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2 years ago

How would you solve this? Please give an explanation.

Mathematics

1 answer:

Neporo4naja [7]2 years ago

4 0

The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)

<h3>How to generate values from a recursive function</h3>

In this question we have a kind of recursive function known as Fibonacci's function, where a value of the series is generated from at least immediately previous elements. In this case, we need to find the first three elements from the fifth and fourth elements of the series:

$a_{n-2} = a_{n-1} - a_{n} + 4$

a₄ = a₅ - a₆ + 4

a₄ = - 2 - 0 + 4

a₄ = 2

a₃ = a₄ - a₅ + 4

a₃ = 2 - (- 2) + 4

a₃ = 8

a₂ = a₃ - a₄ + 4

a₂ = 8 - 2 + 4

a₂ = 10

a₁ = a₂ - a₃ + 4

a₁ = 10 - 8 + 4

a₁ = 6

The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)

To learn more on recursive series: brainly.com/question/8972906

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The sum of the number is -44.84 one of the numbers is 24.6 the other two numbers are equal to eat other what is the value of eac

nikklg [1K]

The answer is -34.72. I have attached a picture of the work. I hope this helps. :)

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3 years ago

What is the value of 2×3 to the third power +1÷7+5×8

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Answer:

The answer would be 94.14

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3 years ago

Read 2 more answers

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

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3 years ago

Which point on the graph is the solution to the system of linear equations? -2x=-y+4 x=-2

Elodia [21]

Answer:

The solution is (-2, 0)

Step-by-step explanation:

Re-write -2x=-y+4 x=-2 in column form:

x=-2

-2x=-y+4

Next, substitute -2 for x in the second equation:

-2(-2) = -y + 4, or:

4 = -y + 4. Thus, y must be 0.

The solution is (-2, 0)

4 0

2 years ago

The median of the marks 10, 13, 3x-1, 3x+1, 18, 18 arranged in ascending order is

Lorico [155]

Answer:

a. Marks = 10, 13, 14, 16, 18, 18

b. mode = 18

c. Range = 8

Step-by-step explanation:

==>Given the following data set arranged in ascending order:

10, 13, 3x-1, 3x+1, 18, 18

Median = 15

==>Required:

a. Marks:

To get each marks, let's find the value of x since we know median to be 15.

10, 13, [3x-1, 3x+1], 18, 18

Our median in this even number of data set would be the average of the 2 middle values which would give us 15.

Thus, we have:

[(3x-1) + (3x+1)] ÷ 2 = 15

[3x-1 + 3x+1] ÷ 2 = 15

[3x+3x-1+1] ÷ 2 = 15

6x/2 = 15

Multiply 2 by both sides

6x = 30

Divide 6 by both sides

x = 5

Now let's plug in the value of x to get out marks:

10, 13, 3(5)-1, 3(5)+1, 18, 18

10, 13, 14, 16, 18, 18

b. Mode is the most appeared data value, which is 18

c. Range is the difference between the highest and lowest value = 18 - 10 = 8

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2 years ago