Solve the differential equation using the method of undetermined coefficients

a) 4y"- 4y'-3y= cos2x

Answers

Answer 1
First: the homogeneous solutions: the characteristic equation is4r^2 - 4r - 3 = 0which has roots r = 3/2, -1/2 hence the homogeneous solution isy = c1.exp(-x/2) + c2.exp(3x/2)

next you need the general form for the guess for yp and that isyp = A1cos(2x) + A2sin(2x)
Now substitute that into the equation and solve for A1, A2.

Related Questions

Please help
F(x)=x^2 +1, g(x)=5x how to solve

Answers

Set them equal to each other and solve for x

x^2+1 = 5x
x^2-5x+1 = 0

using the quadratic formula from here yields 

x = 4.791287848 or x = 0.208712152

which are approximate solutions

Mel Company has a net income, before taxes, of $95,000. The treasurer of the company estimates 45 percent of net income will have to be paid for federal and state taxes. The tax for both federal and state is: ...?

Answers

Net income before taxes $95,000

Tax for federal and state: 45% * $ 95,000 = 42,750

 

The ratio of trumpet players to tuba players at a high school is 5:2 Which statement is true?

A.2/5 of the total tuba and trumpet players are tuba players.
B.The number of trumpet players is 2.5 times the number of tuba players.
C.There are 2 trumpet players for every 5 tuba players.
D.If there are a total of 100 trumpet and tuba players, 52 of them are tuba players.

Answers

The correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.

Let's analyze each statement and determine which one is true:

A. "2/5 of the total tuba and trumpet players are tuba players."

To find out if this statement is true, we need to determine what portion of the total number of players are tuba players. Since the ratio of trumpet players to tuba players is 5:2, for every 5 + 2 = 7 players, 2 are tuba players. So, the proportion of tuba players is 2/7, not 2/5. Therefore, Statement A is false.

B. "The number of trumpet players is 2.5 times the number of tuba players."

According to the given ratio, for every 5 trumpet players, there are 2 tuba players. Thus, the number of trumpet players is indeed 2.5 times the number of tuba players. Therefore, Statement B is true.

C. "There are 2 trumpet players for every 5 tuba players."

This statement matches the given ratio, so it is true. However, it doesn't provide any additional information beyond what's already given in the initial problem.

D. "If there are a total of 100 trumpet and tuba players, 52 of them are tuba players."

To verify this statement, we can calculate the number of tuba players using the given ratio. Since the total ratio parts is 5 (trumpet) + 2 (tuba) = 7, and the total number of players is 100, we can find the number of tuba players as (2/7) * 100 = 28. Thus, Statement D is false.

Therefore, the correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.

Im totally lost! A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon 14 of a contemporary living sample. Estimate the age of the sample ...?

Answers

Final answer:

The sample from the refuse deposit near the Strait of Magellan, with 60% carbon-14 remaining compared to a contemporary living sample, is estimated to be approximately 7777 years old, based on the known half-life of carbon-14 being 5730 years.

Explanation:

The age of a sample can be estimated using radiocarbon dating, which measures the decay of carbon-14 (14 C). Since the half-life of 14 C is known to be approximately 5730 years, we can use this information to estimate the age of the sample. Radiocarbon dating works on the principle that living organisms continually replenish carbon while alive, maintaining a constant level of 14 C relative to 12 C. When an organism dies, it no longer absorbs carbon, and the 14 C begins to decay at a known rate.

In the case of the refuse deposit near the Strait of Magellan, the sample had 60% of the carbon-14 of a contemporary living sample. To determine the age, we use the half-life formula, which is Time = Half-life / log2 (Starting amount / Remaining amount). Here, starting amount is 100% (contemporary living sample), the remaining amount is 60%, and the half-life is 5730 years.

So the calculation will be: Age of sample = 5730 / log2 (100/60). Calculating this, we get:

Age of sample = 5730 / log2 (1.6667)

Age of sample = 5730 / 0.737

Age of sample ≈ 7777 years

Thus, the sample from the refuse deposit near the Strait of Magellan is estimated to be approximately 7777 years old.

