Find the nth term of this quadratic sequence
4, 9, 16, 25, 36,

The total fencing material needed for the triangular plot is 537.03 feet.

A trigonometric law: the square of a plane triangle's side equals the sum of the squares of a remaining sides minus double the the product of such sides as well as the cosine of a angle between them.

If the triangle ABC is having the sides a, b and c.

Then, the formula for law of cosine is;

c² = a² + b² - 2abcosC

Now, as per the given question;

The first step is to compute the length of the fence's third side. The following formula can be used to calculate the length of a third side:

c² = a² + b² - 2abcosC

Where a,b and c are the three sides and C is the angle forming between sides a and b.

The sides are a = 160 feet, b = 160 feet.

The angle between the sides a and b is 85 degrees.

Now, estimate for c by substituting all the value in the formula.

c² = 160² + 160² - (2 x 160 x 160)cos85

c² = 51,200 - 51200 x0.087

c = √47104

c = 217.03 feet

Now, the total length of the perimeter = 160 + 160 + 217.03

                                                               = 537.03 feet                

Therefore, the total length of the perimeter of the fencing material is found to be 537.03 feet.

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Qualitative data depicts qualities or characteristics. This type of data is qualitative and nominal.

Qualitative data are the conceptual and descriptive findings gathered by surveys, interviews, or observation. We can explore concepts and provide more context for quantitative findings by analyzing qualitative data.

Qualitative data exist as measures of "types" and can be represented by a name, symbol, or number code, whereas quantitative data exist as information on numerical variables (such as how many, how much, or how frequently).

Numbers are used to expressing measures of values or counts in quantitative data. Binary, nominal, and ordinal are the three primary forms of qualitative data.

Qualitative data comes in a wide variety of forms, including those used in statistics, work, and research. This type of data is qualitative and nominal.

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Answer:

12 inches = 1 foot

Step-by-step explanation:

Really?

Answer:

6 1/3

Step-by-step explanation:

Well 5 goes into 15 3 times because 5 * 3 = 15.

So the answer would be 1/3 for the fraction and 6 1/3 for the answer.

Answer:

6 1/3

Step-by-step explanation:

6 is already in its simplest form.

5/15 = 1/3

^ 5/15 is equivalent to 1/3

Answer:

x=3

Step-by-step explanation:

8x-3x=27-12

5x=15

x=15/5=3

x=3

Answer:

x=3

Step-by-step explanation:

8x + 12 = 3x + 27

Subtract 3x from both sides.

5x+12=27

Subtract 12 from both sides.

5x=15

Divide 5 from both sides.

x=3

Hope this helps!

Please mark as brainliest if correct!

The domain of the function that models Salvatore's price scale is;  {x 0 < x < 8}.

The domain of a graph is defined as the set of possible input values of a function.

Now, we are told that he charges $100  for all work that is completed in less than 2 hours and also that he charges $400 for work that takes between 5 and 8 hours.

This means that the number of hours will be less than 2 but cannot be zero but it is less than or equal to 8

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Answer:

A is the answer.

Step-by-step explanation:

The lower line has slope 2 and passes through (0, 0). The clear circle indicates that the point where x = 1 is not included.

So, if x < 1 the function is  2x.

if x >= 1 the line is 1/2x + 5/2.

Step-by-step explanation:

2x - 11 = 3

2x = 3 + 11

2x = 14 (divide both sides by 2 to get x)

2x/2 = 14/2

x = 7

Answer:      x= neagtive 4

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

8d-3=5+9d

8d-9d=5+3

-d=8

d=-8

Answer:

d = -8

Step-by-step explanation:

Hello!

Solve for d by isolating the variable.

The value of d is -8.

Answer:

h = (S - 2nr) / 2nr

Step-by-step explanation:

S = 2nr + 2nrh

2nrh = S - 2nr

h = (S - 2nr) / 2nr

Based on the total budget of Mr. Bell for the incentive and the cost of a pizza box, the equation that matches the word problem is 60 ≥ 9.25x

The amount that Mr. Bell will spend at the most is the budget for the incentive of $60.

