Which of the following tables represent a proportional relationship?

The expansion of  (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1

A type of number pattern is Pascal's Triangle. The triangle-shaped arrangement of integers known as Pascal's Triangle provides the coefficients for the expansion of any binomial statement.

The arrangement of the numerals creates a triangle when they are reflected. The number 1 is first placed at the top, and then the numbers are arranged in a triangle design.

The expansion of (x + y)ⁿ is is given by

(x + y)ⁿ = a₀xⁿ + a₁xⁿ⁻¹y + a₂xⁿ⁻²y² + … + a[tex]_{n -1}[/tex] xyⁿ⁻¹ + a[tex]_{n}[/tex]yⁿ  

Here we have (z+1)⁶

Write out Pascal's triangle starting from 1 and up to 6 rows

                                1

                           1         1    

                      1         2         1      

                 1         3         3        1          

            1        4          6         4       1    

      1         5        10         10      5        1  

1          6         15         20      15      6        1    

So coefficients of expansion are 1, 6, 15, 20, 15, 6, and 1  

(z+1)⁶ =  (1)z⁶ + (6)z⁵(1)+ (15)z⁴(1)² + 20z³(1)³ + 15z²(1)⁴ + 6z¹(1)⁵ + (1)z⁰(1)⁶

=> (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z¹ + 1

Therefore,

The expansion of  (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1

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The illustration shows that (A) spring x has a higher elastic potential energy.

The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy.

Until the force is released and the object springs back to its original shape, doing labor in the process, the energy is retained.

Kinetic energy is the power that an object has while in motion.

For instance, a stretched rubber band contains elastic potential energy because, when released, it will spring back to its resting position, converting the potential energy to kinetic energy.

So, according to the given image, spring x has more elastic potential energy.

Therefore, the illustration shows that (A) spring x has a higher elastic potential energy.

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Correct question:

Two identical springs ( x and y ) are stretched to different lengths and held there

Which of the following statements is true

A) spring x has more elastic potential energy

B) spring y has more elastic potential energy

C) spring x has more kinetic energy

D) spring y has more kinetic energy

The least whole number possibility for the third side is 8 cm. The greatest whole number possibility for the third side is 22 cm.

A triangle is a three-sided polygon. It is a geometric shape that has three edges and three vertices. Triangles can be classified based on their side lengths (such as equilateral, isosceles, or scalene) or based on the angles between their sides (such as acute, right, or obtuse). Triangles are a fundamental shape in geometry and are used in many branches of mathematics and physics. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Using this rule, we can find the possible range of values for the third side of the triangle.

The least possible length of the third side would be:

8.5cm + 15cm - 15cm = 8.5cm

The greatest possible length of the third side would be:

(8.5cm + 15cm) - 1cm = 22.5cm

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Answer:

72 divided by 12 is 6 so 6 hours she needs to babysit

Answer: 30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

(34 + 3) -7

37 - 7

30

A series of numbers known as coordinates can be used to display a point's precise location on a coordinate plane. Coordination Plane Definition. The intersection of the x-axis and y-axis, two perpendicular lines that create a 2D plane known as a coordinate plane.

There are three types of co-ordinates are:

(i) Cartesian co-ordinates

(ii) cylindrical co-ordinates

(iii) spherical co-ordinates

The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.

Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane. Two axes, the x (horizontal) and y (vertical), and four quadrants make up a coordinate plane (vertical).

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Step-by-step explanation:

The question is a bit confusing, so I am going to reword it to what I assume it means, which is, “Sergio initially has “p” paintings. There are 12 art collectors total, including Sergio. All the art collectors together donate a total of 48 paintings, and each art collector donates the same number of paintings. How many paintings does Sergio have left?”

p = number of Sergio’s paintings at the start.

p-X = the number of Sergio’s paintings at the end.

48 = the total number of paintings donated by all art collectors

12 = number of art collectors

48/12 = 4 = the number of paintings that each art collector donated

4 = X = the number of paintings that Sergio donated

p-4 = the number of paintings Sergio has left (answer)

(My regrets if my understanding of the question was something other than the above.)

The perimeter of triangle DEF is 10.8 units.

What is perimeter of triangle?

The area around any two-dimensional figure determines its perimeter. We can calculate the perimeter of any closed shape by adding the lengths of its sides.

