Write an equation for a parabola that has a vertex at (2, 3), focus at (2,5), and directrix at y = 1.
f(x) = (x - 2)² +3
f(x) = 2(x - 5)² + 2
f(x)=(x-3)² + 2
f(x) = 2(x - 3)² + 1

As side EG is the largest side at 15, and the greatest angle is the opposite side's angle,  ∠F.

Given that it consists of sides and three vertices, a triangle qualifies as a polygon. It connects to the fundamental geometric shapes. Triangle ABC is the term used to refer to such a triangle with the points A, B, and C. When the three points are not collinear, a unique plane and triangle in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the four structures of the triangle converge are referenced to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

Find the smallest angle by finding the angle opposite the smallest side, then the medium-sized angle by finding the angle opposite the medium-sized side .

Then the greatest angle by finding the angle opposite the largest side when there are three side lengths available.

As side FG is the smallest side at 7, and the smallest angle is the one across from it, ∠ E.

The opposing angle,  ∠G, is the medium-sized angle, just as side EF is a medium-sized side as measured by 12.39.

As side EG is the largest side at 15, and the greatest angle is the opposite side's angle,  ∠F.

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The complete question is :-

a) Order the angle measures m∠E , m∠F and m∠EGF from least to greatest ad well as side length .

The reaccepts 10 integers from the user using an array and a loop is explained below.

To start, you need to declare an array variable that can store 10 integers. For example, you can declare an array variable called "numbers" as follows:

int numbers[10];

Next, you will use a loop to repeatedly ask the user to input an integer. The loop will run 10 times to receive 10 integers. You can use the for loop for this purpose.

Here is an example:

for (int i = 0; i < 10; i++) {

 printf("Enter integer %d: ", i + 1);

 scanf("%d", &numbers[i]);

}

In this code, the for loop starts with the value of i being 0. It runs until i is less than 10. After each iteration, i is incremented by 1.

After the loop finishes, all 10 integers received from the user are stored in the numbers array. You can access them using the index of the array.

In conclusion, to receive 10 integers from the user using an array and a loop, you need to declare an array variable, use a for loop to repeatedly ask the user for input, and store the input in the array using the scanf function.

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For a particle having a position of function e^-(t - 3)², the velocity at 2.9s is obtained as 0.198008 m/s.

What is velocity?

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

The position of a particle is denoted by a function x(t) = e^-(t - 3)², where x is the distance and t is the time.

Differentiate the function -

v(x) = d/dt(x) = d/dt[e^-(t - 3)²]

v(x) = e^-(t - 3)²[-2(t - 3)]

Now, substitute the value of t = 2.9 in the equation -

v(2.9) = e^-(2.9 - 3)²[-2(2.9 - 3)]

v(2.9) = e^-(-0.1)²[-2(-0.1)]

Use the exponent formula a^-b = 1/a^b -

v(2.9) = 1/e^(-0.1)²[0.2]

Square the digit (0.1) -

v(2.9) = 1/e^(0.01)[0.2]

Substitute the value ofe^0.01 = 1.01005 -

v(2.9) = (1/1.01005)[0.2]

Use the arithmetic operation of division -

v(2.9) = (0.99004)[0.2]

v(2.9) = 0.198008

Therefore, the velocity of the particle is 0.198008 m/s.

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The horizontal distance of a raindrop that falls from the end of the roof to the center of the base of the house, obtained from the linear equation for the height of the roof is; x = 18 feet

A linear equation is an equation that has one as the highest index, and which when graphed, forms a straight line.

The linear function for the height of the roof is, h(x) = -|x| + 34

Where;

h(x) = The height of the roof

x = The horizontal distance from the center of the roof

The minimum height of the roof, obtained from the diagram = 16 feet

Therefore, we get, when h(x) 16, substituting the value h(x) = 16, in the function for the height of the roof, we get;

h(x) = -|x| + 34

h(x) = 16

Therefore, 16 = -|x| + 34 (substitution property)

|x| = 34 - 16 = 18

The distance from the center of the house, which corresponds to the least height of the roof, which is the end of the roof and the location at which the raindrop falls is; x = 18 feet

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Hey there!

|2x + 1| < -4

Since you have an absolute value that is LESS than 0, we can say that it doesn’t have any solutions.

