At which root does the graph of f(x) = (x+4)⁶(x+7)⁵ cross the x axis ?

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The graph that represents the function f(x) = 4[x] is option C.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4 [x]

[x] is the greatest integer function.

We see that,

f(0) = 4 [0] = 0

f(0.5) = 4 [0.5] = 4 x 0 = 0

f(x) = 0 for 0 ≤ x < 1

f(1) = 4 [1] = 4

f(1.5) = 4 [1.5] = 4 x 1 = 4

f(x) = 4 for 1 ≤ x < 2

f(2) = 4 [2] = 4 x 2 = 8

f(2.5) = 4 [2.5] = 4 x 2 = 8

f(x) = 8 for 2 ≤ x < 2

Thus,

The graph on option C has the required coordinates.

f(x) = 0 for 0 ≤ x < 1

f(x) = 4 for 1 ≤ x < 2

f(x) = 0 for 2 ≤ x < 2

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the function is [tex]f(x) = x^2.[/tex] The graph is what is known as the basic parabola. Take note of the graph's symmetry about the y-axis. The symmetry axis of this function is known as the y-axis.

Something bowl-shaped at the intersection of a right circular cone and a plane parallel to an element of the cone: a plane curve produced by a moving point so that its distance from a fixed point is equal to its distance from a fixed line (such as an antenna or microphone reflector). Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. Conic section is a topic that includes parabola, and this article covers all of its principles.

equation of tangent line = [tex]y - y1 = m (x - x1)[/tex]

equation of a circle =  [tex]x^2 + y^2 + 2gx + 2fy + c = 0[/tex]

equation of hyperbola =  [tex][(x2/a2) - (y2/b2)] = 1[/tex]

equation of a line = [tex]y = mx + c[/tex]

equation of slope = [tex]m= \frac{y_2 - y_1}{x_2 - x_1}[/tex]

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1) The function is P(t) = 6.79e^ 0.0317t

2) There would be 8.18 million people in 2018

3) It would take 9 years to reach a population of 9 million

4) The doubling time is 22 years

We know that population growth has to do with the increase in the population of a place. Let us recall that population growth occurs exponentially and this would help us as we write the function for the population growth.

a) The population growth function is obtained as;

P(t) = 6.79e^ 0.0317t

t = Number of years since 2012.

b) In the year 2018, six years would have passed hence we have;

P(t) = 6.79e^ 0.0317 * 6

P(t) = 8.18 million people

c) The population would be 9 million when;

9 =  6.79e^ 0.0317t

9/6.79 =e^ 0.0317t

1.33 = e^ 0.0317t

ln(1.33) = 0.0317t

t = ln(1.33)/0.0317

t = 9 years

d) The doubling time would be;

2(6.79) =6.79e^ 0.0317t

2(6.79)/6.79 = e^ 0.0317t

ln 2 =  0.0317t

t = ln 2 / 0.0317

t = 22 years

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Open the Word document. then Go to the Insert tab on the ribbon and click on the Chart option under the Illustrations group.

When does a graph represents a function?

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.

How do you insert a 4 quadrant graph in Word?

Open the Word document.

Go to the Insert tab on the ribbon and click on the Chart option under the Illustrations group.

An Insert Charts dialog box will appear on the screen.

Select the XY (Scatter) option from the left pane

and pick a line graph that you want to insert.

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Answer:

17.5%

Step-by-step explanation:

We know that there are 35 out of 200 allergic to peanut

So we take

35 divided by 200, then times 100% = 17.5%

So, 17.5  of children are allergic to peanut

Answer:

Congruent means the same shape but perhaps moved or rotated or reflected

Similar means a shape that has been enlarged by a scale factor

Step-by-step explanation:

A pair of Political affiliation and residential status can be used as pair of varibles for which the researcher conduct the chi-square test of independence.

We have a researcher survey random sample of 750 college students about their political views.

This survey contains the following variables,

A Chi-square test of independence is conducted by researcher and the pair of variables can the researcher use here is political affiliation and residential status. Because the Chi-square independence test is used to determine if there is a significant relationship between two nomial categorical variable.

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The required coordinates of point P, following the given coordinate points, are (5.5, -1).

Let's assume that point P has coordinates (x, y). We want to find the coordinates of point P along the directed line segment AB, such that the ratio of AP to PB is 1 to 4.

The coordinates of point A are (8, 0), and the coordinates of point B are (3, -2).

According to the ratio given, we have:

AP/PB = 1/4

Now, we can use the midpoint formula to find the coordinates of point P. The midpoint formula states that the coordinates of the midpoint M between two points (x₁, y₁) and (x₂, y₂) are given by:

Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's use the midpoint formula to find the coordinates of point P:

x = (8 + 3) / 2
  = 5.5

y = (0 + (-2)) / 2
  = -1

So, the coordinates of point P are (5.5, -1).

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The median of given data is 4.

Given:

A data

2, 3, 4, 7, 5, 1, 6

To find: The median of given data.

The median of given data is 4.

To answer this question, we will follow the following steps:

As given, we have a data

2, 3, 4, 7, 5, 1, 6

To find the median, we will arrange the data in ascending order.

So, we have,

1, 2, 3, 4, 5, 6, 7

Here,

Total number of observations = 7

As we know if there is an odd number (n) of observations in a data, then its median is obtained by:

So,

The median of given data

Now,

4th observation is 4.

Hence, the median of given data is 4.

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The simplest solution for this problem is to traverse the entire array and store the minimum and maximum values.

C++ implementation for the following problem

#include <iostream>

int main(){  

int arr[] = {1,2,3,4,5,6,7,8,9...........................99,100}; //initialize array

int min = arr[0]; //start value

int max= arr[0];  //start value

for(int i:arr) {

 if(i<min) min=i; // if current number lower update min

 if(i>max) max=i; // if current number bigger update max

}

std::cout<<"Min Value: "<<min<<"\nMax Value: "<<max<<"\n";

return 0;

}

The simplest solution for this problem is to traverse the entire array and store the minimum and maximum values.

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The operation that maps(moves)the preimage onto the image is called a transformation.

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.

In mathematics, there are five different transformations:

Dilation is the process of an image "shrinking" or "enlarging," depending on the size of the preimage.

Reflection: The picture is a preimage that has been reversed; "a flip."

Rotation: The picture is the preimage turned around a fixed axis; this is referred to as "a turn."

Shear: When a preimage is sheared, all the points along one side remain stationary while all the other preimage points move parallel to that side in proportion to the distance from the given side; this is also known as "a skew."

Translation: The image is "a slide" away from the preimage by a fixed amount.

The operation that maps(moves)the preimage onto the image is called a transformation.

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