Find the value of x and show your work.
5x+10
7x-6​

The [tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex] when n is a positive integer for nth Fibonacci number is true.

Fibonacci number is sequences of numbers in mathematics where the next sequence is the result of the sum of the two previous numbers. So we can written for Fibonacci number formula as,

[tex]f_{n}[/tex] = [tex]f_{n-1}+f_{n-2}[/tex].

Usually in mathematics the Fibonacci number is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... with 0 is the 0 order of Fibonacci number.

For the given equation, we can prove that with many ways. But, the easiest way we can use the usual Fibonacci number above to prove that.

We assume n = 3 so the number is 2.

[tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex]

(3)(1) - (2^2) = (-1)^2

3 - 4 = -1

-1 = -1

We also can assume n = 5 so the number is 5.

[tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex]

(8)(3)-(5^2) = (-1)^5

24 - 25 = -1

-1 = -1

Thus, the given equation is true.

You question is incomplete, but most probably your full question was

T/F. [tex]f_n[/tex] is the nth Fibonacci number. show that [tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex] when n is a positive integer.

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Answer:

  108, 110, 112

Step-by-step explanation:

You want three consecutive even integers whose sum is 330.

Let x represent the middle integer. Then the other two are (x-2) and (x+2). The expression for their sum is ...

  (x -2) +x +(x +2) = 330 . . . . . an algebraic expression

  3x = 330

  x = 110

  x -2 = 108

  x +2 = 112

The three integers are 108, 110, 112.

__

Additional comment

"Consecutive integer" problems are often worked easily by considering the average value of the integers. For three consecutive integers, their average is the middle one.

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Answer: A. 111 degree

Step-by-step explanation:

Because they are Alternate Interior angles! Which means the two angles are congruent and have the same degree!

As per the unitary method, the price of the cup is $2.958

Unitary method in statistics is defined as in which the value of one article is first obtained to find out the value of any required articles

Here we have given that the 3-gallon container of laundry detergent cost $33. 60.

And we need to find the price per cup.

While we looking into the given question, we have identified the following details that cost of 3 gallon container of laundry detergent is $33.60.

So, the cost for 1 gallon container of laundry detergent cost,

=> 33.60/3

=> 11.20

Let us consider that the cup can hold 1 liter.

As we know that 1 gallon = 3.78541 liter.

Then the cost of 1 liter is calculated as,

=> 11.20/3.78541

=> 2.958

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The vertex form of a quadratic equation is a standard form of a quadratic equation that is written in the form:

y = a(x-h)^2 + k

where a, h, and k are constants. This form is called the vertex form because it represents the graph of the quadratic equation as a parabola, with the vertex of the parabola located at the point (h,k).

The vertex form of a quadratic equation is useful because it allows us to easily identify the vertex of the parabola and the direction in which the parabola opens. If a is positive, the parabola opens upwards and the vertex is the minimum point of the parabola. If a is negative, the parabola opens downwards and the vertex is the maximum point of the parabola.

Overall, the vertex form of a quadratic equation is a standard form that represents the graph of a quadratic equation as a parabola with a specific vertex location. It is useful for identifying the characteristics of the graph and for solving problems involving quadratic equations.

The graph of scatter point is attached below. The correlation is linear.

The mass of a cake and cooking time are related linearly.

What is scatter points?

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).

Given points are (20,610), (30, 680), (20, 700), (50, 750), (40, 825), (30, 840), (50, 845), (75, 965), (45, 1000), (85, 1100).

Plot the points on the graph.

The line of best is a straight line.

Thus the correlation is linear type.

Also, the mass of a cake and cooking time are related linearly.

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To solve for R in Ohm's Law, you can rearrange the formula to isolate R on one side of the equation. To solve for R, you can divide both sides of the equation by I:

R = E/I

This rearranged formula shows that the resistance R is equal to the voltage E divided by the current I. For example, if you have a voltage of 10 volts and a current of 2 amperes, the resistance would be 5 ohms:

R = 10 volts / 2 amperes = 5 ohms

Let's prep ourselves before attempting to answer the question. What do we need to know?

We'll need to know a couple of basic concepts before we tackle the problem. Namely, we'll need these ones:

What are equality properties? These are the equality properties:

From the problem, we are given Ohm's Law, which is E = IR. The problem states that it wants to solve this equation for R.

