1 point
Calculate the rate of change for each function over the interval [0, 3], then tell which function is
growing faster.
f(x) = 2x + 3
g(x) = 2² +3
Of(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So f(x) is growing faster
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So f(x) is growing faster

Answers

Answer 1

If f(x) = 2x + 3 then Δy/Δx = 2 and g(x) = 2² +3 then Δy/Δx = 2.33.

The correct answer is option A.

f(x) has a rate of change of 2

g(x) has a rate of change of 2.33

So g(x) is growing faster

How to estimate the rate of change of a function over the interval  [0, 3]?

Let f(x) = 2x + 3 and g(x) = 2² +3

Let, ∆y /∆x denotes the ratio of y change and x change when x change exists relatively large.

If f(x) = 2x + 3

Δy/Δx = [f(3) - f(0)]/3 - 0

f(3) [tex]= 2*3+3 = 9[/tex]

f(0) [tex]= 2*0+3 = 3[/tex]

[f(3) - f(0)]/3 - 0 = (9 - 3)/3

= 6/3 = 2

g(x) = 2² +3

Δy/Δx = [g(3) - g(0)]/3 - 0

[tex]$= (2^3 +3)-(2^0 +3)/3[/tex]

[tex](2^3 +3)-(2^0 +3) = 7[/tex]

[tex](2^3 +3)-(2^0 +3)/3[/tex] = 7/3 = 2.33

Therefore, the correct answer is option A.

f(x) has a rate of change of 2

g(x) has a rate of change of 2.33

So g(x) is growing faster

To learn more about functions refer to:

https://brainly.com/question/11388036

#SPJ9


Related Questions

bryan is starting a tutoring company that charges 10 as an initial fee and 7.50 dollars per hour of tutoring. Laura is starting her own company and she wants to charge less for the initial fee, but more per hour. which equation could represent her charges? please explain why you chose this answer. i will mark you brainliest

Answers

The function that could represent Laura's charges is given by -

y = 5x + 12

What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that bryan is starting a tutoring company that charges $10 as an initial fee and 7.50 dollars per hour of tutoring. Laura is starting her own company and she wants to charge less for the initial fee, but more per hour.

The function representing the amount charged by Brayan is -

{B} = 10 + 7.5x

Amount charged by Bryan per hour is -

$7.5

Amount charged by Bryan as an initial fee -

$10

The function which charge less for the initial fee, but more per hour is -

y = 5x + 12

Therefore, the function that could represent the amount charged by Laura is given by -

y = 5x + 12

To solve more questions on expression evaluation, visit the link below -

brainly.com/question/1041084

#SPJ1

A slushy recipe calls for 4 cups of fruit juice, but you only have 3 1/2 cups. By what percentage do you need to cut back all the ingredients to make the recipe turn out correctly?

Can u guys pls help me I'm not good at math (TT~TT)

Answers

Answer:0.125% on all ingredients or go to the store and buy more

Step-by-step explanation:

what persent is 3 1/2 out of 4 is 87.5%

87.5% - 100% = 0.125%

The table represents a function. X y 0 6 2 8 4 10 6 12 complete the statement by selecting from the drop-down menu. The rate of change in the function y = x + 4 is choose. The rate of change of the function represented in the table.

Answers

The table represents a function. X y 0 6 2 8 4 10 6 12 complete the statement by selecting from the drop-down menu. The rate of change in the function y = x + 4 is  equal to the rate of change of the function represented in the table.

Consider the function shown in the table.

The table's coordinates are as follows:

(0,6) (2,8) (4,10) and (6,12) (6,12)

Take into account the first two coordinates (0, 6) and (2,8)

x₁=0, y₁=6, x₂=2, y₂=8

Linear equation is provided by (y-y₁) =m(x-x₁)

Where 'm' is the slope (rate of change), the following formula is used:

m = y₂ - y₁

      x₂ - x₁

So,

m = 8 - 6 = 1

      2 - 0

So, the line's equation is:

(y-6)= 1 (x-0) (x-0)

y-6=x

y=x+6

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

Now,

We will calculate the slope for the function y=x+4

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

The rate of change in the function y=x+4 is therefore equal to the rate of change of the function shown in the table.

Learn more about rate of change at https://brainly.com/question/11740959

#SPJ4

1
6
m25=
5
3
If 41 42 = 23, 24 = 25, and m 24 = m23 +10°, What is m/45?
D
4

PLEASE HELP MEEE!! ASAPP!!!

Answers

The value of m∠5 = m∠4 + 10° or  m∠3 + 20°.

How to calculate exterior angle of polygon?

The exterior angle of a polygon is the angle formed by one side of the polygon and the extension of the adjacent side. The measure of each exterior angle of a polygon is equal to the sum of the interior angles of the polygon divided by the number of sides of the polygon.

To calculate the exterior angle of a polygon, use the following formula:Exterior angle = (Sum of interior angles of the polygon) / (Number of sides of the polygon)For example, if a polygon has 6 sides, the sum of its interior angles is equal to (6 − 2) × 180° = 720°. Therefore, the exterior angle of the polygon is 720° / 6 = 120°.Knowing how to calculate the exterior angle of a polygon is helpful in solving problems related to geometry and trigonometry. It is also important in understanding the properties of polygons and their characteristics.

Solution:

The given value of m∠4 = m∠3+ 10°

The value of m∠5 is increase in 10° of m∠4

The answer is m∠5 = m∠4 + 10°.

