What is line segment Theorem?

All of the coefficients of a zero polynomial's variables are equal to zero. In other words, it indicates that the powers of all the variables are equal to zero.

Zero polynomials are any polynomials that have all of their variables' coefficients set to zero.

Thus, a polynomial with a value of zero has no value.

A constant function or zero map is the function that defines it, and it is typically written as P(x) = 0, where x is the variable of the polynomial whose coefficient is 0.

A zero polynomial is a polynomial that has zero as its coefficient and an endless number of terms and variables of various powers.

Like this: 0x^2 + 0x + 0.

The graph of the zero polynomial is the x-axis, and the zero polynomial function is defined as y = P(x) = 0.

Real numbers are believed to be the domain, while 0 is the range.

The range is the set of values for the dependent variable y, whereas the domain is the set of values for the variable x for which the function is defined.

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -When two parallel lines cross one other, the horizontal line is divided into two angles. Interior angles develop between the parallel lines, whereas alternative outside angles develop outside the parallel lines.

1 - A

2 - C

3 - B

4 - D

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Answer:12+2y

Step-by-step explanation:Multiple the -2 by each value inside of the parenthesis, -2 * -6 = 12, -2 * -y = 2y, then add these together to get 12+2y.

A recursive formula for the sequence is:  f(n+1) = f(n)-99.4, n ≥ 1

Consider the given sequence.

99.4, 0, -99.4, -198.8, . . .

We can observe that each next term of the sequence is decreased by -99.4

i.e., f(0) = 99.4

f(1) = f(0) - 99.4

f(1) = 99.4 - 99.4

f(1) = 0

f(2) = f(1) - 99.4

f(2) = 0 - 99.4

f(2) = -99.4

From these calculations we can say that the n-th term would be,

f(n) = f(n - 1) - 99.4

Therefore, recursive formula:  f(n+1) = f(n) - 99.4

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The sample space of the experiment is 52.

The possibility that an event will occur among all potential events is known as probability. It ranges from 0 to 1. The probability is calculated by dividing the number of things by all of the items. Population includes the sample. When studying the entire population is challenging, it is studied.

52 cards in a deck

There are 12 face cards.

The experiment needs a sample space of 52 to find the face cards.

Given that a regular deck of cards is available.

The sample space required for the experiment to determine the probability of face cards must be found.

A face card may or may not be revealed when we pull a card from the deck. So, in order to rule out the possibility that a face card is present at the end of the deck, we must draw every card from a regular deck.

52 samples are therefore required for the experiment.

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The x-intercept of the line 4x-y =- 4  is (1,0).

At x-intercepts, y=0  and at

y-intercepts, x=0.

So, to find the,

x-intercept, set y=0

4x−0=4

4x=4

x=1.

The points at which the graph of a function or an equation crosses or "touches" the x-axis of the Cartesian Plane are referred to as the x-intercepts. This could be thought of as a point with a y-value of zero. Let y equal 0 and then solve for x to determine the equation's x-intercepts.

Because the line crosses the x-axis when y=0, the equation for x must be solved in order to determine the x-intercept. We can solve for the intercepts when an equation is not in the form y = mx + b by solving for the remaining variable and plugging in 0 as necessary. To locate the y-intercept: solve for y and set x to zero.

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Answer:

quadrilateral?

Step-by-step explanation:

Answer: Ok to solve this question you would have to do $7.50 divided by  

3 and your answer should come out to be $2.5 or $2.50 per each pound.

Step-by-step explanation:

$7.50 divided by 3 = 2.5

and with money if you get a $2.5 it would be $2.50 because you have to add the zero to the end of it.

The time that it will take for the object to reach maximum height is given as follows:

3 seconds.

The maximum height is given as follows:

304 feet.

The object's height is modeled by a quadratic function in the following format:

h = -16t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 96, h(0) = 160.

Hence the function is defined as follows:

h(t) = -16t² + 96t + 160.

Meaning that the coefficients of the quadratic function are given as follows:

a = -16, b = 96, c = 160.

The coefficient a is negative, meaning that this is a concave down quadratic function, thus the vertex of the quadratic function represents the maximum height.