In order to solve Ohm's Law for R, we can use the Division Property of Equality. What does this property state? It states that if you divide something (number, variable, etc.) on one side, you must do the same for the other.

Now, let's apply this property to find our answer. We divide by I on both sides to isolate R:

[tex]\displaystyle\begin{aligned}E & = IR \\IR & = E \\\frac{IR}{I} & = \frac{E}{I} \\R & = \boxed{ \frac{E}{I} } \\\end{aligned}[/tex]

[tex]\displaystyle \boxed{ R = \frac{E}{I} }[/tex]

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156 pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added

You will need to consider four cases.

when _999 and _000 are the last three digits of consecutive numbers. Just possible cases are 1999, 2000

At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. 5 possible scenarios (corresponding to (0,1), (1,2), (2,3), (3,4), and (4,5) at the hundredth place) exist.

when the last digit of consecutive numbers is in the form ____ 9 and ____ 0. 5*5 = 25 possible scenarios.

when none fall into that category, possible case=. 5*5*5 = 125,

and the answer is 125+25+5+1 = 156.

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Answer:

B. 53 degrees

Step-by-step explanation:

Because the ?-angle is equal to the 53-degree angle. So, the answer is B. 53 degrees

Answer:

Step-by-step explanation:

iven, the equation is (x - 1)² + 2(x + 1) = 0. We have to determine if the equation has a real root. By using algebraic identity, (a - b)² = a² - 2ab + b² (x - 1)² = x² - 2x + 1.

Answer:$2.25x

Step-by-step explanation:

Lets use X to denote the amount of stickers How and his friends bought.  so he buys them at 1.25x.  An easy trick when doing percentages of a number is thinking of the percent as a fraction.  So instead of 180, think of 180/100.  Think of 1.25 as 125/100

multiply 180/100 by 125/100

you get 22500/10000 which equals 2.25

or 2.25x

Answer

x=10.5 , y=6.25

Step by Step ^

The solution is, the values of x and y is, x=10.5 , y=6.25.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

we know,

perimeter of rectangle is:

P = 2*( a+ b)

given that,

A rectangle with a length of (x+2) cm and a width of y cm has a perimeter of 37.5 cm.

i.e. we get,

2( x+2 + y ) = 37.5

or, 2x + 2y = 33.5 ........(1)

and, we have,

A second rectangle has twice the perimeter, with a length of (2x - 6.5) cm and a width of (x+2y) cm.

i.e. we have,

2( 2x - 6.5 + x + 2y ) = 75

or, 3x + 2y = 44.5 .....(2)

solving (1) & (2) , we get,

x=10.5 , y=6.25

Hence, The solution is, the values of x and y is, x=10.5 , y=6.25.

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its D

. . . . . ... . . . . . . . . . . . .. . .

Answer: 10 kg

Step-by-step explanation:

3% = 0.03

First, take 20 times 0.03 = 0.6kg of salt

We know that the 2% solution of seawater

So, we take 100 times 0.6, then divide by 2 = 30kg

Then take 30 - 20 = 10kg

So, to make a solution from 3% to 2%, we have to add  10 kg of water with a 20 kg solution.

Answer:

8+5x

Step-by-step explanation:

Perimeter = sum of the all sides of triangle

= 6+3x-4+2x + 6

= 8+5x

Answer:

5x + 8

Step-by-step explanation:

To find the perimeter, add up all the sides

6 + 3x-4 + 2x +6

Combine like terms

5x + 8

The statement dog was running towards the trainer to receive a treat.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that  graph represents the distance of a dog from a trainer after a command is given.

A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10,

The vertical axis shows Distance (yards) numbered 4 to 40.

The line shows an increase, then decrease, then constant distance.

At the point on the graph where time is 5 seconds, the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer.

The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.

Hence, the statement dog was running towards the trainer to receive a treat.

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According to the information in the table, the weights in pounds would be: 1. 1 pound, 2. 6 pounds, 3. 6 pounds, 4. 3 pounds.

To calculate the total pounds of cheese we must follow the instruction of the statement. In this case, we must multiply the fractions by the frequency number to find the total weight in pounds of the cheese orders. Here are all the procedures:

A.

1/4 * 4 = 1

b.

3/4 * 8 = 6

c.

1 1/2 * 4 = 6

d.

