Which function represents the sequence: 4, 7, 10, 13, 16,...

Answers

Answer 1

Answer:

3n + 1

Step-by-step explanation:

Note the sequence has a common difference between consecutive terms, that is

7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3

This indicates that the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 4 and d = 3, thus

[tex]a_{n}[/tex] = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1

Answer 2

Answer:

[tex]\large\boxed{a(n)=3n+1}[/tex]

Step-by-step explanation:

It's an arithmetic sequence:

[tex]a(1)=4\\\\a(2)=a(1)+3=4+3=7\\\\a(3)=a(2)+3=7+3=10\\\\a(4)=a(3)+3=10+3=13\\\\a(5)=a(4)+3=13+3=16\\\vdots[/tex]

An explicit formula of an arithmetic sequence:

[tex]a(n)=a(1)+(n-1)d[/tex]

d - common difference

We have

[tex]a(1)=4,\ d=3[/tex]

Substitute:

[tex]a(n)=4+(n-1)(3)[/tex]            use the distributive property

[tex]a(n)=4+3n-3[/tex]

[tex]a(n)=3n+1[/tex]


Related Questions

Which is the largest number? 8.2, 7.98, 8 9/10, 7 8/9

Answers

Answer:

8 9/10 is the largest number

Answer:

8 9/10

Step-by-step explanation:

8 is first off larger than 7 so that rules out all the 7 numbers

And 9/10 is .9 so that would make it 8.9 which is greater than 8.2

How many seconds are in 35 minutes

Answers

Answer:

there are 2100 seconds in 35 minutes

2100

There are 60 seconds in a minute, if you times 60 by how many minutes there are, you get how many seconds there are. Here is how I got the answer:

60 x 35 = 2100

I hope this helps you and you can use it for future reference! :)

Michael's father brought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal size lengths for his shelves.

The saw blade that Michael will use to cut the board will change the length of the board by -0.125 inches for each cut. How will this affect the total length of the board?

Answers

Answer:

The remaining wood will be 1.25 inches shorter.

Step-by-step explanation:

Only 10 cuts are required to cut the board into 11 equally sized lengths.  Thus, the length of the board after these cuts have been made will be

10(0.125 inches), or 1.25 inches, shorter.

Final answer:

By making 10 cuts, the total length of the board will be reduced by 1.25 inches due to the saw blade reduction. After converting this to feet, Michael will have approximately 15.896 feet of board left.

Explanation:

Michael has a 16-foot board that he plans on cutting into 11 equal lengths. This means he will need to make 10 cuts (as the 11th 'cut' is actually the end of the board not actually needing a cut). The saw blade will decrease the length of the board by -0.125 inches for each cut. To solve this, we multiply the number of cuts by the length that will be reduced by the saw blade. That gives us 10 x -0.125 = -1.25 inches. That means that the total usable length of the board will be reduced by 1.25 inches. We need to convert this to feet since the original length of the board is in feet. There are 12 inches in foot, so -1.25 inches is about -0.104 feet. Thus, the total length of the board after all the cuts will be 16 - 0.104, or approximately 15.896 feet.

Learn more about Saw Blade Reduction here:

https://brainly.com/question/38347669

#SPJ2

1. Write the next two terms in the pattern.
11, 18, 25, 32.

A.42. 49
B.39, 46
C.38, 45
D.40, 48

2. Find the missing term.
180. 30.5

A.1080
B.900
C.330
D.210​

Answers

Answer:

1. B

2. A

Step-by-step explanation:

1. The terms seem to be increasing by a constant of 7.

11+7=18

18+7=25

25+7=32

Therefore, the next two terms should be 32+7 and 32+7+7. This equals 39 and 46.

2. The terms in this pattern are being divided by 6

180/6=30

30/6=5

In order to find the missing number before 180, we need to multiply 180 by 6. 180 times 6 is equal to 1080.

hi ur answer would be 39,46

Step-by-step explanation: here's my explanation as u can see it 11 into 18 is adding 7 and for all of them the pattern is plus 7 so u do 32+7=39 and then u do 39+7=46 and thats how u get B.39,46

Mrs. Bailey had 12 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy? PLEASE SHOW YOUR WORK. thank you

Answers

Final answer:

Mrs. Bailey had a 75% decrease in the number of candies she had after giving away 9 out of the original 12 pieces.

