Part 1 : write an equation for the nth term of the given sequence

Part 2: What is the given term of the sequence?

The coordinates of point W which is equidistant from M and N ( 7, 1 / 2).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the points are M(3, 7) and N(11, -6). The coordinates of the midpoints are,

W = ( x₁ + x₂ ) / 2, ( y₁ + y₂ ) / 2

W = ( 3 + 11 ) / 2, ( 7 - 6 ) / 2

W = 14 / 2, 1 / 2

W = 7, 1 / 2

Hence, the value of the coordinate of the midpoint is ( 7, 1 / 2 ).

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Answer:

-72

Step-by-step explanation:

Answer:

-72

Step-by-step explanation:

multiply-12 x3^2 and then add 36

Required, after 12 days Claire will have the day where she has gone to the gym and the park an equal number of times.

The least common multiple (LCM) of two numbers represents the smallest multiple that is divisible by both numbers.

Here,
In this case, the LCM of 4 and 6 is 12, which is the smallest number that is divisible by both 4 and 6. This means that after 12 days, Claire will have gone to the gym and the park an equal number of times, and will thus be back at the same point. Therefore, the answer is LCM.

Thus, the required, after 12 days Claire will have the day where she has gone to the gym and the park an equal number of times.

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Answer:

Infinitely Many

Step-by-step explanation:

Both answer are equal to each other

Answer:

(2.4, 2)

(4, -3.4)

Step-by-step explanation:

Brainliest Please

Answer:

g=4f-k+h

Step-by-step explanation:

f=g-h+k

4

4f=g-h+k

4f-k=g-h

4f-k+h=g

The system of inequalities is.

x + y ≤ 20

x*7.5 +  y*6 ≥ 90

And some solutions can be:

(10, 5)

(11, 5)

(12, 6)

Let's define the variables we will be using:

x = number of hours dog-waling

y = number of hours at the car wash.

We know that you can work at most 20 hours, then:

x + y ≥ 20

And you need toearn at least $90, then wecan write:

x*7.5 +  y*6 ≥ 90

The system of inequlities is:

x + y ≤ 20

x*7.5 +  y*6 ≥ 90

And the graph is the one below. The solutions are all the points in the dark blue region, some solutions we can see there are:

(10, 5)

(11, 5)

(12, 6)

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The length of RT is 13 units

A triangle is a three-sided polygon that consists of three edges and three vertices.

As T is the centroid of the given triangle.

TN=TP

x+10=4x-17

Now solve for x

27=3x

x=9

Now TP=4(9)-17

TP=36-17

TP=19

Now from pythagoras theorem we find the length of RT

19²=14²+RT²

361-196=RT²

165=RT²

Take square root on both sides

RT=13

Hence, the length of RT is 13 units

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The scale floor's perimeter is 34 inches.

To solve, we can set up fractions:

21/7 = 30/x

Cross multiply and you get:

21x = 210

Divide each side by 21:

x = 10

You can apply the following equation since you're attempting to determine the floor's perimeter:

2w + 2l = p

Substitute to solve:

2 ( width = 10 )

2 ( length = 7 )

2 (7) + 2 (10) = p

14 + 20 = p

34 = p

The complete question is:

The rectangular floor of a classroom is 21 feet in length and 30 feet in width. A scale drawing of the floor has a length of 7 inches. What is the perimeter, in inches, of the floor in the scale drawing?

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The area of the basement will be 576 square feet.

The area is defined as the space covered by the object in a two-dimensional plane. The area of the rectangle is calculated by the multiplication of the length and the width.

Given that a basement floor plan for a house is being created by an architect. He drew the plans as they are seen. On the plan, one-fourth of an inch corresponds to four feet in the house.

