An ant went 2 meters away from its nest searching for food. The next time, the ant went 3 meters away. Each successive time the ant leaves the nest to search for food, the ant travels the sum of the two previous times. How far will the ant travel on his fifth trip?

Answers

Answer 1

Answer:

The first time, the ant went 2m away, then we have a₁ = 2m

The second time, the ant went 3m away, then we have a₂ = 3m

The next time, the ant went a distance equal to the sum of the two previous ones, so we can write it in a general case as:

aₙ = aₙ₋₁ + aₙ₋₂

Only if n > 2.

then the third time, we have n = 3.

a₃ = a₂ + a₁ = 2m + 3m = 5m

a₄ = a₃ + a₂ = 3m + 5m = 8m

a₅ = a₄ + a₃ = 5m + 8m = 13m

This means that in the fifth trip, the ant went 13 meters away from its nest.

And if we consider the fact that the ant must go and return, then it will move a total distance of 13 meters two times, or 2*13m = 26 meters.


Related Questions

it must be a equivalent fraction

Answers

In the picture there is 3 question. The equivalent fraction.

1. We get 9/25=18/50

2. We get 26/39=2/3=8/12

3. We get 1/4=5/20

Given that,

In the picture there is 3 question.

Equivalent fractions state that two or more fractions are identical if, after simplification, they both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.

For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.

1. We get 9/25=18/50

Multiply by 2

2. We get 26/39=2/3=8/12

Multiply by 13 and 4

3. We get 1/4=5/20

Multiply by 5

To learn more about equivalent visit: https://brainly.com/question/14055345

#SPJ1

1. Which equation best represents the relationship between x and y
in the graph?












Answers

Answer:

rises down 4 and moves forward 4

I need help on thiss

Answers

Answer:

1/3

Step-by-step explanation:

Convert the Fractions Into decimal to know the detailed information as almost to whole numbers then use the Integer number system to figure out which is bigger or smaller.

2/8 = 0.25

1/3= 0.33

1/5= 0.2

1/7= 0.14

The largest of them all is 0.33

Solve this equation
m+6=2m-6
2​

Answers

Answer: +6=2−62 its =68

Answer:

[tex]m = 12[/tex]

Step-by-step explanation:

[tex]m + 6 = 2m - 6 \\ 2m - m = 6 + 6 \\ m = 12 \\ \\ hope \: it \: helps... \\ pls \: mark \: as \: brainliest[/tex]

PLEASE ANSWER FAST 33 POINTS

Answers

Answer:

it clearly says 17 points not 33

Step-by-step explanation:

Answer:

(-5)+5=0

Step-by-step explanation:

What place do we always round money to?

Answers

Answer:

Hundredths place

50.51

the ones is in the hundredths place

Can someone please help mee (40 points
brainliest!!!)

Answers

a. $650

b. 50? Not sure about that one

What does Jing-mei`s mother want her to be?

Answers

Answer: Jing-mei's mother wants her to be a prodigy because her friend Lindo Jong's daughter Waverly is a chess prodigy. She also wants her daughter to be successful.

Step-by-step explanation:

Can you help me with explanation will give brainiest

Answers

Answer:

Area of rectangular garden = lxb = 10*5

                                             = 50 sq. inch

when area increases by six times

new area = 50*6 = 300 sq inches

now,

let x be increasement in both  length and width

(5+x) (10+x) = 300

50 + 5x + 10x + x² = 300

x² + 15x - 250 = 0

x²+ 25x-10x -250 = 0

x(x+25) - 10 (x+25) = 0

( x-10) (x+25) = 0

either x + 25 =0

x = -25 length can be negative

0r x-10 = 0

x = 10

so 10 inches is increase on both side

Step-by-step explanation:

Hi I’m trying to do 9th grade algebra hw x+(-2)=8

Answers

answer is

x=10 because 10-2=8

i need some help
will someone help me

Answers

Answer:yes

Step-by-step explanation: why not whatcha need

1. If 4 lbs of apples cost $36, How much would 2 lbs cost?​

Answers

Answer:

18

Step-by-step explanation:

divide 36 by 2

Answer:

18

Step-by-step explanation:

36/4=9

1lb=9

2lbs=18

How many hours do they have to work before they go to the movies

Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?
I got two different answers last time. One said 25 and the other said 11. Are either of them correct?

Answers

Answer:

25 months

Step-by-step explanation:

Plan A : $70 per month

Plan B : $50 per month + $500 as a one time cost.  

So for A $70 a month would take 8 months to be at least $500

And for B it in those 8 months it would cost you $900

But we have to keep going up until they are equal

25*70 = 1750

(25*50) = 1250+500=1750

So yes 25 months is correct

Which graph best represents y = 4x + 1?

