A sequence defined by f (1) = 3 and f (n) = 2 - f (n - 1) for n ≥ 2. Which of the following
statements defines the n' term of f?

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:3(3x + 5)[/tex]

now plug in the value of x as 5

[tex]\qquad \sf  \dashrightarrow \:3(3(5) + 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \:3(15 + 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \:3(20)[/tex]

[tex]\qquad \sf  \dashrightarrow \:60 \: [/tex]

So, the equivalent value is 60

[tex]sin60 = \frac{opp}{hyp} \\ sin60 = \frac{y}{12 } \\ \frac{ \sqrt{3} }{2} = \frac{y}{12} \\ 2y= 12 \sqrt{3} \\ y = 6 \sqrt{3} [/tex]

[tex]cos60 = \frac{adj}{hyp} \\ cos60 = \frac{x}{12} \\ \frac{1}{2} = \frac{x}{12 } \\ 2x = 12 \\ x = 6[/tex]

Hope it helps

Please give brainliest

Answer:

Step-by-step explanation:

we have 9 letters

3 vowels: A , E , I

6 consonant: B, C, D, F, G , H

Consider the event V : «choosing at least 1 vowel»

[tex]\Longrightarrow \overline{V} \ \colon \ \text{choosing 2 consonant}[/tex]

[tex]p(V) =1-p\left( \overline{V} \right) =1-\frac{C^{2}_{6}}{C^{2}_{9}}=0.583333333333[/tex]

The set of parallel lines in a quadrilateral leads to the parallelogram.

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

Line M

x - y + 3 = 0,

y = x + 3

m = 1

Line L

y = x - 2,

m = 1

Line N

y = -1/2x + 5,

m = -0.5

Line P

x+2y+12=0

y = -x/2 - 6

m = -0.5

Here we can see that the slope of line M and L are equal and slope of line N and P are equal.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Hence, the set of parallel lines in a quadrilateral leads to the parallelogram.

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Answer:

A

Step-by-step explanation:

the domain are the value on the x coordinate

i.e 3, 6, -1, 5, -4 = {-4,-1,3,5,6}

Answer:

have income be greater than expenses

Step-by-step explanation:

I hope this helps you! Feel free to give feedback :)

Answer:

Both C and D are basically right but I would mainly lean towards D

Create Personal Savings

Step-by-step explanation:

this isn't a math question btw

Have a nice day! :)

Answer:

A≈78.54

Step-by-step explanation:

A¹=7.7×6.6=50.82(area of rectangle inside)

16.1-7.7=8.4/2=4.2

A²=6.6×4.2=27.72(area of triangles)

A=50.82+27.72=78.54

The values that could represent this data set include 5, 6, 9, 10, 12, 10, 4, 6, and 19.

It should be noted that a mean simply means the average of a set of numbers.

In this case, the values that could represent this data set include 5, 6, 9, 10, 12, 10, 4, 6, and 19. Therefore, the mean will be:

= (5 + 6 + 9 + 10 + 12 + 4 + 6 + 19)/9

= 81/9

= 9

When a 10th basketball player on this team scored 12 points in the last game, the new mean will be:

= (81 + 12)/10

= 93/10

= 9.3

Therefore, there's an increase in mean.

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f(x) = 4²ˣ, this is an exponential function. Then the correct option is E.

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

y = aˣ + b

The exonentuial functions are given below.

a. f(x)=x³ + 2x²² -6, this is not an exponential function.

b. f(x) = 5/x, this is not an exponential function.

c. f(x) = 5x + 2, this is not an exponential function.

d. f(x) = 4x², this is not an exponential function.

e. f(x) = 4²ˣ, this is an exponential function.

Then the correct option is E.

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The answer is one in seven or (1/7)!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

the answer is C since y is less than. meaning that the line should be dashed and below the graph.

comment if you have any doubts.

An expression is defined as a set of numbers, variables, and mathematical operations. The expression that can represent the total income of Sheryl is 7e+13n.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Since Sheryl makes $7 per pair of earrings and $13 per necklace, therefore, the expression that can represent her total income of Sheryl is 7e+13n.

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Work Shown:

C = 2*pi*r

78.5 = 2*3.14*r

78.5 = 6.28r

r = (78.5)/(6.28)

r = 12.5

Answer:

A≈804.25m²

Step-by-step explanation:

A=πr2=π·162≈804.24772m²

Answer:

6 km

Step-by-step explanation:

1000 meters equals 1 kilometer

Answer:

B

Step-by-step explanation:

if we consider the coordinates of the points

(2, 3 )

(5, 6 )

(7, 8 )

we can see that the y - coordinate in each case is 1 more than the x- coordinate, then

y = x + 1 is the required rule

Using the quotient rule, it is found that the derivative of the function is given as follows:

[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}[/tex]

Suppose a quotient function defined as follows:

[tex]f(x) = \frac{g(x)}{h(x)}[/tex]

Then, the derivative is given by:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}[/tex]

In this problem, we have that:

Then, since g'(x) = 0, the derivative is given by:

[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}[/tex]

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Volume is a three-dimensional scalar quantity. The volume of the right-triangular pyramid is 1.008 m³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of a right-triangle pyramid is one-third of the product of its base area and its height. Therefore, the volume is,

Volume = (1/3) × 0.5 × 1.4 × 1.8 × 2.4

             = 1.008 m³

Hence, the volume of the right-triangular pyramid is 1.008 m³.