Explanation:

To calculate the percent decrease of candy Mrs. Bailey had, we begin by identifying the initial amount and the final amount of candy. Mrs. Bailey started with 12 pieces and ended with 3 pieces, which means she gave away 12 - 3 = 9 pieces of candy. To find the percent decrease, we use the formula: “part over total, times one hundred, equals percent.” Here, the “part” is the amount of candy she gave away (9), and the “total” is the original amount she had (12).

The formula for the percent decrease is:

9 / 12 × 100 = 75%

So, the percent decrease in the number of candies Mrs. Bailey had is 75%.

How can you describe the graph of the equation y = m
+ b?

Answers

Answer:

Step-by-step explanation:

y=mx+b is the formula for slope y-intercept form.

Use the scale drawing below to determine how wide the duck pond is.

A.
9 feet


B.
18 feet


C.
27 feet


D.
36 feet

Answers

Answer: The answer is C. 27 feet

Explanation: This is because the width of the Duck Pond is 6 squares. You multiply 6 by 4.5 because each square is 4.5 feet

Hope this helped!!

Answer:

C 28ft on edg 2021

Which polynomials are in standard form?

Choose all answers that apply:

(Choice A)

5-2x

(Choice B)

x^4-8x^2-16

(Choice C)

5x^3+4x^4-3x+1

(Choice D)

None of the above

Answers

Polynomials are in standard form when their terms are written in descending order of exponents. Choice B [tex](x^4 - 8x^2 - 16)[/tex] is in standard form. The correct answer is Choice B.

A polynomial is in standard form when its terms are written in descending order of their exponents. Let's evaluate each of the choices:

(Choice A) 5 - 2x is not in standard form because the term with the x exponent should come first. The correct order should be -2x + 5.(Choice B) [tex]x^4 - 8x^2 - 16[/tex] is in standard form because the terms are in descending order of exponents: 4, 2, and 0.(Choice C) [tex]5x^3 + 4x^4 - 3x + 1[/tex] is not in standard form because the term with the highest exponent [tex](x^4)[/tex] should come first. The correct order should be [tex]4x^4 + 5x^3 - 3x + 1.[/tex](Choice D) This is incorrect because there is at least one polynomial (Choice B) that is in standard form.

Therefore, the correct answer is Choice B.

What is the unit price if a package of 12 candy canes cost $4?

Answers

Answer:

$1 for every 3 candy canes

The drawing will help

what is the first step when using order of operations​

Answers

Answer:

If there are parentheses, then you solve what's in those first.

Step-by-step explanation:

Use PEMDAS to help you remember.

P- Parentheses

E- exponents

M- multiplication

D- division

A- addition

S- subtraction

Enter the equation of the line in slope-intercept form. Slope is − 1 /2 , and (−3, 4) is on the line. The equation of the line is y =

Answers

Answer:

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Here m = - [tex]\frac{1}{2}[/tex], thus

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 4 - [tex]\frac{3}{2}[/tex] = [tex]\frac{5}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex] ← equation of line

Answer:The equation of the line is;

Step-by-step explanation:

What is what is the answer for this 2x+3-x>5

Answers

Answer:

[tex]\large\boxed{x>2\to x\in(2,\ \infty)}[/tex]

Step-by-step explanation:

[tex]2x+3-x>5\qquad\text{subtract 3 from both sides}\\\\2x-x>5-3\\\\x>2[/tex]

answer for this problem would be x>2

“A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin V, which is 250 % of the daily recommend allowance of vitamin C for adults. What is 100% of the daily reccomended allowance of vitamin C for adults?”

Answers

Answer:

80 milligrams

Step-by-step explanation:

Write a proportion and solve.

200mg / 250% = x / 100%

x = 80mg

Find the prime factorization of 70

Answers

Answer:

2*5*7

Step-by-step explanation:

2*5=10

10*7=70

what is x minus 5 equals negative 13​

Answers

x-5=-13

move -5 to the other side

sign changes from -5 to+5

x-5+5=-13+5

x=-13+5

answer:

x=-8

A price was first decreased by 12%, then it was decreased again by an additional 5%. What is the percent of the total decrease?

