Write a formula to find the number of sides N in a regular polygon given that the measure of one interior angle is x

N= ?

Answer:

9 and 10

Step-by-step explanation:

x = 1st positive integer

x+1 = 2nd positive integer

(x+1) is the next positive integer after x (Ex. 3 aka 2+1 is next integer after 2).

Larger Integer: x+1  ==> being squared

Smaller Integer: x ==> being multipled by 9

9x + 19 = (x+1)^2  ==> the square of (x+1) is 19 more that 9 multiplied by x.

9x + 19 = (x+1)(x+1)  ==> simplify

9x + 19 = x(x+1) + 1(x+1)   ==> distribute (x+1) to x and 1.

9x + 19 = (x*x + 1*x) + (1*x + 1*1)  

9x + 19 = x^2 + x + x + 1  ==> simplify

9x + 19 = x^2 + 2x + 1

19 = x^2 - 7x + 1  ==> subtract 9x on both sides

Make one side of the equation equal to 0 so you can factor the equation:

0 = x^2 - 7x - 18  ==> subtract both sides by 19

0 = x^2 + 2x - 9x - 18  ==> 2x - 9x = -7x and 2 * (-9) = -18

0 = x*x + 2x - 9x - 18  

0 = x(x + 2) - 9(x + 2)  ==> factor

0 = (x - 9)(x + 2)

x - 9 = 0         x + 2 = 0

x = 9                     x = -2

Out of x = 9 and x = -2, only x = 9 is positive.

Hence, x = 9 and x+1=10.

Hence, the answers are 9 and 10.

Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.

The following is the equation for a horizontal ellipse of center with coordinates (h,k):

(x - h)²/a² + (y - k)²/b² = 1.

In relation to this issue, we have that:

The origin is where the center is.

Since the major axis is 70, 2a = 70 and a = 35.

The maximum height is 20, therefore b is equal to 20.

As a result, the ellipse's equation is as follows:

x²/35² + y²/20² = 1.

It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:

25²/35² + y²/20² = 1

0.51 + y²/20² = 1

y²/20² = 0.49

y² = 20² x 0.49

y =√(20² x 0.49)

y = 14 feet.

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a) The equation of line is y = 270x + 10640.

b) The annual cost value in 2013 for age 17 is $15,320.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Points (8, 12800) and (14, 14420)

So, the slope is

= (14420 - 12800)/(14-8)

= 1620/6

= 270

and, the slope intercept form

(y - 12800) = 270 (x - 8)

y- 12800 = 270 x  - 2160

y = 270x + 10640

b) Now, x= 17

y= 270(17) +10640

y = 15, 320

Thus, In 2013 at age of 17 the amount is $15320.

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As follows is the Midpoint Formula: [tex](x,y) = [\frac{(x_{1} +x_{2}) }{2} , \frac{(y{1} +y_{2}) }{2} ][/tex]

A mathematical equation called the midpoint formula is used to determine where two data points meet midway. Its ability to compute percentage changes based on the difference between starting and ending values is this equation's defining feature.

How to Calculate the Midpoint:

Using this midpoint formula, we can determine the coordinates of the terminus of the given line and use them to determine the midpoint of the straight line on the graph.

Suppose the endpoints of the line is (x₁,y₁) and (x₂,y₂)  then the midpoint is given as:

The Midpoint Formula is given as,

[tex](x,y) = [\frac{(x_{1} +x_{2}) }{2} , \frac{(y{1} +y_{2}) }{2} ][/tex]

Where x₁ and x₂ are the coordinates of the x-axis. y₁ and y₂  are the coordinates of the y-axis.

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We have many distance formulas in a coordinate system that can be used to find the distance between two points, the distance between a point to a line, the distance between two parallel lines, and the distance between two parallel planes.

The Distance Formula is a useful tool for calculating the distance between two points that can be arbitrarily represented as points:

A (x1,y1) and B (x2,y2) are on the coordinate plane.

Distance between two points:

(x₁,y₁),(x₂,y₂)

d=√(x₂-,y₂)²,(x₁-y₁)²

Distance between three points:

(x₁,y₁,z₁),(x₂,y₂,z₂)

d=√(x₂-,y₂)²,(x₁-y₁)²+(z₂-z₁)²

At point (x₁,y₁) and a line ax+by+c=0 is

d=|ax₁+by₁+c|/√a²+b²

Two parallel lines ax+by+c₁=0 and ax+by+c₂=0

d=|c₂-c₁|/√a²+b².

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Therefore , the solution to the given problem of linear equation comes out to be  we bought 6 videos and 3 CDs.

The term "linear" refers to any function that has the algebraic form y=mx+b. m is the y-intercept, while B is the slope. The previous sentence contains a two-variable linear equation since both y and y are factors. Equations involving two variables are called bivariate equations. y + z = 2 and 3z - 6 + x = 3 are two of the many applications for linear equations. The equation y=mx+b, where m stands for the slope and b for the y-intercept, is referred to as a linear equation. The formula is Y=mx+b, where m denotes the inclination and b the y-intercept.