He will not spend more than this amount but will spend a maximum of it. This amount of $60 is therefore equal to or greater than the cost of the pizzas:

60 ≥ cost of the pizza

The cost of the pizza is:

= Cost per pizza box x number of boxes

= 9 × x

= 9x

The equation is therefore:

60 ≥ 9.25x

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The blanks in the  question has same value and it is equal to 9

Given data

6x​ + ____ =7x-​____ ​, solution is 18

let the missing number be in the left hand side of the equation be equal to  the missing number at the right hand side of the equation and both be represented by y.

if the solution is x which is 18 we substitute for y as follows

6x + y = 7x - y

y + y = 7x + 6x

plugging in the values of x

y + y = 7 * 18 - 6 * 18

2y = 126 - 108

2y = 18

y = 9

testing y = 9 in both equations

6x + y = 6 * 18 + 9 = 108 + 9 = 117

7x + y = 7 * 18 - 9 = 126 - 9 = 117

Hence we can say that the blanks in the  question has same value and it is equal to 9

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Answer:

let's say (5x + 2) = y

then that means 118° + y = 180°(angle in a straight line)

therefore y =180 - 118= 62°

since y = 5x + 2

and y= 62°

therefore 5x + 2 = 62°

5x = 62- 2= 60°

therefore 5x = 60°

this means that x = 60 ÷5 = 12°

Answer:

EFBGCADHI

That one is confusing, I'm not really sure.

The quotient of 6/8 divided by 1/4 is 3.

It should be noted that the information is to find the quotient of 6/8 divided by 1/4.

This will be:

= 6/8 ÷ 1/4

= 6/8 × 4/1

= 3

Therefore, the quotient is 3.

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Answer:

f(0) = 1

Step-by-step explanation:

f(0) means what is the value of y when x = 0

locate x = 0 on the number line, at the origin, go vertically up to meet the graph at (0, 1 ) , then

f(0) = 1

Required coordinate proof of distance formula between two points in 3 dimension is:

[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]

As given,

Let points  A(x₁, y₁, z₁) and  B(x₂, y₂, z₂) be referred to a system of rectangular axes OX , OY, OZ.

Through the points A and B, we draw planes parallel to rectangular coordinate plane as rectangular parallelepiped with AB as diagonal.

Pythagoras Theorem

[tex]AB^2 = AC^2 + CB^2....(1)[/tex]

[tex]AB^2=CD^2+DB^2...(2)[/tex]

From equation (1) and (2) we have,

[tex]AB^2=AC^2+DB^2+CD^2[/tex]

As coordinates of the points, A and B as known,

[tex]AC =y_{2}-y_{1}, CD = x_{2} -x_{1} and DB= z_{2}-z_{1}[/tex]

Distance formula :

[tex]AB^2=(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2[/tex]

Therefore, required coordinate proof of distance formula between two points in 3 dimension is  ,

[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]

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If the total charge on 8 particles is -56 units and all the particles have the same charge, then the charge on each particle is equal to -7 units.

The charge on each particle can be determined by division.

Division is a part of the basic operations of arithmetic which are four in number, the rest being addition, subtraction, and multiplication. It can be considered the opposite of multiplication and involves separating into equal parts or groups.

The change on each particle can be calculated by dividing the total charge units by the total number of particles. Hence,

charge on each particle = total charge units ÷ total number of particles

charge on each particle = -56 / 8

charge on each particle = -7

Therefore, the charge on each particle is equal to -7 units if all the particles have the same charge.

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The given sentence about polygon is true.

A statement is given in the question.

We have to tell whether the statement is true or false.

What is a polygon ?

A polygon is a two-dimensional geometric figure that has a finite number of sides i.e., triangle has three sides.

As per the question ;

The statement given is , "An included side is the side located between two consecutive angles of a polygon."

Let's check whether it is true or false ;

We know that ,

Included side is one which links two angles together.

For example in a right angle triangle ABC ;

Side (base) AC links two angles one a right angle at A and other angle at C.

So ,

We can conclude that the given statement is true i.e., an included side is located between two consecutive angles of a polygon.

Thus , the given statement about polygon is true.

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The two numbers include 1.6682 and 4.3378 and this will give a sum of 6.006.

From the information, the sum of two numbers is 6.006 One number has a 6 in the tenths place and a 2 in the thousandths place and the other number has a 3 in the ones place and a 7 in the hundredths place.

In this case, the two numbers include 1.6682 and 4.3378 and this will give a sum of 6.006. The sum will be:

= 1.6682 +4.3378

= 6.006

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$59 increase in her bank account during that week.

Any of the basic arithmetic operations—addition, subtraction, multiplication, division, raising to the power of a whole number, and taking roots (fractional power)—is considered an algebraic operation. These procedures could be applied to numerical data, in which case they are frequently referred to as arithmetic operations. Similar operations can be carried out on variables, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of a set to the same set.