Answers

Answer:

17% ?

Step-by-step explanation:

that seems like the most logical answer

Answer:

16.4

Step-by-step explanation:

this is right

Elliot is standing at the top of a store escalator that leads to the ground floor below. The angle of depression from the top of the escalator to the floor is 42.51 degree, and the escalator is 16 feet long. How far the top of the escalator from the ground floor? Round your answer to the nearest foot.

A. 41 feet
B. 17 feet
C. 12 feet
D. 11 feet

Answers

Answer:

The answer is 11

Step-by-step explanation:

Final answer:

The distance between the top of the escalator and the ground floor is approximately 12 feet.

Explanation:

To find the distance between the top of the escalator and the ground floor, we can use trigonometry. We have the length of the escalator (16 feet) and the angle of depression (42.51 degrees). The distance we need to find is the opposite side of the right triangle formed by the top of the escalator, the floor, and the length of the escalator. We can use the sine function to find this distance.

The formula is sin(angle) = opposite/hypotenuse. Plugging in the values, we get sin(42.51) = opposite/16. Solving for opposite, we have opposite = sin(42.51) * 16.

Using a calculator, we find that opposite ≈ 12.014 feet. Rounding to the nearest foot, the distance between the top of the escalator and the ground floor is approximately 12 feet.

Robert has 20 blueberries. He has 10 more blueberries than Janessa. He has 14 fewer blueberries than Amari. How many blueberries does Janessa have? How many blueberries does Amari have?

Answers

Answer: Janessa has 10 Amari has 34

The number of blue berries with Janessa and Amari are 10 and 34 respectively.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Robert who has 20 blueberries such that he has 10 more blueberries than Janessa and 14 fewer blueberries than Amari.

Assume that the number of blue berries with Janessa and Amari are x and y respectively. We can write the following modelled equations as -

20 = x + 10

20 = y - 14

Solving, we get -

x = 10

y = 34

Therefore, the number of blue berries with Janessa and Amari are 10 and 34 respectively.

To solve more questions on Equation modelling, visit the link below-

https://brainly.com/question/5403673

#SPJ2

The following table list two investment plans, A and B. Given this information, determine which investment is an ordinary annuity
and the future value of the ordinary annuity after one year, given that both investments, A and B, compound interest monthly at
the rate of 3.5%. Round to the nearest cent.
Sept.
oct.
Nov
a.
b.
C.
d.
Jan Feb Mar Apr May Jun Jul Aug Sept.
350 350 350 350 350 350 350 350 350 350 350
350 350 350 350 350 350 350 350 350 350 350
Investment A is an ordinary annuity with $3.918.03 in the account after 1 year
Investment B is an ordinary annuity with $3,918.03 in the account after 1 year
Investment A is an ordinary annuity with $3,906.64 in the account after 1 year
Investment B is an ordinary annuity with $3,906.64 in the account after 1 year

Answers

Answer:

its D my  man go the answer sheet

Step-by-step explanation:

Answer:

d.

Investment B is an ordinary annuity with $3,906.64 in the account after 1 year

Step-by-step explanation:

Factor completely.
X^4-10x^2+24

Answers

Answer:

(x^2-6)(x+2)(x-2)

Step-by-step explanation:

x^4-10x^2+24

(x^2-6)(x+2)(x-2)

An expression can be written in rational form by

writing it as a fraction with a denominator of

Answers

Answer:

denominator of 1

Step-by-step explanation:

An expression can be written in rational number by writing 1 in the denominator then it will become a fraction and  a rational number

Answer:

A rational numbers can be defined as numbers that can be expressed as the quotient between two integers.

This means that a whole number can be expressed as a rational number by just adding 1 into its denominator

[tex]2 \implies \frac{2}{1}[/tex]

That way the whole number would be a rational number, becase 2 and 1 are integers.

Therefore, an expression can be written in rational form by  writing it as a fraction with a denominator of 1.