The t-coordinate of the vertex is given as follows:

t = -b/2a = -96/-32 = 3 seconds.

Then the maximum height is of:

h(3) = -16(3)² + 96(3) + 160

h(3) = 304 feet.

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The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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The stated statement states that 139 of said animals Margie counted had two legs, mostly two-legged birds.

An arithmetic value used to compute and portray a quantity would be a number. In writing, numerical symbols like "3" are used to represent numbers. A decoder is a logical approach the portray a number using digits or symbols.

Assume that there are x two-legged birds and y four-legged animals. Now, we can employ equation systems to find a solution to this issue.

Enter two equations here:

2x + 4y = 522

x + y = 200

Add two to the latter equation now.

2x + 4y = 522

2x + 2y = 400

We discover that; by deducting the following equations from the first equation.

2y = 122

y = 61

There were 139 two-legged birds due to the 200 heads, which indicated a total of 200 animals.

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The complete question is-

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

A). 61

B). 122

C). 139

D). 150

E). 161

Answer:468

Step-by-step explanation:cause of the max mark is 650 /100=6.5 (1%)

then 6.5*72=468

Answer:

Step-by-step explanation:

i don't know if this help :/

The perimeter of rectangle could be  50.6 if a rectangle has an area of 7. 5 and One of the sides is 0. 3m in length.

What is Area of rectangle ?

area of rectangle could be the product of its sides that is length and breadth.

Given the area of rectangle is 7.5

one of its side, length = 0.3

let other side be x .

area = length*breadth

7.5 = 0.3 * x

x = 25

hence , other side could be 25.

perimeter of rectangle = 2 (length+breadth)

= 2 * (25+0.3)

= 2 * (25.3)

= 50.6

Hence, The perimeter of rectangle is 50.6

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Answer:

Step-by-step explanation:

D. 1

Answer:

D) 1

Step-by-step explanation:

-3 | 1  0  -8  10  22

____-3_9_-3_-21_

     1  -3  1   7 |  1

Hence, [tex]\frac{x^4-8x^2+10x+22}{x+3}= x^3-3x^2+x+7\,\,\,R1[/tex]

Answer: 8 feet

Step-by-step explanation:

you take 33-25 to get the sum of 8. so the squid is 8 feet longer than the shark.

Therefore , the solution of the given problem of scatter plot comes out

to be  2 regions contain 2 x 40 (or 80) students.

Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).

Here,

A box plot separates a data set into four areas, each identified by five lines. The lowest line displays the result, while the highest line displays the result. 25% of the data points are distributed across each region, and the median score is indicated by the middle line.

In this box plot, for instance, there are lines at 10, 30, 48, 70, and 100. The fact that no student received a score exactly equal to 30, 48, or 70 allows us to deduce the following:

Because the middle two sections represent the interquartile range (IQR), which comprises the middle 50% of the data, they are frequently "boxed" together.

We are informed that 120 students received test scores below 70. Additionally, since there are three regions with scores below 70 and each region has a 25% weighting, 3 x 25% (or 75% of the students) had scores below 70.

In other words, 75% of 120 students.

If there are 120 students total throughout the three regions, then each

region has 40 pupils, or one-third of the total.

The box plot indicates that there are two areas, and since each region has 40 students, there are 80 students total in the two regions.

As a result, two zones with two sets of 40 students each make up the solution to the scatter plot problem.

Therefore , the solution of the given problem of scatter plot comes out

to be  2 regions contain 2 x 40 (or 80) students.

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Answer:

x = 90

Step-by-step explanation:

The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.

So, set the 1st and 4th angles equal to each other.

3x-160 = x+20

2x = 180

x=90

Answer:x=90

Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.

Answer:

1.   f(x)=1-1/2

4.   y=10x

5.   yes

Step-by-step explanation:

1)
f(x) = 4(2 + 3x) + 3 is a linear function.

2)

The slope of the function is 6.

3)

The linear function is (1/2)x - 4.

4)

y = x² + 2 is not a linear function.

5)

No, it is not a linear function.

6)

Graph D does not represent a linear function.