Thus, your answer should be:

NO SOLUTIONS

REMEMBER: If your absolute value is smaller/less than 0, you would NOT have any solutions to the particular equation (like this one you have provided just now)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

-1+p<15

=-1+1+p<15+1

=p<16

Answer:

Step-by-step explanation:

13)  5.38  Slightly off

14)  10.4   Correct

15)  Can't read the numbers

16)  11.7  slightly off

17)  Can't read (be careful with which side goes where in the Pythagorean Theorem calculation.  a^2 + b^2 = c^2 where a and b are the two sides and c is the hypotenuse (across from the right angle).  

18)   16.46

19)  10.57

20)  7.04

21)   4.87    It seems that the hypotenuse is given as 7.2, so the equation should be 5.3^2 + x^2 = 7.2^2

22)   Same as in 21:  2.7^2 + x^2 = 6.5^2  x = 5.91

[But I'm having difficulty reading the problems due to fuzziness]

Different Quadrilateral Types

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Answer:

x=33

Step-by-step explanation:

[tex]180=2x-24+4x+6[/tex]

[tex]180=6x-18[/tex]

[tex]198=6x[/tex]

[tex]x=33[/tex]

The patterns are:

Line 1: T A C G T T T A A T G A G G C C C T A G T G

Line 2: T C C C C T A G T C G T G G C C T A A A G T C

Line 3: A C T G C T A G C T A C G T T A T C G T C C G

Base pairing rule refers to the specific pairing of nitrogenous bases in DNA. According to this rule, adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G) through hydrogen bonds. This base pairing results in a complementary sequence of nucleotides on the two strands of DNA, forming a stable double helix structure.

The base pairing rule ensures the accurate replication and transmission of genetic information from one generation to the next. The DNA strands become:

a. Original: A T G C A A A T T A C T C A C C G G G A T C A C

Complementary: T A C G T T T A A T G A G G C C C T A G T G

b. Original: A G G G G A T C A G C A C C G G A T T T C A T G

Complementary: T C C C C T A G T C G T G G C C T A A A G T C

c. Original: T G A C G A T C G A T G C A C A T G C A T G G C

Complementary: A C T G C T A G C T A C G T T A T C G T C C G.

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Answer:

ladder has to be at least 13 ft long

Step-by-step explanation:

l = length of the ladder

12.6² + 3.2² = l²

l² = 158.76 + 10.24 = 169

√l² = l = √169 = 13

The ladder is the hypotenuse of a right triangle with sides 12.6 and 3.2

The value of the variable x in the given right angle expression is; x = 11

We know that a right angle simply means an angle that is equal to 90 degrees.

Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.

Thus;

5x + 35 = 90

Subtract 35 from both sides to get;

5x = 55

x = 55/5

x = 11

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Her rate at the end of the summer is 20 miles per hour.

We can define the rate in this case as the change in position as a function of the time.

So, the rate would be something like a speed (exactly a speed, actually).

Initially, the camper travles at a rate of 10mi/h in 2 hours, so the total distance is:

d = (10mi/h)*2h = 20mi

And at the end of the sumer, the camper travels that distance in one hour, so the rate at the end of the summer is:

R = 20mi/1h = 20mi/h

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Answer:

$538

Step-by-step explanation:

The minimum payment in the first month would be:

Minimum payment = 1.5% * $19,500 + 3% * $19,500 = $292.25

At the end of the first month, the balance would be:

Balance = $19,500 + $19,500 * 1.5% - $292.25 = $19,318.375

In the second month, the minimum payment would be:

Minimum payment = 1.5% * $19,318.375 + 3% * $19,318.375 = $291.26

At the end of the second month, the balance would be:

Balance = $19,318.375 + $19,318.375 * 1.5% - $291.27 = $19,138.89

In the third month, the minimum payment would be:

Minimum payment = 1.5% * $19,138.89 + 3% * $19,138.89 = $290.26

At the end of the third month, the balance would be:

Balance = $19,138.89 + $19,138.89 * 1.5% - $290.26 = $18,961.62

So, Ellen would have paid off $19,500 - $18,961.62 = $538.38. The answer rounded to the nearest cent is $538

The perimeter of this rectangular field is equal to 1,100 meters.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Note: Area = 6 × 10,000 = 60,000 m^2.