40 point question ....... pls urgent
the minute hand in a clock is 17cm long. find the area swept by it in 12 mins. the clock is a circle. no spamssssssssss pls

Answers

The area swept by the minute hand in 12 minutes is 181.58 cm²

Step-by-step explanation:

In the circle clock

The circumference of the circle is divided into 12 equal arcsThe central angle of each arc is 30°, because the measure of the circle is 360° and divided by 12 The central angle between each two consecutive hours is 30°There are 5 minutes between each two consecutive hours, then the central angle between each two consecutive minutes is 6° because 30° ÷ 5 = 6°When the minute hand is moved than the radius of the circle is the length of the minute handWhen the hour hand is moved than the radius of the circle is the length of the hour hand

∵ The minute hand is swept by 12 minutes

∵ The central angle between each two consecutive minutes = 6°

∴ The central angle when the minute hand swept 12 minutes =

   6 × 12 = 72°

∵ The area of a sector of a circle = [tex]\frac{x}{360}*\pi r^{2}[/tex] ,

   where r is the radius of the circle and x is the central angle of

   the sector

∵ The radius of the circle is the length of the minute hand

∵ The minute hand in a clock is 17 cm long

∴ r = 17 cm

∵ The measure of the central angle is 72°

∴ x = 72°

- Substitute these values in the rule of the area of a sector

∵ Area = [tex]\frac{72}{360}*\pi (17)^{2}[/tex]

∴ Area = 181.58 cm²

The area swept by the minute hand in 12 minutes is 181.58 cm²

Learn more:

You can learn more about the area of the sector in brainly.com/question/3456442

#LearnwithBrainly

A fraction with a zero in the numerator equals

Answers

Answer: With any number if the 0 is at the Numerator it will always be 0

Step-by-step explanation:

If a 0 is at the Denominator it will be Undifined

Which equation can be used to find the unknown length, a, in this triangle?
15 m
17 m
3+15² = 172
152 +172 - a
2² +15= 172
at 15² = 17²

Answers

Answer:

Here is the complete question.(attachment)

The correct choice is [tex]a^2+15^2=17^2[/tex]

Step-by-step explanation:

We will apply the Pythagoras formula to calculate the perpendicular length (a).

Pythagoras formula [tex]=(base)^2+(perpendicular)^2=(Hypotenuse)^2[/tex]

The right angle is formed between [tex]a[/tex] and [tex]15\ m[/tex] length.

So [tex]17\ m[/tex] is the hypotenuse opposite to right angle is the longest side and called the hypotenuse.

So

[tex](a)^2+(15)^2=17^2[/tex]

[tex]a=\sqrt{17^2-15^2}= 8\ m[/tex]

So the measure of side length [tex]a[/tex] is [tex]8\ m[/tex].

That can be calculated from the option A that is [tex](a)^2+(15)^2=17^2[/tex].

Note:Please don't look to the marked answers that was wrong in the attachment.

Answer:

Yes it is A

Step-by-step explanation:

2 to the 3rd power times 5 to the 2nd power

Answers

Answer:

2^3 * 5^2

2*2*2 * 5*5

8 * 25 = 200

Step-by-step explanation:

2^3 * 5^2

2*2*2 * 5*5

8 * 25 = 200

The seventh grade class supplied bags of snacks and beverages for the school dance They supplied19 more beverages than bags of snacks The dance was supplied with a total of 371 items.

Answers

Answer:

The number of number of bags of snacks = m  = 176

The number of beverages supplied = m + 19  = 176 +9 = 185

Step-by-step explanation:

Let us assume the number of bags of snacks = m

So, the number of beverages supplied = m + 19

Total number of items supplied  =  371

⇒ Number of (snacks + beverages) supplied=  371

⇒   m + (m +19)  = 371

or, 2 m = 371 - 19 =  352

or, m =  352 / 2 = 176  

⇒  m  = 176

Hence the number of number of bags of snacks = m  = 176

So, the number of beverages supplied = m + 19  = 176 +9 = 185

A triangle has a perimeter of 450.


Natalie creates a scale drawing of the triangle with the scale factor 1/15.