Given that : Sheila made four withdrawals of each from an ATM. . She also made a $156 purchase with her check card. She then deposited her $375 salary.

It's difficult to determine the solution because we don't know how much money she had in her bank account before making 4 withdrawals, thus a like and rating would be really appreciated. We know she took out $40 four times, which is $160. She also used her card to make a $156 purchase, so when we sum the two amounts, we get $316. She then placed a check for $375 into the bank account, therefore we must deduct $316 from that sum to get at $59; but, since we deducted, Given that we end up with $59 rather than the money we wasted at the beginning, the fact that the price is higher than $316 indicates that there has been an increase.

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The missing angles of triangles are - 30°, 50°, 40°.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the internal angles of a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

There are 5 triangles in the given diagram,

We will see them anti - clock wise.

All the triangles are right - angled triangle.

The measures of 1 triangle are -

90°, Let the other 2 angles be x,y

The measures of the 2nd triangle are -

Given,

60°, 90°

Using angle sum property,

The measure of third angle = 180°

= 60 + 90 + third angle = 180

third angle = 180 - 150

= 30.

The measures of 3rd triangle are -

Given,

40°, 90°

Using angle sum property,

The measure of third angle = 180°

= 40 + 90 + third angle = 180

third angle = 180 - 130

= 50.

The measures of 4th triangle are -

50°, 90°

Using angle sum property,

The measure of third angle = 180°

= 50 + 90 + third angle = 180

third angle = 180 - 140

= 40.

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True, The sequence an = 8, 13, 18, 23, ...is the same as the sequence a₁ = 8,

an = an-1 +5.

An arithmetic sequence is a set of integers which follow a specific pattern. It is an arithmetic sequence if you pick any number in the sequence and subtract it from the preceding one, and the result is always the same or constant.

The common difference, indicated by the letter d, is the constant difference between all pairs of consecutive or succeeding numbers in a sequence. To transition from one phrase to another, we use the common difference. How? To get to the following term, take the current term and add the common difference, and so on. That is how the sequence's terms are formed.

The first equation is as follows: a(sub n) = 8, 13, 18, 23.

The second equation is: a(sub 1)=8; a(sub n)= a(sub n-1)+5

To obtain the second term, enter two into the equation for n 8+5=13. To find the third, enter the second term, 13, into the equation for n 13+5=18.

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The amount deposited by Shilpi is 8850

The final answer if I have this same question would be 8850

We are to use simple interest to find out the initial amount deposited

The formula for getting Simple Interest is

SI = (P × R ×T) / 100

Thus,

8850= P * 0.06 * 3

8850= 0.18P

P= 8850 * 0.18

P= 1593

Therefore, the amount deposited by Shilpi is 1593

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The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .

The given expression is 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y.

We have x = 2 and y = -2 as per the question.

To evaluate the expression, first we need to simplify the given expression and then we can substitute the given value of  x and y in simplified expression.

The given expression can be simplified as,

   12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y

⇒ 9x - (1/2)y - 3x - (3/4)y

⇒ 6x - ((1/2)+(3/4))y

On taking LCM of coefficient of y, we will get

6x - (5/4)y

Now on substituting x = 2 and y = -2, we get

6(2) - (5/4)(-2)

= 12 + (5/2)

= 29/2 = 14.5

The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .

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After simplifying the expression we get the answer as ₋3x²/8¹³.

Given the expression is (₋8)³ 6x (1/2)²2x(₋8)⁻¹⁶

expand the powers.

(₋8×₋8×₋8) 6x (1/2 × 1/2)2x × 1/8¹⁶

we get:

(₋512) 6x (1/4) 2x × 1/8¹⁶

(₋8)³ 6x (1/4) × 2x × 1/8¹⁶

cancel 8 from numerator and denominator.

₋6x × 1/4 × 2x × 1/8¹³

divide the numbers.

₋3x² × 1/8¹³

₋3x²/8¹³

Hence we get the simplified answer as ₋3x²/8¹³.

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Answer:

slope of ST = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

calculate the slope of PT using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = P (2, 2 ) and (x₂, y₂ ) = T (- 1, - 4 )

[tex]m_{PT}[/tex] = [tex]\frac{-4-2}{-1-2}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{ST}[/tex] = - [tex]\frac{1}{m_{PT} }[/tex] = - [tex]\frac{1}{2}[/tex]

Answer: 4

Step-by-step explanation: We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.