Next, we would determine the width of this rectangle:

60,000 = 400W

W = 60,000 /400

Width, W = 150 m.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

Perimeter of a rectangle = 2(L + W)

Perimeter of a rectangle = 2(400 + 150)

Perimeter of a rectangle = 2(550)

Perimeter of a rectangle = 1,100 meters.

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The perimeter of the rectangular field with an area of 6 hectares and length of 400m is 1100 meters.

The perimeter of a rectangle is expressed as;

P = 2( length + width )

Given the data in the question;

First, we determine the width of the field using the area formula.

Area = Length × width

Plug in the values and solve for width

60,000m² = 400m × width

60,000m² / 400m = Width

Width = 150m

Now, the perimeter will be;

P = 2( 400 + 150 )

P = 2( 550 )

P = 1100 meters.

Therefore, the perimeter is 1100 meters.

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The solution to the original system is:x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1

The given matrix is in row echelon form, meaning that the leading entry of each non-zero row is to the right of the leading entry of the previous row. In this form, the solution to the linear system can be found by back substitution.

Starting from the bottom row, we have the equation:

-1 * x4 + 4 * x5 = -1

Solving for x4, we have:

x4 = -4 * x5 + 1

Moving up to the next row, we have:

0 * x1 + 0 * x2 + 3 * x5 = 3

Solving for x5, we have:

x5 = 1

So, x4 = -4 * 1 + 1 = -3.

Next, the third row gives us:

0 * x1 + 0 * x2 - 3 * x3 + 4 * x4 = 4

Substituting the value of x4, we have:

0 * x1 + 0 * x2 - 3 * x3 + 4 * (-3) = 4

Solving for x3, we have:

x3 = -1

Since there are no more non-zero rows in the matrix, we have found a complete solution for the linear system.

The solution set of the original system is the set of all possible values of (x1, x2, x3, x4, x5) that satisfy the system of equations represented by the matrix. Since the given matrix is in row echelon form, this solution set is unique and consists of a single point in the 5-dimensional space.

The solution to the original system is:

x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1

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Answer:

Infinitely many solutions

Explanation:

1) subtract “1” from both sides to get y by itself

Y=-2x-1

2) 4y+8x=-4 share a gcf of “4” so you can divide the whole equation by 4

y+2y=-1

Now substitute “-2x-1” as y

(-2x-1)+2x=-1

-2x and 2x cancel each other and so does -1 and -1

Hence, this system has infinitely many solutions

Answer:

x = 0, y = 1.

Step-by-step explanation:

We can solve for the variables x and y by using substitution. Let's start by solving the first equation for one of the variables:

-1 = 2x - y

y = 2x + 1

Next, we'll substitute y = 2x + 1 into the second equation:

8x - 4y = -4

8x - 4(2x + 1) = -4

Expanding the second equation:

8x - 8x - 4 = -4

-8x - 4 = -4

-8x = 0

x = 0

Finally, we can use one of the equations to find y:

y = 2x + 1

y = 2(0) + 1

y = 1

So, the solution is x = 0, y = 1.

Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.

When use the formula to solve a problem, the "discriminant" is the value that helps in recognizing the various sorts of solutions. In a mathematical formula (a quadratic equation), it is a special function of a cross that reveals information out about bases of the equation. The "b" term must be square-rooted before the "a" term and "c" term may be isolated by four times to calculate the discriminant. It has a (delta) next to the letter "D" that stands for discrimination. Positive discriminant describes a quadratic equation with two unique real number solutions. Repeated positive integer solutions exist for a quadratic equation with a characteristic of zero. A negative discriminant reveals that none of the solutions is a real number.

given

x2 - 5x + 2 = 0

the roots of the equation

x = -b ±[tex]\frac{\sqrt{b^{2} - 4ac} }{2a}[/tex]

x = 5 ± [tex]\sqrt{17} / 2[/tex]

Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.