What is the perimeter of the scale drawing?
First one to answer will get Brainleist !!!

Answers

Answer: The perimeter of the scale drawing is [tex]30[/tex].

Step-by-step explanation:

You need to analize the information provided in the exercise.

You know that the perimeter of rectangle is [tex]450[/tex] and the scale factor Natalie used to create the scale drawing, was:

[tex]scale\ factor=\frac{1}{15}[/tex]

From this you can identify that, in order to find the perimeter of the scale drawing of the triangle (Which can be represented with [tex]P_2[/tex]), you must multiply the original perimeter ((Which can be represented with [tex]P_1[/tex]), by the scale factor Natalie used.

Therefore, you get that the perimeter is:

[tex]P_{2}=\frac{1}{15}P_1\\\\P_2(\frac{1}{15})(450)\\\\P_2=30[/tex]

The 300 students at a school voted on four possibilities for an end-of-the-year event. The results are shown in the graph below.How many more students wanted to go to an amusement park than to a baseball game?

Answers

Step-by-step explanation:

44-18=26

if 300=100 percent

? =26 percent

26×300=7800

7800÷100=78

the answer is 78 students

Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister,
He used twice as many 32-сent stamps as 20 cent stamps. Determine how many of each type of stamp
he used.

Answers

Answer:

Charlie used 4 20-cent stamps and 8 32-cent stamps.

Step-by-step explanation:

Let the number of 20 cents stamps be [tex]x[/tex]. Then, as per question, Chalie used twice as many 32-сent stamps as 20 cent stamps.

Therefore, number of 32-cent stamps is [tex]2x[/tex].

Now, total cost of the stamps is $ 3.36 = 336 cents

Cost of 1 20-cent stamp is 20 cents. So, cost of [tex]x[/tex] 20-cent stamps is [tex]20x[/tex]. Similarly, cost of [tex]2x[/tex] 32-cent stamps is [tex]32(2x)=64x[/tex]

Total cost = [tex]20x+64x=84x[/tex]

As per question,

[tex]84x=336\\x=\frac{336}{84}=4[/tex]

Number of 20-cent stamps = [tex]x = 4[/tex]

Number of 32-cent stamps = [tex]2x=2\times 4=8[/tex]

So, Charlie used 4 20-cent stamps and 8 32-cent stamps.

Answer:

No. of 32 cent stamps = 8

and that of 20 cent stamps = 4

Explanation:

Let no. of 32 cent stamps used be x and the number of 20 cent stamps used be y.

We are given that total postage on a package put by Charlie by using only 32 and 20 cent stamps is equal to $3.36.

So, since 100 cents make one dollar, $3.36 = 336 cents.

So,

32x + 20y = 336

Also we are given that Charlie used twice as many 32 cent stamps as 20 cent stamps which can be written as,

x = 2y

Substituting this equation in previous equation we get

32 [tex]\times[/tex]2y + 20y = 336

=> 64y + 20y = 336

=> 84y = 336

=>y = 4

Putting the value of y in x = 2y we get x = 2*4 = 8

So, no. of 32 cent stamps = 8 and that of 20 cent stamps = 4

Answer fast!!!!
Match the careers with the career clusters

Answers

Answer:education and training- speech Language pathologist And curriculum developer

Government and public administration- tax auditor and federal aid coordinator

Law, public safety corrections and security- attorney and paralegal

Step-by-step explanation:

Final answer:

The career clusters and some example careers within each cluster are Agriculture, Food, and Natural Resources (e.g. agricultural engineer, food scientist, forester), Business, Management, and Administration (e.g. accountant, human resources specialist, operations manager), and Health Science (e.g. medical doctor, nurse, medical laboratory technologist).

Explanation:

The career clusters and some example careers that fall under each cluster are as follows:

1. Agriculture, Food, and Natural ResourcesAgricultural engineerFood scientistForester2. Business, Management, and AdministrationAccountantHuman resources specialistOperations manager3. Health ScienceMedical doctorNurseMedical laboratory technologist

These are just a few examples, and there are many other careers within each career cluster.