What is the value of the expression when a = 4, b = 3 ,and c = 10? 3a4b−c

Answers

Answer:

9yb

Step-by-step explanation:

The two interior angles that are not adjacent to an exterior angle are called ________.
remote exterior angles
remote interior angles
alternate exterior angles
corresponding angles

Answers

If a triangle has an exterior angle, the remote interior angles are the two angles not adjacent to the exterior angle

So, option B is your answer!

Hope this helps!

Answer: Second option is correct.

Step-by-step explanation:

The two interior angles that are not adjacent to an exterior angle are called "Remote interior angles"

As remote interior angles are those interior angles that are inside the are inside the triangle but opposite to the exterior angles.

Hence, Second option is correct.

What is 36/60 as a decimal?

Answers

It would be: 36/60 = 6/10 = 0.6

So, in decimal form, it would be 0.6

Hope it helped.

The first step in solving 7/8 = 3x - 5/11 is to subtract 5/11 from both sides of the equation.

True
False

Answers

False because -5/11 should be add on both sides

Answer:

false

Step-by-step explanation:

<3

If Martha earns $6.50 per hour for babysitting, how much will she earn in: 1.5 hours? 2.5 hours? 3.5 hours?

Answers

in 1.5 hours she will get 9.75 
in 2.5 hours he will get 16.25
and in 3.5 hours she will get 22.75 

Martha earns $6.50 per hour, so for 1.5 hours, she will earn $9.75; for 2.5 hours, she will earn $16.25; and for 3.5 hours, she will earn $22.75. We simply multiply her hourly wage by the number of hours to find the total earnings for each duration.

If Martha earns $6.50 per hour for babysitting, we can find out how much she will earn for different numbers of hours by multiplying her hourly rate by the number of hours worked.

For 1.5 hours: $6.50 * 1.5 = $9.75For 2.5 hours: $6.50 * 2.5 = $16.25For 3.5 hours: $6.50 * 3.5 = $22.75

As a result:

Martha will earn $9.75 for 1.5 hours of babysitting.Martha will earn $16.25 for 2.5 hours of babysitting.Martha will earn $22.75 for 3.5 hours of babysitting.

The hu family goes out for lunch and the price of the meal is $45 the sales tax on the meal is 6% and the family also leaves a 20% tip on the pre-tax amount what is the total cost of the meal ?

Answers

$56.70 Is your answer

Are 37 and 65 71 82 are prime or composite number

Answers

I hope this helps you




37=1.37 prime


71=1.71 prime


65=5.13 composite


82=2.41 composite

true or false.
The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. ...?

Answers

Answer:  The given statement is FALSE.

Step-by-step explanation:  We are given to check whether he following statement is true or false :

"The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. "

Let us consider the right-angled triangle ABC as shown in the attached figure below.

With respect to acute angle C, we can see that

perpendicular, p = AB

base, b = BC

and

hypotenuse, h = AC.

We know that

sine of an angle in a right-angled triangle is equal to the ratio of the perpendicular to the base.

So, we must have

[tex]\sin \angle C=\dfrac{p}{h}\\\\\\\Rightarrow \sin \angle C=\dfrac{AB}{AC}.[/tex]

Since AB is the opposite side to angle C, not adjacent, therefore

sine of any angle in a right-angled triangle is the ratio of the length of the OPPOSITE SIDE to length of the hypotenuse.

Thus, the given statement is FALSE.

Final answer:

The statement is false; sine is the ratio of the opposite side to the hypotenuse, not the adjacent side to the hypotenuse.

Explanation:

The statement is false. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse, not the adjacent side to the hypotenuse. Therefore, the sine of angle A would be expressed as sin(A) = opposite/hypotenuse. The ratio of the adjacent side to the hypotenuse, on the other hand, defines the cosine of the angle, which is cos(A) = adjacent/hypotenuse.

You need to have at least $100 in your checking account to avoid a low balance fee. You have $247 in your account, and you make withdrawals of $20 per week. What are the possible numbers of weeks that you can avoid paying the fee? Solve this problem using two different methods. PLEASE HELP

Answers

7 WEEKS is how long you can last.

First off, you need at least $100 in your account to avoid the fee and you currently have $247. With that being said, you're taking out $20 every week.

The first thing you can do would be to start at $147 (since that's $100 less than what you can use) and divide that by 20 (since that's what you're taking out every week) 147 / 20 = 7.35. That's 7 weeks because you have to round down to the nearest whole number.