Answers

The graph of y = 4x + 1 is a linear graph with a slope of 4, and a y-intercept of 1

The function is given as:

[tex]y = 4x + 1[/tex]

A linear equation is represented as:

[tex]y = mx + b[/tex]

Where:

m represents the slope,b represents the y-intercept.

So, by comparison:

[tex]m=4[/tex]

[tex]b =1[/tex]

This means that,

The slope of the graph is 4, and the y-intercept is 1

See attachment for the graph of [tex]y = 4x + 1[/tex]

Read more about linear equations at:

https://brainly.com/question/11897796

Answer:

For the Algebra 2 A U7L8 Exponential and Logarithmic Functions Unit Test Part 1 I got 100%

1. Graph c

2. 5,559.92

3. Graph C

4. 1/2 logb57-1/2logb74

5. 1/2

6. 0.3797

7. 998/3

8. 2% exponential decay

9. 1.0797

10. Logb(y5x6)

11. written you have to do this one

PS get like one or two random answers wrong

hope this helps

Hunter owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $6.50. Yesterday Hunter made a total of $520 in revenue from selling a total of 120 tacos and burritos. Graphically solve a system of equations in order to determine the number of tacos sold, x,x, and the number of burritos sold, yy.

what are the two equations?

Answers

Answer:

x=80 y=40

Step-by-step explanation:

(-2,1); m = 5
Find the equation of the line

Answers

Here’s the correct answer, how I got it, and something to help you for next time :)

What is the image of (7, -3) after a reflection over the x-axis?

Answers

Answer:(7,3)

Step-by-step explanation:

what is a solution to the compound inequality 85 [tex]\leq[/tex]17m[tex]\leq[/tex] 136?

Answers

Given:

The compound inequality is

[tex]85\leq 17m\leq 136[/tex]

To find:

The solution of given compound inequality.

Solution:

We have,

[tex]85\leq 17m\leq 136[/tex]

On dividing all sides by 17, we get

[tex]\dfrac{85}{17}\leq \dfrac{17m}{17}\leq \dfrac{136}{17}[/tex]

[tex]5\leq m\leq 8[/tex]

Therefore, the solution of given compound inequality is [tex]5\leq m\leq 8[/tex]. It can be written as [5,8].

Which graph represents a linear function? (4 points)

Answers

Graph C because it is a straight line with no curves

What is an equivalent equation to 1/4n-16

Answers

Answer:

15/4z+12

Step-by-step explanation:

Consider the points Q(23, 48) and R(7, 62). What is the component form of Vector Q R?

LeftAngleBracket negative 16, 110 RightAngleBracket
LeftAngleBracket negative 16, 14 RightAngleBracket
LeftAngleBracket 30, negative 14 RightAngleBracket
LeftAngleBracket 30, 110 RightAngleBracket

Answers

Answer:

The correct option is;

LeftAngleBracket negative 16, 14 RightAngleBracket which is [tex]\left \langle -16, 14 \right \rangle[/tex]

Step-by-step explanation:

The given coordinates of the points are;

The starting point, Q(23, 48) and the final point, R(7, 62)

Therefore, we have;

The x component = The x-value of R - The x-value of R = 7 - 23 = -16

The y component = The y-value of R - The y-value of R = 62 - 48 = 14

Therefore, the component form of the vector QR = [tex]\left \langle -16, 14 \right \rangle[/tex]

Answer:

B on Edg.

Step-by-step explanation:

Yay

Statement: At a store, 3 bags of peanuts were sold for $18. Determine if each statement has the same unit rate as the original statement or a different unit rate. Click the box for each statement to indicate "Same unit rate" or "Different unit rate." Same unit rate Different unit rate A jar of jam sold at $25 for 5. Sandwiches sold at $20 for 3. Cups of fruit sold at $48 for 8. Ham sold at $12 for 2.​

Answers

Answer:

The original statements unit rate is $6.

A. 25/5=5-Different unit rate

B.20/3=6.67 Different unit rate

C. 48/8=6 Same unit rate

D. 12/2=6 Same unit rate

Step-by-step explanation:

A study of a population of 1,500 moths revealed that 15 out of every 75 moths in the population have gray stripes on their wings. Based on the results of this study, how many moths in the population have gray stripes on their wings?

Answers

Answer: 300 moths

Step-by-step explanation:

Since 15 out of every 75 moths in the population have gray stripes on their wings, this means the fraction of moths that have gray stripes on their wings is 15/75 = 1/5.