Here,

A collection of equations will be constructed.

Let V = the number of videos purchased.

C will stand for the quantity of purchased CDs.

Since there are eight nephews in all, and each nephew received either a video or a CD, the sum of the numbers of movies and CDs is nine.

So V + C = 9.

We are also aware of how much each CD and film cost and how much money was wasted.

So 14.95V + 16.88C = 140.34

Here, let's experiment with substitution.

Let's just solve for V since it doesn't matter whichever variable we do it for. V = 9 - C

Therefore, replace "V" in the second equation with "9-C," and the result will be 134.55 - 14.95C + 16.88C = 140.34 1.93C = 5.79 C = 3

You can add C = 3 straight into either of the original equations, though I believe I know which one is simpler for you.

V + 3 = 9

V = 6

So we bought 3 CDs and 6 videos.

Therefore , the solution to the given problem of equation comes out to be  we bought 6 videos and 3 CDs.

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Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh

Now, According to the question:

The surface area of a triangular prism is also known as the total surface area. Therefore, it is calculated using the formula, Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh; where:

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Answer:

90 feet.

Step-by-step explanation:

The horizontal beam is parallel to the base of a triangular roof, and the vertical beam is perpendicular to the horizontal beam and the base of the roof. So the length of the horizontal beam is the same as the base of the roof which is 90 feet.

The maximum value of f(x, y) = x3y4 for x, y on the unit circle is 1.

The unit circle is defined as the set of points on a plane that satisfy the equation x2 + y2 = 1. This means that the maximum value of f(x, y) = x3y4 on the unit circle can be found by substituting x2 + y2 = 1 into f(x, y) and solving for x3y4.

We can begin by writing the equation in the following form:

f(x, y) = x3y4 = (x2 + y2)4 = 1⁴ = 1

Therefore, the maximum value of f(x, y) = x3y4 for x, y on the unit circle is 1.

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Sophie would have $15,786 more than Sydney.

We know that the compound interest has to do with the kind of interest that we have to compound but on the principal and the the interest. In this case, we can see that we have;

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

A = amount

P = principal

r = rate

t = time

n = Number of times compounded

Then we have For Sophie;

A = 26000(1 + 0.06/365)^20 * 365

A = $86315

For Sydney;

A =26000(1 + 0.05/12)^12 * 20

A = $70529

It then implies that; $86315 -  $70529

= $15,786

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Answer: The correlation coefficient (also known as Pearson's correlation coefficient or r) is a measure of the strength of the linear relationship between two variables. The value of the correlation coefficient ranges between -1 and 1, with a value of 1 indicating a perfect positive linear relationship, a value of -1 indicating a perfect negative linear relationship, and a value of 0 indicating no linear relationship.

In this case, the correlation coefficient that represents the strongest linear relationship is

0.9

The absolute value of the correlation coefficient measures the strength of the linear relationship, regardless of whether it is positive or negative. So, the absolute value of 0.9 and -0.3 are both 0.9. but as we are looking for the strongest linear relationship, the value of 0.9 is closer to 1 than -0.3 is and it indicates stronger positive relationship.

In summary, the closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the variables is. In this case, 0.9 has the strongest linear relationship of the given options.

Step-by-step explanation:

Answer:

------------------------------------------

Let the number be x.

Set up equation to reflect all the operations:

Solve it in below steps:

When we are walking along the forest, the action-reaction pair that will not occur is d) you pushing down on earth and earth pushing you forward.

According to Newton's third law of motion, two bodies exert equal and opposite forces on each other in every interaction. These forces form action-reaction pairs.

Examples of action-reaction combinations/pairs include: pushing the ball with the gun - the ball pushes the gun back (recoil), or the player applies hand force to the ball and throws the ball forward - the ball pushes back with the hand. The properties of action-reaction pairs are: They must arise from the same interaction. The acting force and the reaction force are equal. Action and reaction forces are directed in opposite directions. The forces act on different bodies and are therefore unbalanced.

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The value of x calculated by using the Pythagorean theorem is equal to 6.

This can be found by using the Pythagorean theorem to solve for the length of side bc, which is the base of the triangle. By using the two given side lengths of 8 and 12, we can find that the length of the hypotenuse (bc) is equal to the square root of 8^2 + 12^2, which is equal to 16.

Since the base is divided into two equal parts, we can divide 16 by 2 and get 8. We then subtract the given length of 2x + 1 from 8 and get 7, which means x is equal to 6.

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Answer:

c

Step-by-step explanation:

Answer:Answer: c ( 8m^9n^3)

Step-by-step explanation:

(see image)

Answer: -x+5/(x-1)(x+3)

Step-by-step explanation:

Subtract 3/(x-1)-4(x+3)

3(x+3)/(x-1)(x+3)-4(x-1)/(x+3)(x-1)

= 3x+9/(x-1)(x+3)-4x+4/(x+3)(x-1)

= -x+5/(x-1)(x+3)

Using the commutative property of multiplication the solution of the equation is solved to be

The addition and multiplication arithmetic operations are covered by the commutative property.