We are given that triangle ABC is similar to triangle DEF

So,

⇒AB/DE = BC/EF = AC/DF

We are given AB=5, BC=6 and DE = 3

Therefore,

⇒AB/DE = BC/EF

⇒5/3 = 6/EF

⇒EF = 3.6

Similarly, we are given AC =7

So,

⇒AB/DE  = AC/DF

⇒5/3  = 7/DF

⇒DF = 4.2

Perimeter of triangle = DE + EF + DF

⇒Perimeter of triangle = 3 + 3.6 + 4.2

⇒Perimeter of triangle = 10.8 units

Hence, the perimeter of triangle DEF is 10.8 units.

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The value of the test statistic is given as 1.341

We will solve for the test statistic through the use of the following data. We have the level of significance as 0.1, the standard deviation is given as 10, sample = 24, mean = 444

test statistic is solved with the formula: (x - µ )/SE =

hence we would have: ( 447 - 444 ) / 2.2371 = 1.341

Therefore the test statistics is given as 1.341

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Choice B, with a y-intercept of 0, is the correct response and provides a table that depicts a linear and proportionate relationship that is

x y

0 0

2 1

4 2

What do you mean By graph Intercept function?

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Answer:

It would be 6 because the exponent is 2 so you multiply 3 twice which equals 6

Step-by-step explanation:

3 to the 2nd exponent is 3^2 = 9.

If the bases of two exponential expressions are different, they cannot be directly compared or combined.

You can convert one of the bases to match the other by using logarithm properties. For example, if you want to compare or combine 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log3(3²) = 2, so 3² can be rewritten as 2^(log3(3²)) = 2².

If you want to add or subtract exponential expressions with different bases, you can convert one of the bases to match the other by using logarithm properties, then combine the exponents. For example, if you want to add 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log2(3) = 1.58496, so 3² can be rewritten as 2^(log2(3)*2) = 2^3.18992. Now you can add the two exponents: 2³ + 2^3.18992 = 2³ (1 + 2^0.18992).

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So on provided question we cans ay that Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

here,

Group the first two terms first, followed by the last two terms. Remove a GCF from each each binomial. Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.

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The formula in coordinate geometry for Class 9 include distance formula, midpoint formula, section formula, equation of a line, slope of a line, equation of a circle, equation of a parabola, equation of an ellipse, equation of a hyperbola, area of a triangle, and area of a circle.

The distance formula is used to determine the distance between two points in a coordinate plane. The midpoint formula is used to find the midpoint between two points. The section formula is used to calculate the area of a triangle formed by three points. The equation of a line is used to define the line in terms of its slope and intercept. The slope of a line is used to calculate the angle of the line in relation to the x-axis. The equation of a circle is used to determine the equation of a circle with a given center and radius. The equation of a parabola is used to determine the equation of a parabola with a given focus and directrix. The equation of an ellipse is used to determine the equation of an ellipse with a given center and major and minor axes. In coordinate geometry the equation of a hyperbola is used to determine the equation of a hyperbola with a given center and asymptotes. The area of a triangle is used to find the area of a triangle given the three vertices. The area of a circle is used to find the area of a circle given the radius.

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Answer: For the GCF one, the GCF would be [tex]3y^{3}[/tex] because you are factoring from both [tex]15y^{4}[/tex] and [tex]12y^{3}[/tex], the reason it cannot be [tex]3y^{4}[/tex] is because that exponent value exceeds the exponent value of [tex]12y^{3}[/tex].

Step-by-step explanation:

So when you find a greatest common factor (GCF) you are basically trying to simplify the expression by extracting numbers to put it into its simplest form. The GCF of 15 and 12, is 3. And the GCF of the exponents would be [tex]y^{3}[/tex] .

Using arithmetic operations it can be seen that if Susan had $20 to start, she does not have enough money to buy 3 clay pots pricing $4.15 each after buying plants costing $2.75 each. She can buy 2 clay pots.

What are the types of arithmetic operation?

The four basic arithmetic operations in Maths, for all real numbers, are -

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Susan bought 3 plants that cost $2.75 each.

Using arithmetic operation of multiplication -

Total cost of the plants = number of plants bought × cost of each plant

Total cost of the plants = 3 × 2.75

Total cost of the plants = $8.25

Susan wants to buy 3 clay pots that cost $4.15 each.

Using arithmetic operation of multiplication -

Total cost of the clay pots = number of clay plots × cost of each clay pot

Total cost of the clay pots = 3 × 4.15

Total cost of the clay pots = $12.45

The total amount of money Susan has is $20.