Second What you can do to find how many weeks you can take this out by starting at $100 and adding $20 for every week. So 120, 140, 160, 180, 200, 220, 240. This also gives you 7.

You can take $20 out of your account for 7 WEEKS until you have to pay the low-balance fee.

May I have brainliest please? :)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division

The possible number of weeks to withdraw avoiding the low balance fee is 7 weeks.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total amount in account = $247

Amount withdrawals per week = $20

Amount needed in account to avoid low balance fee = $100

The possible number of weeks to withdraw avoiding the low balance fee:

= (247 - 100) ÷ 20

= 147÷ 20

= 7.35

This means 7 weeks.

Thus,

The possible number of weeks to withdraw avoiding the low balance fee is 7 weeks.

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A basketball player scored 19 times during one game. She scored a total of 25 points, two for each two-point shot and one for each free throw. How many two point shots did she make? How many free throws?

Answers

6 two-pointers and 13 free throws

Answer:

Step-by-step explanation:

It said free points

Simplify (x − 4)(x2 + 3x − 1).
A.x^3-x^2+11x+4
B.x^3-x^2-13x+4
C.x^3+7x^2+11x+4
D.x^3+7x^2-13x+4

Answers

 (x − 4)(x2 + 3x − 1)
=x^3  + 3x^2 - x -4x^2 - 12x +4
=x^3  -x^2 - 13x +4

answer is B.x^3-x^2-13x+4

Final answer:

To simplify (x - 4)(x^2 + 3x - 1), use the FOIL method to distribute each term and combine like terms, resulting in x^3 - x^2 - 12x + 4 (option B).

Explanation:

To simplify the expression (x − 4)(x2 + 3x − 1), we need to use the distributive property, also known as the FOIL method, which stands for First, Outside, Inside, Last. We will multiply each term in the first binomial by each term in the second binomial.

Multiply the first terms: x * x2 = x3.Multiply the outside terms: x * 3x = 3x2.Multiply the inside terms: (-4) * x2 = -4x2.Multiply the last terms: (-4) * (3x) = -12x.Multiply the last terms: (-4) * (-1) = 4.

Combine like terms:

x3 + 3x2 - 4x2 - 12x + 4

Simplify the expression by combining 3x2 and -4x2:

x3 - x2 - 12x + 4

Therefore, the simplified form of the expression is x3 - x2 - 12x + 4, which corresponds to option B.

Solve for y. y 1.05 = 7.26 y = 8.31 y = -8.31 y = 6.21 y = -6.21

Answers

You haven't written the question properly because we have nothing to base y on.

Move all terms not containing  y  to the right side of the equation. You should get y=6.21

lizzy is tiling the kitchen floor for the first time. she had a tough time at first and placed only 5 tiles the first day. she started to go faster, and by the end of day 4 she had places 35 tiles. she worked at a steady rate after the first day. use an equation in point slope form to determine how many days lizzy took place all of 100 tiles needed to finish the floor

Answers

Answer:

10.5 days

Step-by-step explanation:

Point slope form

y-5=10(x-1)

Substitute for y

100-5=10(x-1)

Distribute the 10

100-5=10x-10

Combine like terms

95=10x-10

Add ten to both sides

105=10x

Divide by 10

X = 10.5

Write 1 ft. 7 in. in inches.

Answers

1 ft. = 12 in.

So that'd be 19 inches.
Since there are 12 inches in one foot, we can rewrite 1 ft. 7 inches as 12 inches plus 7 inches.

7 + 12 = 19, so the answer is 19 inches

if sin theta =1/4, theta in quadrant II, find the exact value of cos[theta +pi/6]

Answers

Using cos addition formula:
use x for theta
cos(x+π/6)=cosx*cos(π/6)-sinx*sin(π/6)
sinx=1/4
cosx=√15/4
cos(π/6)=√3/2
sin(π/6)=1/2
cos(x+π/6)=(√15/4*√3/2)-(1/4*1/2)
cos(x+π/6)=(√45/8)-(1/8 )
cos(x+π/6)=(√45-1)/8)

The exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II is (-√(45) - 1)/8, found by using the Pythagorean identity and the angle sum identity.

