A population of 100 insects tripled in size every month. Write a function formula to represent the insect population after x months

The eigen vectors are :

\(\left[\begin{array}{ccc}-4&8\\-8&-4\end{array}\right]\) = 4\(\sqrt{5}\) \(\left[\begin{array}{ccc}cos(arctan(2)+π)&−sin(arctan(2)+π)\\sin(arctan(2)+π)&cos(arctan(2)+π)\end{array}\right]\)

given that

M = \(\left[\begin{array}{ccc}-4&8\\-8&-4\end{array}\right]\)

using the P\(D^{n}\)\(P^{-1}\) method

λ1=−4+8i  with the respective eigenvector which leads \(\left[\begin{array}{ccc}-i\\1\end{array}\right]\) factoring out the i out giving

\(\left[\begin{array}{ccc}0\\1\end{array}\right]\) + i \(\left[\begin{array}{ccc}-1\\0\end{array}\right]\)  which means P = \(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) and \(P^{-1}\) = \(\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\)

D = 4\(\sqrt{5}\) \(\left[\begin{array}{ccc}cos(arctan(2)+π)&−sin(arctan(2)+π)\\sin(arctan(2)+π)&cos(arctan(2)+π)\end{array}\right]\)

I means \(\pi\)

\(\left[\begin{array}{ccc}-4&8\\-8&-4\end{array}\right]\) = 4\(\sqrt{5}\) \(\left[\begin{array}{ccc}cos(arctan(2)+π)&−sin(arctan(2)+π)\\sin(arctan(2)+π)&cos(arctan(2)+π)\end{array}\right]\)

To learn more about eigenvector :

https://brainly.com/question/13050052

#SPJ4

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

For more questions on comparisons

https://brainly.com/question/30097421

#SPJ8

The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

Below

Step-by-step explanation:

Points   (-3,5)   and   ( 3,1)

distance d can be found using the distance formula ( modified Pyhtagorean theorem)

d^2 = ( x1-x2)^2 + ( y1-y2)^2

d^2 = ( -3 -3)^2  + ( 5-1)^2

d^2 = 36 + 16

d^2 = 52

d = sqrt(52) = 2 sqrt(13)

Answer:

1

Step-by-step explanation:

\(\frac{1}{2}=.5 \\ \frac{1}{4}=.25\)

0.5 + 0.25 + 0.25 = 1

espero que esto ayude :)

The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

To know more about Percentage check:

https://brainly.com/question/29306119

#SPJ1

Answer:

70 square units

Step-by-step explanation:

1 box is 2 units

Width = 7 units

Length = 10 units

7 × 10 = 70 square units

The exponential function that can model the county population, y, x decades after Tiana was born, is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

\(y = a(b)^x\)

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 when y = 600000, hence:

\(y = 641000(0.99)^x\)

\(600000 = 641000(0.99)^x\)

\((0.99)^x = \frac{600000}{641000}\)

\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)

\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)

\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)

x = 6.6 decades.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:  j(x) = (x-1)(x+2)

The x-1 part is because of the root x = 1

The root x = -2 leads to the factor x+2

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

$3.24

Step-by-step explanation:

Cost for the coffee + Cost for the bagel

$1.39 + $1.85

$3.24

The absolute value inequality that models the function is given by:

\(|x| = x, x \geq 0\)

\(|x| = -x, x < 0\)

In this problem, the leading candidate will receive 52% of the votes with a margin of error of no more than 5%. Hence, the difference between his percentage of votes x and 0.52 should be at most plus/minus 0.05, that is:

\(|x - 0.52| \leq 0.05\)

Hence, option b is correct.

You can learn more about absolute value inequality at https://brainly.com/question/24005819

x= 4.5

18x - 9 = 72 are the equations

Stay safe!! God bless!

<3

- Elisha

Answer:

£1.6

Step-by-step explanation:

we can round 1.252 to 1.25

to find how much 2 euros is, we first have to make 1.25 into 2.

to do that, we will use the same equation to get the answer for £

1.25/5*8=0.25*8=2. now we repeat for £1

1/5*8=0.20*8=1.6

hope it helps

Answer:

She can make 1,145 gifts.