She has already bought the plants.

So, the money left with her after buying the plants is -

Using arithmetic operation of subtraction -

Money left with Susan = Total money - Total cost of the plants

Money left with Susan = 20 - 8.25

Money left with Susan = $11.75

Therefore, Susan has enough money to buy only 2 clay pots and not 3.

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To write 3 exponents, you can use the following format: base^exponent.

An exponent is a small number that is written slightly above and to the right of a base number. The base is the number being multiplied, and the exponent tells you how many times the base is being multiplied by itself.

For example, to write 3 raised to the power of 2, you would write it as 3^2, which means 3 multiplied by itself 2 times, which is equal to 9.

It's important to note that the exponent is also known as the power, so 3^2, 3^3 and 3^4 are also read as 3 to the power of 2, 3 to the power of 3, 3 to the power of 4.

In summary, to write 3 exponents, you can use the format: base^exponent, where the base is the number being multiplied and the exponent tells you how many times the base is being multiplied by itself. In this case, 3^2, 3^3, and 3^4 represent 3 multiplied by itself 2, 3, and 4 times respectively.

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The principal should use Square meters because the average length and width of the parking spaces will determine the number of parking spaces created in the rectangular parking lot.

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The solution to the equation 8.4 = 1.4x for the unknown variable x is 6.

8.4 = 1.4x

divide both sides by the variable of x

x = 8.4 / 1.4

x = 6

Check:

8.4 = 1.4x

8.4 = 1.4(6)

8.4 = 8.4

Using inverse relationship

8.4 = k / 1.4

cross product

8.4 × 1.4 = k

11.76 = k

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25/2 is simplest form of fraction.

In math, what is a fraction?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                      Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other. The Latin word fraction, which meaning "to break," is where we get the English word fraction.

Fraction = 12  1/2

              =   25/2

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Answer:

x = -2.65865384615

Step-by-step explanation:

-91x - 13x = 276.50

First, Combine Like Terms

-91x + (-13x) = -104x

-104x = 276.50

Second, divide

276.50 / -104 = x

x = -2.65865384615

Answer:19.28   or 125/7

Step-by-step explanation:

first, replace all the a's with 1's, the b's with 2's, and the c's with 4's. you end up with  (-3(1)+4(2))  ³/2(4)-1

then you would solve that until you get,   (-3+8)³/8-1

then,  (5)³/7

and once you've solved that you get 19.28 or 125/7

equation of first line -> y = x - 3

equation of second line -> y = 7x + 3

to get intersection, equate both equation

-> y = y

-> 7x + 3 = x - 3

Answer:

x=8

Step-by-step explanation:

5(2)=10

4(2)=8

Angela's sample size for the study on predicting how many 7th graders earned an A, is 57 students

The number of observations used to calculate estimates for a certain population is known as the sample size. The sample size was determined by drawing from the population. Sampling is the practice of choosing a portion of the population from which to draw conclusions about the characteristics of the entire population.

In engaging in sampling, Angela wanted to sample 15 % of the 7th graders which means that her sample size would be :

= Percentage to be sampled x Number of 7th graders

= 15 % x 380

= 57 students

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Therefore , the ratio of the triangles ABC and XYZ's corresponding sides will therefore be the same.

A triangle is regarded as both a polygon since it has 4 elements or segments. It is a basic geometric form. Triangle ABC denotes a triangle having angles A, B, or C. Therefore, in Euclidean geometry, a single planes and square are produced whenever sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where a triangle's three sides come together are at its corners. The three triangular angles add up to 180 degrees.

Here,

An dilation is a change that produces an image that is smaller but still exactly the same shape also as original. A particular degree of stretching or contraction is possible for the initial figure.

We can see that in the problem, a 5x dilatation causes ABC to constrict to produce XYZ.

As a result, the triangles ABC or XYZ will have the same ratio of their corresponding sides.

A/B/C/D = A/C/X/Y/Z = 5

The ratio of the adjacent angles of the triangle ABC and XYZ will therefore be the same.

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Angles F and C are congruent. An angle inside a form is called an interior angle.

From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .

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Angles F and C are congruent. An angle inside a form is called an interior angle.

An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees.

A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.

From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .

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Answer:

1/3

Step-by-step explanation:

please give me brainliest

Answer:

4/16

Step-by-step explanation:

The answer is actually 4/16 because you cannot either divide or multiple by any number to get 4/16.