To find the exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II, we can use trigonometric identities and properties of angles. First, we use the Pythagorean identity to find cos θ. Since θ is in the second quadrant, cos θ is negative and solving for cos θ gives cos θ = -√(1 - sin² θ) = -√(1 - (1/4)²) = -√(15)/4.

Next, we apply the angle sum identity for cosine, which is cos(α + β) = cos α cos β - sin α sin β. Using this identity, we find:

cos(θ + π/6) = cos θ cos(π/6) - sin θ sin(π/6) = (-√(15)/4)(√(3)/2) - (1/4)(1/2) = -√(45)/8 - 1/8 = (-√(45) - 1) / 8.

3. All but one of the following statements contains a blunder. Which statement is correct? (a) There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight. (b) The correlation between number of seeds planted and amount of grass grown was found to be r = 0.23 acres. (c) The correlation between the gas mileage of a car and its weight is r = 0.71 MPG. (d) We found a high correlation (r = 1.09) between the height and age of children. (e) We found a correlation of r = -.63 between gender and political party preference.

Answers

I'm pretty sure it's b.. when in doubt choose b
Final answer:

The correct statement is (a), 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' Correlation values range from -1 to +1, and units or nominal variables can't be used.

Explanation:

The correct statement among the given options is (a) 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' In a correlation, the value ranges from -1 to +1 where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The other statements, (b), (c), (d) and (e), are blunders because the correlation value (r) in (d) exceeds +1 which is impossible, the units in (b) and (c) are incorrectly applied as correlation doesn't have physical units, and in (e), gender is a nominal variable for which correlation cannot be calculated.

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Which statement describes the graph of f(x) = 4x2 + 20x + 25?

The graph does not intersect the x-axis.
The graph touches the x-axis at (–2.5, 0).
The graph intersects the x-axis at (–0.4, 0) and (0.4, 0).
The graph intersects the x-axis at (2, 0) and (5, 0).

Answers

the answer is 

y = f(x) = 4x2 + 20x + 25= (2x+5)²
(2x+5)²=0 implies (2x+5)=0 implies 2x=-5, x = –2.5

finally the answer is 
The graph touches the x-axis at (–2.5, 0).

The graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0)

Graph of a quadratic function

The given function is f(x) = 4x² + 20x + 25

The table of values for the function from -1 to -4 is

x          -1     -2   -3    -4

f(x)       9      1   1      9

The graph of the function is attached below

From the graph, we can observe that the graph touches the x-axis at the point (-2.5, 0)

Hence, the graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0).

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FIND MISSING ANGLES

D1=
D2=
D3=
D4=
D5=
D6=

Answers

1= 45
*there is no 2?*
3= 110
4= 45
5= 110

You deposit 6000 in an account that pays 5.25 interest compounded semiannually. after 10 years, the interest rate is increased to 5.4% compounded quarterly. what will be the value of the account after 18 years. (round to the nearest dollar)

Answers

Final answer:

The account value after 18 years with an initial deposit of $6,000 and a change in interest rate and compounding periods is approximately $15,526 when rounded to the nearest dollar.

Explanation:

To calculate the value of the account after 18 years with a change in the interest rate and compounding periods, we need to use the compound interest formula separately for the two different periods and rates.

First, we compound the original $6,000 at 5.25% semiannually for 10 years:

A = P(1 + r/n)(nt)

A = $6,000(1 + 0.0525/2)(2*10) = $6,000(1.02625)20 = $9,984.21 (rounded)

Now, we take the amount after 10 years and compound it at 5.4% quarterly for the remaining 8 years:

A = P(1 + r/n)(nt)

A = $9,984.21(1 + 0.054/4)(4*8) = $9,984.21(1.0135)32 = $15,526.14 (rounded)

So, after 18 years, the value of the account would be $15,526 (rounded to the nearest dollar).

Proportion is ________________

Answers

Final answer:

Proportion is a mathematical concept that describes the relationship between two or more quantities. It is often represented using ratios and can be used to solve for unknown values, scale measurements, and interpret data.

Explanation:

Proportion is a mathematical concept that describes the relationship between two or more numbers or quantities. It is a way of expressing that one quantity is equal to another quantity, or that one quantity is a fraction or multiple of another quantity. Proportions can be represented using ratios, which compare the relative sizes of different quantities.