Therefore, out of 1500 moths, the number of moths in the population that have gray stripes on their wings would be calculated as:

= 1/5 × 1500

= 300 moths

Work out
3
9
+
2
3
Give your answer in its simplest form
ITS A FRACTON CAN U HELP ASAP

Answers

Answer:

The correct answer is 1.

Step-by-step explanation:

In order to solve the problem [tex]\frac{3}{9}[/tex]  + [tex]\frac{2}{3}[/tex], we need can use two methods.

Method 1: Make the denominators the same.

3/9 + 2/3 =

3/9 + 6/9 =

9/9 =

1

Method 2: Turn both fraction into decimals (by dividing the numerator by the denominator.)

3/9 or 3 ÷ 9 = 0.3 (when rounded to the nearest tenth)

2/3 or 2 ÷ 3 = 0.7 (when rounded to the nearest tenth)

0.3 + 0.7 = 1

Therefore, the answer to this question is 1.

Answer 1 or 9/9


Explanation: First we need to find a common denominator which the easiest would be nine and then multiply those to equal nine and then you will get 3/9+6/9 which is equal to 9/9 which reduces to 1 have a nice day (:

Multiply. Write answer in box below.
(3x - 4)(x+4)

Answers

Answer:3x^2+8x-16

Step-by-step explanation:

-3/4-5/8=
This is a simple math problem
But it’s to hard for me
And I really need help
Not from someone who doesn’t know the answer

Answers

-11/8 because you turn the first one into -6/8 and then subtract to get -11/8

Someone please help me match the name with the Polynomial. Thank you in advance, I will give Brainliest to the correct answer. :)

Answers

Answer:

[tex]1.\ -117 ----> Constant\ Monomial\\As\ it\ is\ an\ expression\ with\ only\ 1\ term,-117\ which\ has\ a\ degree\ of\ 0\ as -117x^0 ,and\ is\ a\ constant.\\ 2.\ x^2- x^4-10 -----> Quartic\ Polynomial\\\As\ it\ is\ a\ polynomial\ \ with\ a\ degree\ 4\ as\ it\ has\ (-x^4).\\ 3.\ 16x-x^8------> 8th\ degree\ binomial.\\As\ it\ is\ a\ polynomial\ with\ the\ term\ -x^8\ which\ gives\ the\ polynomial\ its\ 8th\ degree.\\[/tex]

[tex]4.\ x-3x^2-9-x^3---->Cubic\ Polynomial\ with\ 4\ terms\\As\ it\ is\ a\ polynomial\ containing\ 4\ terms(x, -3x^2,-9,-x^3)\\ and\ having\ a\ degree\ of\ 3\ due\ to\ -x^3.\\ 5.\ x^2-4x+1 ----> Quadratic Polynomial\\As\ it\ is\ a\ polynomial\ with\ the\ degree\ 2\ due\ to\ x^2.[/tex]

What is the value of 3x+7 when x=3

Answers

Answer:

The answer will be 16

Step-by-step explanation:

If x is 3, then 3x will become 3 * 3 which will get you 9. And then 9 adds 7 and gets 16

Answer:

16

Step-by-step explanation:

3x+7

3(3)+7

9+7=16

I hope this is correct and have a great day

Help HELP HELP HELP HELP- I have 40 missing assignments and I want to make my mom proud!!!!

Answers

Answer:

1.   70

Step-by-step explanation:

2.  105

Answer:

A: 70.311 repeat

B: 105.53

Step-by-step explanation:

im not sure if im correct but hope this helps

Choose the answer that validates that the rate of change is constant by showing that the ratios of the two quantities are proportional and equivalent to the unit rate (simplified constant rate of change): NUMBER OF TEXTBOOKS Number of Students Number of Textbooks 7 35 14 70 21 105 28 140

Answers

Given:

The table of values is

Number of Students   :  7    14   21    28

Number of Textbooks : 35  70  105  140

To find:

The rate of change and showing that the ratios of the two quantities are proportional and equivalent to the unit rate.

Solution:

The ratio of number of textbooks to number of students are

[tex]\dfrac{35}{7}=5[/tex]

[tex]\dfrac{70}{14}=5[/tex]

[tex]\dfrac{105}{21}=5[/tex]

[tex]\dfrac{140}{28}=5[/tex]

All the ratios of the two quantities are proportional and equivalent to the unit rate.

Let y be the number of textbooks and x be the number of students, then

[tex]\dfrac{y}{x}=k[/tex]

Here, k=5.

[tex]\dfrac{y}{x}=5[/tex]

[tex]y=5x[/tex]

Hence the rate of change is constant that is 5.

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