The area of the basement will be calculated as:-

Area = 12 x 6

Area = 72 square inches

Area = 72 x 8 feet

Area = 576 square feet

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Answer:

32

Step-by-step explanation:

Substitute values given into the expression :

3[2(1)+(3)]-4[((1)-(3)]+(3)²

3[5]-(-8)+9

15+8+9 =

32

Hope this helped and have a good day

From the given information provided, the cube root of 12,167 by prime factorization method is approximately 23.

You can find the cube root of 12,167 using a calculator or by using the prime factorization method.

Using the prime factorization method, we can express 12,167 as the product of its prime factors:

12,167 = 19 × 641

Since the cube root of a product is equal to the product of the cube roots of the factors, we can find the cube root of 12,167 as follows:

∛12,167 = ∛(19 × 641)

∛12,167 = ∛19 × ∛641

∛12,167 = 2.7144 × 8.0186

∛12,167 = 23.1649 (rounded to four decimal places)

Therefore, the cube root of 12,167 is approximately 23.

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Answer:

Abc

Step-by-step explanation:

2b + c + 3a = Abc

The original fraction described in the question is; 25/31

Let the numerator be x and let the denominator be y.

We are told that the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. Thus;

4x/(y - 2) = 4

4x = 4y - 8

4x - 4y = -8   -----(1)

The numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Thus;

(x + 15)/(2y - 2) = 5/4

4x + 60 = 10y - 10

4x - 10y = - 70   ----(2)

Subtract eq 2 from eq 1 to get;

6y = 62

y = 31/3

Thus;

4x - 4(31/3) = -8

Multiply through by 3 to get;

12x - 124 = -24

12x = 100

x = 25/3

Thus, the fraction is;

(25/3)/(31/3) = 25/31

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A statement which best describes the function include the following: A. f(x) is a linear function because x and f(x) are both increasing.

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

Next, we would determine the slope by using the points contained in the table as follows;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 1)/(0 + 1)

Slope (m) = 4.

Slope (m) = (13 - 5)/(2 - 0)

Slope (m) = 4

Slope (m) = (21 - 13)/(4-2)

Slope (m) = 8/2 = 4.

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Answer:

-1.33333333333

Step-by-step explanation:

Answer:

-1 1/3

Step-by-step explanation:

A) By using the change of base formula, the solution of the expression is,

⇒ x = - 2/3

B) The solution of the expression is,

⇒ x = - 2/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

Now, We have the change of base formula,

⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]

Here, The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

Take log on both side,

⇒ log 5³ˣ⁻² = log 5⁶ˣ

⇒ (3x - 2) log 5 = 6x log 5

⇒ 3x - 2 = 6x

⇒ - 2 = 6x - 3x

⇒ 3x = - 2

⇒ x = - 2/3

B) By using another method as;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

By comparing we get;

⇒ 3x - 2 = 6x

⇒ - 2 = 6x - 3x

⇒ 3x = - 2

⇒ x = - 2/3

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The difference in housing prices in the fifth year is $7,125.

Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.

$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.

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Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer.

The equation is typically written in algebraic form and includes numerical values.Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer. For example, if an individual is asked to verify the identity [tex]sin^2x + cos^2x[/tex]= 1, they will be given numerical values to plug into the equation. For example, if they are given x = 60, they would enter[tex](sin60)^2 + (cos60)^2[/tex] into the calculator and solve. This should result in an answer of 1, proving the equation is accurate.

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a) There are 36 sample points that are possible.

b) The probability of obtaining a value of 7 is 1/12.

c) The probability of obtaining a value of 8 or greater is 1/6.

(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.

(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.

(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.

Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.

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Answer:

18.4 degrees

Step-by-step explanation:

a complementary angle is 90 degrees and 90 - 71.6 is 18.4. So, the answer is 18.4 degrees.

The shape with two pairs of parallel sides is called a parallelogram.

A parallelogram is a shape that has four sides, in which the two opposite lengths are:

As there are four sides, divided two by two, the shape has two pairs of parallel sides, and is called a parallelogram.

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Answer:

Ben had given away 3/5 of his fraction.