For example, if we have two ratios, such as 1:2 and 3:6, we can determine if they are proportional by cross-multiplying and checking if the products are equal. In this case, 1 × 6 = 2 × 3, so the ratios are proportional.

Proportions are used in many different areas of mathematics, such as solving for unknown values, scaling up or down, and interpreting data. They are also used in real-world applications, such as finding the missing side length of a similar triangle or calculating the unit price of a product.

What is 528−−√+63−−√528+63 in simplest radical form?

Answers

Answer: [tex]13\sqrt{7}[/tex]

Step-by-step explanation:

In the simple radical form there are no square root is remain to find.

Since, the given expression,

[tex]5\sqrt{28} + \sqrt{63}[/tex]

[tex]5\sqrt{4\times 7} + \sqrt{9\times 7}[/tex]

[tex]5\sqrt{4} \times \sqrt{7} + \sqrt{9}\times \sqrt{7}[/tex]

[tex]5\times 2 \times \sqrt{7} + 3\times \sqrt{7}[/tex]

[tex]10 \sqrt{7} + 3\sqrt{7}[/tex]

[tex](10 + 3)\sqrt{7}[/tex]

[tex]13\sqrt{7}[/tex]

Since, we do not need to find further square root of 7.

Thus, the required radical form of [tex]5\sqrt{28} + \sqrt{63}[/tex] is [tex]13\sqrt{7}[/tex].

Answer:

[tex]13\sqrt{7}[/tex]

Step-by-step explanation:

[tex]5\sqrt{28} +\sqrt{63}[/tex]

To simplify the given expression we simplify each radical

[tex]5\sqrt{28} = 5\sqrt{4*7} = 5*2\sqrt{7} =10\sqrt{7}[/tex]

[tex]\sqrt{63} = \sqrt{9*7} =3\sqrt{7}[/tex]

[tex]5\sqrt{28} +\sqrt{63}[/tex]

[tex]10\sqrt{7}+3\sqrt{7}[/tex]

[tex]13\sqrt{7}[/tex]

(4x+20)+(x-10)=180 how do you solve this?

Answers

(4x + 20) + (x - 10) = 180
4x + 20 + x - 10 = 180
5x + 20 - 10 = 180
5x + 10 = 180
5x = 170
x = 34
4x+20+x-10=180
5x+10=180
5x=180-10
5x=170
x=34

ask me if you have a question :D

2 1/2 divided by 4. can you please answer i need help

Answers

The answer would be 5/8, 62.5% in percentage mode, and 0.625 in decimal.

Convert 2 1/2 to a
improper fraction

Simplify 2 * 2 to 4

Simplify 4 + 1 to 5

Simplify

Simplify 2 * 4 to 8

Now fuse it together and it would be 5/8.

Answer:

5/8

Step-by-step explanation:


Jenny's Bakery sells carrot muffins for $2.00 each. The electricity to run the oven is $120.00 per day and the cost of making one carrot muffin is $1.40. How many muffins need to be sold each day for the bakery to break even?

Answers

Break even is a condition where the total production cost is same as the profit produced. In this question, the carrot muffin cost is $1.4 and sold at $2. Then the profit for every muffin should be: $2- $1.4= $0.6/muffin

The electricity cost is $120/day. Then to cover this cost, the muffin need to sold would be:

cost= muffin profit * muffin sold
$120= $0.6/muffin * muffin sold
muffin sold= $120 / ($0.6 / muffin)= 200 muffin

Answer:

D. 200 muffins

Step-by-step explanation:

Break even is a condition where the total production cost is same as the profit produced. In this question, the carrot muffin cost is $1.4 and sold at $2. Then the profit for every muffin should be: $2- $1.4= $0.6/muffin

The electricity cost is $120/day. Then to cover this cost, the muffin need to sold would be:

cost= muffin profit * muffin sold

$120= $0.6/muffin * muffin sold

muffin sold= $120 / ($0.6 / muffin)= 200 muffin

How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8 percent compounded annually? $117,817.20 or $454,144.00 or $112,817.20 or $549,144.