7)

Graph B does not represent a linear function.

8)

Table D is a linear function.

9)

Table B is not a linear function.

10)

3x + 2y = 6 is a linear function.

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,

1)

f(x) = 4(2 + 3x) + 3

f(x) = (1/2)x² - 5

f(x)= 5 - x²

f(x) = 1 - 1/x

The graph of each function is given below.

The red line in the graph represents f(x) = 4(2 + 3x) + 3.

This is a straight line which means it is a linear function.

2)

f(x) = 2(3x - 7)

f(x) = 6x - 14

It is in the form of y = mx + c where m is the slope.

So,

m = 6

3)

f(x) = (1/2)x - 4

f(x) = x³ - 2

The graph is given below.

The red line represents f(x) = (1/2)x - 4.

This is a linear function.

4)

y = 3x + 12

y = x² + 2

y = 10x

y = 9

The graph is shown below.

The green curve is y = x² + 2.

This is not a linear function.

5)

y = 2x² - 6

This is not a linear function because we have x².

The graph is given below.

6)

Graph D represents a non-linear function.

7)

Graph B represents a non-linear function.

8)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table D has the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

= (4 - 7) / (-1 + 2)

= -3/1

= -3

Table D is a linear function.

9)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table B does not have the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

Table B is not a linear function.

10)

The green line on the graph represents a straight line.

The green line is a linear function.

The green line is 3x + 2y = 6.

Thus,

The answers are given above.

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In 2x^3, 3 is the greatest degree of the exponent. 2x^3 is a cubic polynomial as a result.

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.

An example of a polynomial of a single indeterminate x is x² − 4x + 7.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.

For instance, the polynomial 3x+2x-5.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

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Answer:

4

Step-by-step explanation:

3 - h(x + 4) -2y  Substitute in what was given.

3 -(-5)(-5+4)-2(-3)

3 + 5(-1) + 6

3-5+6

-2+6

4

Answer:

3-(-5)(-5+4)-2(-3)

3+5(-1)+6

3-5+6

-2+6

4

To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth: y = -2.2

system of coordinates, Arrangement of reference lines or curves for locating points in space The Cartesian (named for René Descartes) system is the most popular one in two dimensions.

To solve for y in the equation 5x + 2y = 21, we can start by isolating y on one side of the equation. To do this, we can subtract 5x from both sides of the equation:

5x + 2y = 21

5x - 5x + 2y = 21 - 5x

2y = 21 - 5x

To solve for y, we can then divide both sides of the equation by 2:

2y = 21 - 5x

y = (21 - 5x) / 2

To solve for y in the equation -21 + 6y = -34, we can start by isolating y on one side of the equation. To do this, we can add 21 to both sides of the equation:

-21 + 6y = -34

-21 + 21 + 6y = -34 + 21

6y = -13

To solve for y, we can then divide both sides of the equation by 6:

6y = -13

y = -13/6

y = -2.1666666666666665

To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth:

y = -2.2

So, the y-coordinate of the solution is -2.2.

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The sum of length of the parallel sides of a trapezium exists 300 cm.

A trapezoid, which is often referred to as a trapezium, is a flat, closed object with four straight sides and one set of parallel sides. A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. Also possible are parallel legs on a trapezium.

Four sides, four corners/vertices, and four angles make up a trapezium, which is a closed shape or polygon. A trapezium has parallel sides on each of its opposing angles.

One set of the sides of a trapezium is parallel only. Since no trapezium is a rectangle, they are not all the same.

Area of trapezium = (a + b)/2 × h

where h is the perpendicular height, and a and b are parallel sides.

So, (a + b) exists sum of length of bases of a trapezium.

Let the equation be

Area of trapezium = (a + b)/2 × h

substitute the values in the above equation, we get

⇒  4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}

simplifying the equation, we get

⇒ (84/280) × 10000 = a + b

⇒ a + b = 300 cm

Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.

The complete question is:

Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.

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The sum of length of the parallel sides of a trapezium exists 300 cm.