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Answer:

144

Step-by-step explanation:

540 degrees is the sum of angles in a pentagon

Divide 540 by 5(number of sides) =108(interior angle)

Since there are two pentagons you do 108 X 2 = 216 degrees

Do 360 - 216 = 144

so your answer is right

The statements that are true for Trapezoid WXYZ are:

We are told that;

Shape is a trapezoid WXYZ.

Now, In a trapezoid, one pair of opposite sides are parallel and parallel lines have the same slope.

Lastly, the slope of line parallel to x axis is 0 and so If the line starts at the bottom left and goes towards the top right it has negative slope. Thus, all the statements that are true for Trapezoid WXYZ are:

Complete question is;

Four lines are drawn on a coordinate plane to form trapezoid WXYZ. Which statements are true about the lines? Select all that apply.

Line WZ has the same slope as line XY.

Line YX has a greater slope than line ZY.

Line XW has a lesser slope than line YZ.

Line ZW has the same y-intercept as line WZ.

Line XY has a greater y-intercept than line XW

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Answer:

x > 8

Step-by-step explanation:

14 - 2(x + 1) < - 4 ← distribute parenthesis and simplify left side

14 - 2x - 2 < - 4

12 - 2x < - 4 ( subtract 12 from both sides )

- 2x < - 16

divide both sides by - 2 , reversing the symbol as a result of dividing by a negative quantity.

x > 8

Answer:

( x, y) =

[tex]65 \ \frac{15}{11} [/tex]

this is your answer

The probability that you will have missed your friend is 27.78%

The time of meeting is given as:

Time = 90 minutes (i.e 12pm and 1:30pm)

Your time of arrival is given as:

Arrival = 12:25pm

If you missed your friend, it means that your friend arrives earlier.

So, the time spent by your friend is:

Friend= 12:25 - 12 = 25 minutes

The probability that you will have missed your friend is:

P = 25 minutes/90 minutes

Evaluate

P = 27.78%

Hence, the probability that you will have missed your friend is 27.78%

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Answer: 2

Step-by-step explanation:

DE * CE = AE * BE (Two Secants Segment Theorem)

▪︎ DE = 1 + x + 4

▪︎ CE = x + 4

▪︎ AE = 11 + x + 1

▪︎ BE = x + 1

=> (1 + x + 4)(x + 4) = (11 + x + 1)(x + 1)

=> (x + 5)(x+4) = (x + 12)(x + 1)

=> x^2 + 9x + 20 = x^2 + 13x + 12

=> 9x + 20 = 13x + 12

20 - 12 = 13x - 9x

8 = 4x

x = 2

The method which is best for solving the system of equations when you remove one variable by adding them is B Elimination

To answer the question, we need to know what system of equations are

System of equations are pairs of equations that contain two unknowns

We have different ways of solving systems of equations which include

Since we have the system of equations

3x + 2y = 4

-3x + y = 2

The method which we can use to remove one variable by adding them is the elimination method.

Adding them, we have

3x + 2y = 4

+

-3x + y = 2

3y = 6

y = 6/3

y = 2

So, the method which we can use to remove one variable by adding them is B Elimination

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Step-by-step explanation:

y + 1 = 2(x + 5) = 2x + 10

y - 9 = 2x

2x - y = -9

Based on the definition of sequence and the characteristics of the given sequence, the complete sequence is: 4, 543, 65432, 7654321, 876543210.

Sequences are sets whose elements observes at least a condition. In this question we have a sequence formed by numbers formed by decimal digits ordered in descent way. Where the consecutive element has more digits than the previous one.

Then, we conclude that the complete sequence is: 4, 543, 65432, 7654321, 876543210.

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The inequality which is used to find the number of minutes taken by the solution to begin caramelising is 310 < 250 + 5x <338. The correct answer is option A.

The complete question is given below:-

A sugar solution currently measures 250 degrees Fahrenheit. The temperature of the solution increases 5 degrees per minute. The sugar solution will caramelize at temperatures greater than 310 and less than 338 degrees Fahrenheit. Which inequality can be used to find x, the number of minutes it will take for the solution to begin caramelizing? 310 < 250 + 5x < 338 310 < 250 + 5x < 338 310 < 5(x + 250) < 338 310 < 5(x + 250) < 338

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is called an inequality.

According to the given question.

The current temperature of a sugar solution is 250 degrees Fahrenheit. Per minute the temperature of the solution increases by 5 degrees. Also, x is the number of minutes taken by the sugar to caramelize.

⇒ The total increase in the temperature in x minutes = 25 + 5x

Since the sugar solution caramelizes at a temperature greater than 310 and less than 338.

Inequality will be given as:-

310 < 250 + 5x < 338

Therefore, the inequality which is used to find the number of minutes taken by the solution to begin to caramelize is given by 310 < 250 + 5x < 338.

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