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The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:

Input the initial value of x, for example x=0.

Calculate f(x) and g(x):

If f(x) is less than g(x), then x should be increased and vice versa.

Increase or decrease x accordingly and calculate the new values of f(x) and g(x).

Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

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Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.

What is rectangle ?

A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other

Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:

V = l * w * h = 62500 cm^3 (Given)

Since the base is a square, have w = l. Therefore,

V = l^2 * h

h = V / l^2 = 62500 / l^2

The surface area of the bin can be expressed as:

A = 2lw + 2lh + 2wh

Substituting the value of w = l and h = V / l^2, get:

A = 2l^2 + 2l * (V / l^2) + 2l * l = 2l^2 + 2V / l + 2l^2 = 4l^2 + 2V / l

To minimize the surface area, differentiate A with respect to l and set it to zero:

dA/dl = 8l + 2V / l^2 = 0

4l^3 = V

l^3 = V / 4

Taking the cube root of both sides,

l = (V / 4)^(1/3)

Substituting the value of V,

l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm

Since w = l,

w = 125 cm

h = V / l^2 = 62500 / (125)^2 = 250 cm

The minimum surface area is then given by,

A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm^2

Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.

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Minimum surface area of rectangular bin with 62,500 cm³ volume and square base is 31250 cm^2.

A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other

Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:

V = l * w * h = 62500 cm³ (Given)

Since the base is a square, have w = l. Therefore,

V = l² * h

h = V / l² = 62500 / l²

The surface area of the bin can be expressed as:

A = 2lw + 2lh + 2wh

Substituting the value of w = l and h = V / l^2, get:

A = 2l² + 2l * (V / l²) + 2l * l = 2l²+ 2V / l + 2l² = 4l² + 2V / l

To minimize the surface area, differentiate A with respect to l and set it to zero:

dA/dl = 8l + 2V / l² = 0

4l³ = V

l³ = V / 4

Taking the cube root of both sides,

l = (V / 4)^(1/3)

Substituting the value of V,

l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm

Since w = l,

w = 125 cm

h = V / l² = 62500 / (125)²= 250 cm

The minimum surface area is then given by,

A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm²

Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm².

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Answer: 2

Step-by-step explanation:The slope of a line is the ratio of the change in y-values to the change in x-values between two points on the line.

To find the slope, we first need to find two points on the line, for example (4,12) and (7,18).

Then, the slope can be calculated as:

(18 - 12) / (7 - 4) = 6 / 3 = 2.

The slope is 2.

We convert the x value from degrees to radians using math.radians. If the sine value is positive, we append it to the y_values list. If the sine value is negative, we append 0 to the y_values list instead.

Here's a code snippet in Python that generates the x and y data for the sine function with a 1 degree increment of x from 0 to 720 degrees:

import math

x_values = []

y_values = []

for x in range(0, 721, 1):

   x_values.append(x)

   y = math.sin(math.radians(x))

   if y >= 0:

       y_values.append(y)

   else:

       y_values.append(0)

In this code, we use the math.sin function to calculate the sine value for a given x in radians. We convert the x value from degrees to radians using math.radians. If the sine value is positive, we append it to the y_values list. If the sine value is negative, we append 0 to the y_values list instead.

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Non-Euclidean geometries provide a different and more general view of geometry that can help better understand the nature of space and the relationships between objects in the world .

Non-Euclidean geometry is a branch of mathematics that studies the properties and characteristics of geometries that are different from Euclidean geometry, which is the traditional study of geometry and the one most people are familiar with .

Non-Euclidean geometries differ from Euclidean geometry in that they have different postulates , or basic assumptions , about the relationships between points, lines, and angles .

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Answer:

The sum is 11c - 14.

A rectangular prism has 6 faces, 8 vertices and 12 edges.

What is rectangular prism?

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.

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Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).

Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.

Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.

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Answer:56

Step-by-step explanation:

You divide 14kg by 2kg and get 7kg. So then you times 7kg by 8 seeds.

Hope this helps :)