A trapezoid, also known as a trapezium, is a closed, flat object with one pair of parallel sides and four straight sides. The parallel bases and the non-parallel legs of a trapezium are called the bases and the legs, respectively. A trapezium with parallel legs is another option.

A trapezium is a closed shape or polygon with four sides, four corners, and four angles. Each of the opposing sides of a trapezium has parallel sides.

A trapezium has only one set of parallel sides. They are not all the same since no trapezium is a rectangle.

Area of trapezium = (a + b)/2 × h

where h is the perpendicular height, and a and b are parallel sides.

So, (a + b) exists sum of length of bases of a trapezium.

Let the equation be

Area of trapezium = (a + b)/2 × h

substitute the values in the above equation, we get

⇒  4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}

simplifying the equation, we get

⇒ (84/280) × 10000 = a + b

⇒ a + b = 300 cm

Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.

The complete question is:

Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.

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In parallelogram, x=7 and AC = 44 units are the values of x and AC .

What do math parallelograms mean?

A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of its opposite sides parallel and equal.

                       A parallelogram ABCD with the coordinates AB II CD and AD II BC can be seen in the provided illustration. Moreover, AB = CD and AD = BC. Non-Example: A parallelogram is not represented by a trapezium.

Here in parallelogram ABCD , AC and Bd are diagonals intersecting at E.

BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6

Using (i)

   BE  = BD/2

 2x + 2 = (5x- 3)/2

2(2x + 2) = 5x - 3

  4x + 4 = 5x - 3

   x = 7

Now , AE = 4(7)-6 = 28-6 = 22

AC =2 AE = 2 (22) =44 units.

Hence, x=7 and AC = 44 units.

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Here the 10th term of this arithmetic sequence is 999.

Given data :

an = n³ - 1

a1 = 1³ - 1 = 1 - 1 = 0

a2 = 2³ - 1 = 8 - 1 = 7

a3 = 3³ - 1 = 27 - 1 = 26

a4 = 4³ - 1 = 64 - 1 = 63

a5 = 5³ - 1 = 125 - 1 = 124

a10 = 10³ - 1 = 1000 - 1 = 999

I saw that these numbers were one less than the cubes. So the answer is

a_n = n^3 - 1

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The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.

1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.

2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.

3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.

4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.

5) Intercepts: The points where the graph of a function crosses the x- and y-axes.

6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.

7) Continuity: A function is continuous if its graph has no breaks or gaps.

8) Smoothness: A function is smooth if its graph has no sharp corners or links.

9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.

10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.

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The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2

How to calculate average rate?

The average rate is a measure of how quickly a quantity changes over a specific period of time. It can be calculated by dividing the change in the quantity by the change in time. The formula for calculating the average rate is:

Average rate = (final value - initial value) / (final time - initial time)

Given a function y, the average rate of change S of y = f(x)  in an interval (Xs, Xf)  will be given by the following equation:

In this problem, we have that:

Interval (1,5), so

Then

S = f(5) - f(1)/4

All options are compared to g(x).

g(5) = 1.8*(5)^2 = 45

g(1) = 1.8*(1)^2 = 1.8

An average rate of change greater than 10.8.

D.=k(x) = 2x^2

k(5) = 2*(5)^2 = 50

k(1) = 2*(1)^2 = 2

Greater than 10.8, this is the answer.

Hence, The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2

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On solving the provided question, we can say that by the help of unitary method total 28 + 40 = $ 68

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

One package of chicken costs  = $7

steaks cost  = $4 per pound.

cost of 4 chicken = 4 * 7 = $28

cost of 10 steaks = 4*10 = $40

total 28 + 40 = $ 68

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Answer:

Refer to the step-by-step

Step-by-step explanation:

To minimize the cost of producing the box, we would want the box to be a cube.

Where the volume, [tex]V=s^{3}[/tex], where s is the length of one side of the box.

We were given the value, [tex]V=4096 cm^{3}[/tex], plug this into the equation above so we can find the dimensions of the box...

[tex]4096=s^{3} = > s=\sqrt[3]{4096} = > s=16[/tex]

Thus the dimensions to minimize the cost of the production of the box would be 16cm by 16cm by 16cm.