This implies that the outcome of adding or multiplying two numbers remains unchanged if the order or position of the numbers are changed.

applying the commutative property of multiplication in the problem we have that

= (2 * 4) * 18

= 8 * 15

= 120

Also

= 2 * (4 * 15)

= 2 * 60

= 120

the answer does not change

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Lifestyle is the area of the physical activity of the pyramid that can be most easily incorporated into an individual's everyday activities.

The physical activity pyramid tells us about the Frequency intensity and time formulae also called FIT formulae of different types of physical activity. It is just like the food pyramid where the lowest level contains the most beneficial activities and the highest level the least.

The physical activity pyramid has 7 levels and they are:

The physical activity pyramid has 5 areas, they are Flexibility, vigorous sports aerobics anaerobic, and lifestyle.  The lifestyle area is the summed up 30-40 mins of self-chosen activities, such as leisure time, occupational or household activity.

Complete question - Which area of the physical activity pyramid can be most easily incorporated into an individual's everyday activities? A. flexibility B. lifestyle C. aerobic D. anaerobic

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Answer: The perimeter of the flower box can be determined by adding up the lengths of all four sides. In this case, we can see that the width of the flower box is represented by the variable x in feet, and the height is given as 2(x+4). To find the perimeter, we need to add up the lengths of the top and bottom (2x) and the left and right sides (2(x+4)). So, the perimeter P(x) can be expressed as:

P(x) = 2x + 2(x+4)

Simplifying this expression:

P(x) = 2x + 2x + 8

P(x) = 4x + 8

So the perimeter of the flower box is 4x+8 feet, based on the width x in feet.

Step-by-step explanation:

3 is not included in the solution set of x>3

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used

Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa

If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

From the question,

x>3 (x should be greater than 3) means the the value of x is more or greater than 3, that is, x is 4,5,6,...

Hence, 3 will not be included in the values of x>3

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Answer: each time you roll a 6-sided die is 1/6 percent to get any number  

Step-by-step explanation:

Therefore , the solution of the given problem of table comes out to be  15 to 20 table are given as follows :  15,30,45,60,75,90,105,120,135 and 150.

A statistical list is a collection of numbers that shows the outcomes of a computation with numerous inputs. Data is made up of descriptions and numbers and is arranged in rows and columns. The table and indeed the pattern of 10 are easily recalled. In numerical order, the numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, then 20. Value mapping is used to show how multiple data pieces are related to one another. Any science class can benefit from including the values table.

Here,

Given :

=> 15,30,45,60,75,90,105,120,135 and 150

=> 16,32,48,64,80,96,112,128,144 and 160

=> 17,34,51,68,85,102,119,136,153 and 170

=> 18 , 36 ,54,72,90,108,126,144,162 and 180

=> 19,38,57,76,95,114,133,152,171and 190

=>20,40,60,80,100,120,140,160,180 and 200

Therefore , the solution of the given problem of tables comes out to be  15 to 20 table are given as follows :  15,30,45,60,75,90,105,120,135 and 150.

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Answer: (x-2, y-1)

Step-by-step explanation:

The total surface area of the prism is 48 square inches.

2 in,6 in.64 square inches

76 square inches Streck Boost.

Units are displayed for convenience only; they have no bearing on the computations. The units, such as ft, ft2, or ft3, are there to indicate the findings' order. If you start with mm and know h, l, and w in mm, for instance, your calculations will provide d in mm, S in mm2, and V in mm3.

a rectangular prism's formulas:

Rectangular prism volume: V = lwh

Rectangular prism's surface area is given by

S = 2(lw, lh, and wh).

64 square inches

76 square inches

The total surface area of the prism is 48 square inches.

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The answer is 387.97

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....

Given here: To find the sum of the geometric series from n=2 to n=34

we know To find the sum of a finite geometric series, use the formula, Sn=a1(1−rⁿ)/1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio

S₃₂= 400 (1-0.93³²) /0.93

       = 430.12×(1-0.098)

       = 387.97

Hence, The answer is 387.97

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Answer:

Step-by-step explanation:

what do you not understand

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction number is given below.

⇒ 35 / 80

⇒ 7 / 16

⇒ 21 / 48

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

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Answer:

For each service call cost of 20$ will be added to fixed cost of 3000$.

Step-by-step explanation:

The total cost for 1 month is the sum of the fixed monthly cost and the cost of all the service calls, so we can write the equation as:

y = 3000 + 20x

This equation is already in slope-intercept form, where "y" is the dependent variable, "x" is the independent variable, 3000 is the y-intercept (the point where the line crosses the y-axis, when x=0), and 20 is the slope of the line.

This equation can be interpreted as

For each service call cost of 20$ will be added to fixed cost of 3000$.