Step-by-step explanation:

total number of marbles Ben give away,

= 65+80+35

= 180

180/300= 3/5

The probability P(red pen, purple pen) without replacement is 10/33.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that a container holds 5 red pens, 4 purple pens and 3 blue pens.

We need to find the probability P(red pen, purple pen) without replacement.

P(red pen, purple pen) = (number of ways to select a red pen and a purple pen) / (total number of ways to select two pens)

Total number of ways to select two pens=¹²C₂=66 ways.

Number of ways to select a red pen and a purple pen = (number of ways to select a red pen) x (number of ways to select a purple pen from the remaining pens)

Number of ways to select a red pen = 5

Number of ways to select a purple pen from the remaining pens = 4

Therefore, the number of ways to select a red pen and a purple pen without replacement is:

Number of ways to select a red pen and a purple pen = 5 x 4 = 20

P(red pen, purple pen) =20/66

=10/33

Hence, the probability P(red pen, purple pen) without replacement is 10/33.

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Answer:

11 feet long

Step-by-step explanation:

20+20=40

62-40=22

22÷2=11

check

11+11+20+20=62

The process of finding the value of a numerical or algebraic expression is called evaluation.

Evaluation involves substituting the given values of the variables in the expression and then simplifying the expression using the order of operations (PEMDAS).

For example, if we are asked to evaluate the expression 3x + 2y when x=4 and y=5, we would substitute these values to get 3(4) + 2(5), which simplifies to 12 + 10 = 22. Therefore, the value of the expression 3x + 2y when x=4 and y=5 is 22.

In algebra, evaluation is an important process because it allows us to find the value of an expression for specific values of the variables, which can help us to solve equations or inequalities, and to simplify expressions.

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The x-intercept and the y-intercept of the line 5x - 2y = 10 include the following ordered pairs:

x-intercept = (2, 0).

y-intercept = (0, -5).

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, the y-intercept is sometimes referred to as an initial value (base value) and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.

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The binary number will be equal to 14 in base 6

1001₂ = 14 (base 6)

Base is defined as a set of digits used to represent numbers. There are different number systems which make use of different combinations of digits as the base.

One of the most common which is the binary number system uses only 2 digits, i.e., 0 and 1 to represent numbers, while the Octal number system uses 8 digits, i.e., 0 to 7, to represent numbers.

The most common number system that is in use is the decimal number system that uses the base 10, which includes digits from 0 to 9 for writing numbers.

1001₂ = 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0

1001₂ = 1 x 8 + 1 x 1

1001₂ = 8 + 1

1001₂ = 9

Converting 9 into base 6

6 9

6 1 r 3

  0 r 1

From downwards pointing up

9 = 13 (base 6)

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Answer:

To find the quarterly rate of population increase, we first need to find the annual rate of population increase in decimal form, which is 2.8% expressed as 0.028.

To find the quarterly rate, we need to divide the annual rate by 4, since there are 4 quarters in a year:

0.028 / 4 = 0.007

Therefore, the quarterly rate of population increase is 0.007 or 0.7%

The length and breadth of the rectangle are 25.33 meters and 12.67 meters,

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

We are given that the breadth of the rectangle is half of its length, so we can write:

B = 0.5L

We are also given that the perimeter of the rectangle is 76m. The perimeter of a rectangle is the sum of the lengths of all four sides, which in this case is:

Perimeter = 2(L + B)

Substituting the value of B from the first equation, we get:

Perimeter = 2(L + 0.5L)

Perimeter = 2(1.5L)

Perimeter = 3L

Now we can solve for L:

3L = 76

L = 25.33

So the length of the rectangle is 25.33 meters.

To find the breadth, we can substitute this value of L back into the first equation:

B = 0.5L

B = 0.5(25.33)

B = 12.67

So the breadth of the rectangle is 12.67 meters.

Therefore, the length and breadth of the rectangle are 25.33 meters and 12.67 meters, respectively.

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