According to the Polygon Interior Angles Sum Theorem, the sum of the interior angle measures of an n-sided convex polygon is (n−2)·180°. Write an equation setting this expression equal to the given angle measure. Then solve for n.

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:

y=-2x+3

Step-by-step explanation:

y=mx+b

Answer: 30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

(34 + 3) -7

37 - 7

30

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 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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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.

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

The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.

The study of mathematics include the study of numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. A function is an association between a number of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs in which each input leads to a single, distinct result.  Usually, the letter f is used to denote functions (x). input consists of x. There are four different types of functions. based on the following elements: one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

given

The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.

If so, all real values, with the exception of these roots, are in the domain of f (x).

It may be necessary to factor by grouping or by applying the factor theorem in order to fully factor both p (x) and q (x).

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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] .

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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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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(a) The exponential growth model is P = 5655 e^(0.014t)

(b) Population of the town in 2022 is 6689.5065.

Population growth is defined as the number of people increasing over years in a specific region calculated using annual growth rate.

(a) The formula to calculate population growth is,

P = P₀ e^(r t)

Given,

Initial population in 2010, P₀ = 5655

Annual growth rate, r = 1.4% = 0.014

Substituting,

P = 5655 e^(0.014t)

(b) To estimate the population of town in 2022,

t = 2022 - 2010 = 12 years

Substituting value of t in the formula in (a),

P = 5655 e^(0.014 × 12)

  = 5655 e^(0.168)

  = 5655 × 1.1829

  = 6689.5065

Hence the population is 6689.5065 in 2022.

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Answer:

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

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 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 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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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.)

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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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

Lilyan took out a 72-month car loan for $17,595. If he had paid a total of $22,556. 79 at the end of the loan, then the interet rate is 6.7%

What is principal amount?

The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.

What is simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is  I=P.r.t

Where P=principal amount, r=rate, t=time.

Lilyan took out a 72-month car loan for $17,595.

If he had paid a total of $22,556. 79 at the end of the loan,

find the interet rate

72 months = 6 years

principal = 17595

amount = 22556.79

we have to calculate interest

A = P ( 1+ r/100) ^ n

 = 17595 ( 1+r/100)^6

22556.79/17595 ^ 1/6= 1+0.00r

r= 6.7%

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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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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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The solution to the equation 1/h-5+2/h+5=16/h^2-25 is H=7 .

An equation’s solution is an array of all values that, when substituted for unknowns, make the equation true. To solve equations with one unknown raised to a power of one, two basic algebra methods using the additive and multiplicative properties are needed. The set of linear equations has three alternative solutions.

They are as follows:

One-of-a-kind solution.

There is no solution.

There are an infinite number of solutions.

False solutions are ones that do not fundamentally address the problem at hand but fool others into believing they do, while also causing additional major problems.

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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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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.

The length of t to the nearest centimeter is 1083 cm.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Given that,

u = 750 cm

m ∠U = 42°

m ∠T = 105°

We have the sine rule to find missing length as,

[tex]\frac{u}{sin U}[/tex] = [tex]\frac{t}{sin T}[/tex]

Substituting the measures given,

[750 / sin (42°)] = [t / sin (105°)]

Cross multiplying,

t = [ 750 × sin (105°)] / sin (42°)

t = 1082.59 ≈ 1083 cm

Hence the length of the missing side is 1083 cm.

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Therefore , the solution to the given problem of equation comes out to be is 19 mph for a boat in calm water.

An equation must always include two equal members and one or more unknown members (the unknown variables). When multiplied by itself, what number, for example, results in 16. To express this maths equation mathematically, use the equation or expression.

Here,

The determining formula is

30/u-4 = 46/u+4

(time equation, where u represents the boat's speed in still water)

Cross-multiply:

30*(u+4) = 46(u-4) (u-4),

30u + 120 = 46u - 184,

120 + 184 = 46u - 30u,

Thus,

304 = 16u

=> 304/16

=> 19.

The answer is 19 mph for a boat in calm water.

Therefore , the solution to the given problem of equation comes out to be is 19 mph for a boat in calm water.

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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