1 1/2 * 2 = 3

According to the above, we can infer that the numbers that complete the table are: 1, 6, 6, and 3 respectively in each of the blank spaces from top to bottom.

Note: This question is incomplete because there is some information missing. Here is the complete information:

table:

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Answer:

10 Joules/second

Step-by-step explanation:

To find the power needed to get up the stairs, we need to divide the amount of work done (30 Joules) by the time it took to do the work (3 seconds):

Power = Work / Time

Power = 30 Joules / 3 seconds

Power = 10 Joules/second

Therefore, it takes 10 Joules/second of power to get up the stairs.

The volume of the Illustrated cone used as an example is 51.3cm³.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A cone is a recognizable three-dimensional geometric shape with a flat and curved surface that is pointed upward. The formula for the volume of a cone is V=1/3hπr²

Let's say the radius is 7cm. The volume will be:

= 1/3 × 3.14 × 7²

= 51.3cm³

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Answer: a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.

Step-by-step explanation:

We will use the Pythagorean Theorem.

a²+b²=c²

c² is the longest side, so 8cm.

lets make the bottom side b², so 3cm

We are trying to find h, so let's make that a².

Applying the Theorem:

a²+3²=8²

--- a² + 9 = 64

subtract 9 from both sides.

-- a² = 55

Take the square root of both sides

a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.

Answer:

22.249 cm^2 (THIS IS ROUNDED)

Step-by-step explanation:

to find the area we first need to find h using Pythagorean theorem

a^2+b^2=c^2

We need to isolate a^2 on one side

a^2+b^2=c^2

     -b^2.   -b^2

a^2=c^2-b^2

a^2=8^2-3^2

a^2=64-9

a^2=55

√.      √

a=7.416

Now we multiply by 3 to find the area

7.416x3

About 22.249 cm^2

Hopes this helps

The value of (408) is (0.1)8(0.9)32 for a local department store estimates that 10 percent of its customers return the merchandise they purchase.

The value of (408)(0.1)8(0.9)32 represents the probability of getting 8 returns out of a sample of 40 customers, given that the store estimates that 10% of customers return merchandise.

This probability is calculated using the binomial probability formula, which is used to calculate the probability of a specific number of successes (in this case, returns) in a certain number of trials (in this case, customer purchases), given a certain probability of success (in this case, the estimated probability of customers returning merchandise).

The value of (408)(0.1)8(0.9)32 ( 40 8 ) ( 0.1 ) 8 ( 0.9 ) 32 describes the probability of getting 8 returns out of 40 customers when the probability of a customer returning the merchandise they purchase is 0.1.

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a brick staircase has a total of number of 12 steps. the bottom step requires 100 bricks.A total of 246 bricks are required to build the staircase.

The total number of steps in the brick staircase is 12. The bottom step requires 100 bricks. Each successive step requires 4 less bricks than the prior one. Therefore, the number of bricks required to build the staircase can be calculated as follows:

The first step requires 100 bricks.

The second step requires 96 bricks (100 - 4 = 96).

The third step requires 92 bricks (96 - 4 = 92).

This pattern continues until all 12 steps are accounted for.

Adding the number of bricks required for each step gives a total of 246 bricks required to build the entire staircase.

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Answer: i belive its B but im not 100%

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

w = 12500p + 250

250 is a fixed number of words.

12500 is the slope

For each dollar the price increases, the number of words increases by 12,500.

Answer: A

Answer:

Common Difference is positive

Step-by-step explanation:

If the common difference is negative, the value is decreasing every time the term increases.

If the common difference is positive, the value is increasing every time the term increases.

Because, in this case,  when the term increases, the value increases, the common difference is positive.

Answer:

the average for 129 is 159 and the average for 47 is 49

Step-by-step explanation:

By solving a linear equation, it can be calculated that

Jamyia wants to sell 4 bracelets.

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let the number of bracelets Jamyia wants to sell be x

Cost of each bracelet = $12x

The materials for each bracelet cost $3.50, and the table rental at the

fair costs $34 for the day.

Her expense = $(34 + 3.5x)

By the problem,

The linear equation is

34 + 3.5x = 12x

12x - 3.5x = 34

8.5x = 34

x = [tex]\frac{34}{8.5}[/tex]

x = 4

Jamyia wants to sell 4 bracelets.

Option C is correct

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Answer:

106

Step-by-step explanation:

(305+13)/3=106