Answers

The best answer will be the $117,817.20. Howard Steele need to invest $117,817.20

What can you say about the end behavior of the function f(x)= 5x-3x+332

Answers

As x → -∞, y → -∞
as x → ∞, y → ∞

Answer:

B.

The leading coefficient is positive so the left end goes down.

done

C.

f(x) is odd so both ends go in opposite directions.

Step-by-step explanation:

APEX

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What is the solution to the system of linear equations A. (-3,0)B. (-3,3)C. (0,2)D. (3,1) A radio commercial for a loan company states: You only pay $0.29 a day foreach $500 borrowed. If you borrow $1,500 for 120 days, what amount will yourepay, and what annual interest rate is the company actually charging? Cesar Chavezs background included which of the following?His parents were business owners.He was once a college student.He was once a community organizer.His family owned several large farms. Which of the following statements is true regarding the role of women during world war i? a. they contributed little to the war effort. b. their role differed very little from their role during peace time. c. they kept their nations economies going during the war. d. they focused their efforts on ending the war.? Write an equation that models the sequence 400, 200, 100, 50, ... A tetherball is tied to the end of a string of negligible mass. The ball is struck so that it moves in uniform circular motion in a horizontal plane, and the string makes an angle of 26 with the vertical pole. The mass of the ball is 1.3 kg. What is the ball's speed Which text in these excerpts from Book 12 of Homer's Odyssey portray the theme of leadership?A) "'Oh stay, O pride of Greece! Ulysses, stay!Oh cease thy course, and listen to our lay!Blest is the man ordain'd our voice to hear,The song instructs the soul, and charms the ear.B) "Meantime, forgetful of the voice divine,All dreadful bright my limbs in armour shine;High on the deck I take my dangerous stand,Two glittering javelins lighten in my hand;Prepared to whirl the whizzing spear I stay,Till the fell fiend arise to seize her prey.C) "Struck with despair, with trembling hearts we view'dThe yawning dungeon, and the tumbling flood;When lo! fierce Scylla stoop'd to seize her prey,D) I turn, and view them quivering in the skies;They call, and aid with outstretch'd arms implore;In vain they call! those arms are stretch'd no more.E) "'O friends! O ever exorcised in care!Hear Heaven's commands, and reverence what ye hear! Paco buys a carton of eggs. the carton has 2 rows of eggs. there are 6 eggs in each carton. how many eggs are in the carton Of the following who emerged as a strong leader and organizer of colonial protests and publicA crispus attuckusB john Adams C Samuel AdamsD George Greenville The Sahara desert is able to support large populations of grazing herbivores. T F Choose the answer that is a TRUE statement. A dominating nation with extensive territories and a powerful ruler such as Rome's is known as an empire. The republic was also known as a socialist government. The Romans' first code of law was established around 200 B.C. The republic lasted over 1000 years. A relation is plotted as a linear function on the coordinate plane starting at point A (0,3)and ending at point B (2,7).What is the rate of change for the linear function and what is its initial value?Select the choices to correctly complete the statements.The rate of change is ? Use one of THESE CHOICES ON THIS SIDE to replace the question mark. A) 0 B) 2 C) 4, D) 7And the initial value is ? Use these choices HERE NOT ABOVE, but here to replace the question mark. A) 0B 2C) 3D) 7 A highway map of Ohio has a coordinate grid superimposed on top of the state. Springfield is at point (1, 4) and Columbus is at point (7, 1). The Springfield youth soccer team is going to Columbus to see a professional soccer match. The map shows a highway rest area halfway between the cities. What are the coordinates of the rest area? What is the distance between Springfield and Columbus? (One unit = 5.38 miles) What kingdom includes organisms credited for breaking down dead plants and animals into rich soil? what is the dependent variable in the experiment In spite of its wealth of natural resources such as coffee, emeralds, and coal, Colombia has had a turbulent history. What is one of the causes for the turmoil?A.An inability to hold democratic electionsB.Lack of education and public health servicesC.Powerful drug cartels and guerilla groupsD.The separation of people caused by the Andes Mountains ...? What did booker t. washington do?? SOLVE. integration of (1-v) /(1+v^2) What is 1/6+1/12=what does this equal? What caused extreme gas shortages in America during 1973?runaway inflationoveruse of autosOPEC oil embargorundown refineries