Step-by-step explanation:

The solution to the inequality is: x <= -8 or x >= -8 and [-24, -11] U [7, 24] for number line.

What is inequality?

An inequality is a mathematical statement indicating that one expression is less than or greater than another expression. It involves the use of inequality symbols such as <, >, ≤, or ≥ to compare two values.

|(1/4)x + 2| + 4 >= 8

First, we isolate the absolute value term on one side by subtracting 4 from both sides:

|(1/4)x + 2| >= 4

Next, we split the inequality into two cases: one where the quantity inside the absolute value is positive, and one where it is negative:

(1/4)x + 2 >= 0 or (1/4)x + 2 <= 0

Solving for x in each case, we get:

(1/4)x >= -2 or (1/4)x <= -2

x >= -8 or x <= -8

Therefore, the solution to the inequality is:

x <= -8 or x >= -8

Or, in interval notation:

(-∞, -8] U [-8, ∞)

B. -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

And the solution would be:

[-24, -11] U [7, 24]

The closed dot at -24 indicates that -24 is included in the solution, while the open dot at -11 indicates that -11 is not included.

The closed dot at 7 indicates that 7 is included, while the closed dot at 24 indicates that 24 is included in the solution.

Therefore, the solution to the inequality is: x <= -8 or x >= -8 and [-24, -11] U [7, 24] for number line.

To learn more about inequality visit:

https://brainly.com/question/30238989

#SPJ1

Answer:

since .45 times 1 = .45 plus  __ zeros bascially move the decimal ____ times (the amount of zeros)

Step-by-step explanation:

weebs rule

Since .45 times 1 = .45 plus 2 zeros basically move the decimal 4 times

log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.

To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.

First, let's find the prime factorization of 24.

24 can be divided by 2, so we have 24 = 2 × 12.

12 can be divided by 2, so we have 12 = 2 × 6.

6 can be divided by 2, so we have 6 = 2 × 3.

Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.

Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.

log₂ 24 = log₂ (2³ × 3)

According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:

log₂ (2³ × 3) = log₂ 2³ + log₂ 3

Since log₂ 2³ is equal to 3, we can simplify the expression further:

log₂ (2³ × 3) = 3 + log₂ 3

For similar question on logarithms.

https://brainly.com/question/30437705

#SPJ11

Answer:

5

Step-by-step explanation:

Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

The coordinates of the point B are given as (2, - 4)

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Under a reflection in the y- axis

A point (x, y) → (- x, y), hence

A(- 2, - 4) → B(2, - 4)

Therefore the coordinates of the point B are given as (2, - 4)

To know more about Coordinate geometry follow

brainly.com/question/18269861

#SPJ1

Answer:

m = 3 , b = - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx  b ( m is the slope and b the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with m = 3 and b = - 4

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

Learn more about ratio here:

https://brainly.com/question/2328454

#SPJ1

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

For such more questions on living room

https://brainly.com/question/31126272

#SPJ8

Answer:

lollllllll

Step-by-step explanation:

Answer:

:)

Step-by-step explanation:

The maximum home value that can be financed is approximately $35,365.85.

Let's represent the maximum home value that can be financed by H.

If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.

Therefore, we have:

H × 82% = $29,000

Multiplying both sides by (1/82%), we get:

H = $29,000 / 82%

= $35,365.85

Hence, the maximum home value that can be financed is approximately $35,365.85.

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

The inequality that describes the given word problem is;

x + 1.5 < 48

Let x represent how tall Keenan was last summer. Thus;

x = Keenan's height last summer in inches

If he was x inches last summer, and has since grown an additional 1.5 inches up to date, then it means that his total height now is;

x + 1.5 inches.

The conditons state "riders must be at least 48 inches tall to ride the Night Eagle roller coaster". So it means that his height must be equal to 48 inches, or larger than 48 inches, to make him eligible to ride the roller coaster.

But since he is still too short to ride, this means the expression x+1.5 is smaller than 48 and as such the inequality of this problem is;

x + 1.5 < 48

Read more about Inequality Word Problems at; https://brainly.com/question/25275758

#SPJ1