Learn more about Career Clusters here:

https://brainly.com/question/38584022

#SPJ2

Other Questions
Which of the following might explain the lack of cloud formation? Choose one or more: A. The air package rises too fast for condensation to occur. B. It is too hot for adiabatic cooling to take place. C. The air package never reaches its dew point. D. There are too few aerosols present in the air package. | Sample Response: Linear relationships can becompared using their initial values, or y-intercepts, andtheir rates of change, or slopes. Initial values can tellyou which relationship started with a greater value.Comparing slopes can tell you which relationship isrising or falling faster.Which of the following did you include in yourresponse? Check all that apply.initial value (y-intercept) of each functionrate of change (slope) of each functioninitial value to compare starting pointsslope to compare rise or fall What volume of benzene (C6H6, d= 0.88 g/mL, molar mass = 78.11 g/mol) is required to produce 1.5 x 103 kJ of heat according to the following reaction?2 C6H6(l) + 15 O2(g) 12 CO2(g) + 6 H2O(g) Hrxn = -6278 kJ A donor pledged $500,000 to a not-for-profit hospital in 2016 to conduct medical research, conditional on the hospital raising $500,000 from other donors. The other donors met the condition in 2016. The donor transferred the funds to the hospital in 2017. In which year would the revenue be recognized? A) 2004 B) 2005. C) 2003. D) None of the above Help me please I need an explanation.! Beginning in 2011, the Dodd-Frank Wall Street Reform and Consumer Protection Act requires corporations with a market value over ________ to allow a nonbinding shareholder vote on executive pay. A. $25,000,000 B. $50,000,000 C. $75,000,000 D. $100,000 E. $750,000 When salt and water are mixed, they form a solution like in the ocean. When sand and water are mixed, they form a mixture where the sand does not dissolve. Which statement might summarize this observation? please draw accurately much appreciated If Peter Piper picked a peck of pickled peppers, Where's the peck of pickled peppers Peter Piper picked? Peter Piper picked a peck of pickled peppers. Which of the following sentences is punctuated correctly? Its' time to get in the car and go. Its's time to get in the car and go. It's time to get in the car and go. Its time to get in the car and go. There are between 24 and 40 students in the class the ratio for boys to girls is 4:7 how many students are in the class While painting the top of an antenna 275 m in height, a worker accidentally lets a 1.00 L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. An insulated thermos contains 106.0 cm3 of hot coffee at a temperature of 80.0 C. You put in 11.0 g of ice cube at its melting point to cool the coffee. What is the temperature of the coffee once the ice has melted and the system is in thermal equilibrium? Treat the coffee as though it were pure water. (Answer in C) Yolanda is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of 'English is Fun' she sells. Suppose that x and y are related by the equation y=1900+80x. a. What is the change in Yolanda's total pay for each copy of 'English is Fun' she sells? b. What is Yolanda's total pay if she doesn't sell any copies of 'English is Fun'? What height (displacement) will a ball reach if thrown upward with an initial velocity of 15 m/s How does the structure of the poem affect itsmeaning?Each stanza describes how thespeaker takes for granted love fromothers.The stanzas alternate betweendescribing love as uplifting and asdisappointingThe stanzas combine to conveythat relationships are complicated.Each stanza explains why thespeaker believes that romance isimportant in life. A hypothetical metal crystallizes with the face-centered cubic unit cell. The radius of the metal atom is 234 picometers and its molar mass is 195.08 g/mol. Calculate the density of the metal in g/cm3. Let D be the region bounded below by the plane zequals=0, above by the sphere x squared plus y squared plus z squared equals 900x2+y2+z2=900, and on the sides by the cylinder x squared plus y squared equals 100x2+y2=100. Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration. a. dz dr dtheta b. dr dz dtheta c. dtheta dz dr An increasingly intricate relationship exists between the gametophyte and sporophyte generations in vascular plants. As vascular plants live longer, they increase in size and complexity and the ____________ generation becomes dominant, while the ____________ generation becomes smaller and of shorter duration. The Antebellum South What was life like for slaves prior to the beginning of the Civil War? Use examples from Harriets narrative or information you gained from other sources to describe the institution of slavery. incidents of a slave girl.