To learn more about exterior angle of polygon refer to:

https://brainly.com/question/29166902

#SPJ1

How many roots exist for polynomial function?

Answers

The Fundamental Theorem of Algebra asserts that this 2 n d degree polynomial must have precisely two roots.

What is algebra?

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.

Here,

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots.

To know more about algebra,

brainly.com/question/24875240

#SPJ4


If a mountain rises 25.0 centimeters (cm) in 125 years:
The rate of uplift is
cm/yr

Answers

Answer: 0.2 cm/yr

Step-by-step explanation:

simply divide centimeters by years

25.0 cm ÷ 125 yr

0.2 cm/yr ... answer



The rate of uplift is 0.2 cm/yr

hope that helps...

If m = −7/2 is slope, y - intercept is 12 and the point ( x, 5 ) lies on the line. What is the value of x ?

Answers

5=-7/2x+12

-7=-7/2x

x=2

Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above the plane and a scale factor between 0 and 1.
Match the dilation with the scale factor used.
Match the image with the letter it belongs with.

image 1

Image 2

Image 3

A) 1/2

B) 3/4

C) 1/4

Answers

In this quadrilateral, Dilation A will have largest scale factor.  Dilation B is smallest and will have smallest scale factor. Now for the given scale factors: 3/4 > 1/2 > 1/4

what is quadrilateral?

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

in this quadrilateral

Dilation A will have largest scale factor.

Dilation B is smallest and will have smallest scale factor.

Now for the given scale factors:

3/4 > 1/2 > 1/4

To know more about quadrilateral visit:

https://brainly.com/question/29934291

#SPJ1

A pizza parlor has a choice of 10 toppings for its pizzas. From these 10 toppings, how many
different 8-topping pizzas are possible?
I

Answers

On solving the provided question, we can say that by permutation, 90  different 8-topping pizzas are possible

what is permutation?

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.

here,

by permutation

[tex]^{10}P_8[/tex] = 10!/2/1 = 10 X 9 / 1 = 90 ways

90  different 8-topping pizzas are possible

To know more about permutation visit:

https://brainly.com/question/1216161

#SPJ1

Find the quotient of 2 7 and 3 5 give your answer as a fraction in its simplest form.

Answers

the quotient is 10/21

Jenny ha 50 quare tile he arrange the tile into a rectangular array of four row how many tile will be left over

Answers

Two tiles will be left over. Jenny will have two square tiles left over after arranging her tiles into a rectangular array of four rows.

50 quare tiles divided by 4 rows = 12.5 quare tiles

12.5 quare tiles per row x 4 rows = 50 quare tiles

50 quare tiles used - 50 quare tiles = 0 quare tiles

Remaining tiles = 0 quare tiles

50 quare tiles - 0 quare tiles = 50 quare tiles

Left over tiles = 2 quare tiles

Jenny has 50 square tiles which she arranges into a rectangular array of four rows. To work out how many square tiles are left over, first divide 50 by 4. This gives us 12.5 tiles per row, however this is not possible so we need to round this number down to 12. Multiplying 12 by 4 gives us 48 tiles used in the rectangular array. Subtracting the 48 tiles used from the 50 tiles that Jenny had originally gives us a result of 2 square tiles left over. In conclusion, Jenny will have two square tiles left over after arranging her tiles into a rectangular array of four rows.

Learn more about rectangle here

https://brainly.com/question/29068457

#SPJ4

Twelve students were asked how long they spent doing homework last week. The scatter plot shows the results of the survey.



Is there an outlier in the data set? If there is an outlier, identify it and explain why it is an outlier.

Answers

The scatter plot shows the results of the survey and yes, there is an outlier in the data set which is the lowest time value of grade 11 and it is an outlier because it is an extremely low data point relative to the nearest data point.

What is an Outlier?

This is referred to as an extremely high or extremely low data point relative to the nearest data point and the rest of the neighboring co-existing values in a data graph.

The outlier is at the lowest time value if grade 11 and it falls under such category because it is an extremely low data point relative to the nearest data point in the given graph.

Read more about Outlier here https://brainly.com/question/29546240

#SPJ1

Doe function g appear to be invertible? Ue complete entece to xplain you reaoning

Answers

Yes, the given function y = g(x) in the attached graph is invertible as each input value of x has unique output y.

As given in the question,

Graph of the function y = g(x) is attached.

Invertible function are defined as when each input value of the function has unique output or for each input there is only one and only one output.

In the given graph of the function y = g(x)

Each input value of x there is only one and only one output.

Given graph y = g(x) is representing the straight line.

Therefore, the given graph of the function y = g(x) represent it is an invertible function as each input as one and only one output.

The above question is incomplete, the complete question is :

Does function g appear to be invertible? Use complete sentence to explain you reasoning?

Graph of the function g(x) is attached.

Learn more about function here

brainly.com/question/12431044

#SPJ4

Given: angle LMN is congruent to angle LNM; angle MPN is congruent to angle NOM

Prove: MP is congruent to NO

Answers

The prove that segment MP is congruent to segment NO (MP ≅ NO) can be presented as follows;

Statement [tex]{}[/tex]                             Reasons

1. ∠LMN ≅ ∠LNM [tex]{}[/tex]                 1. Given

∠MPN ≅ ∠NOM

2. MN ≅ MN  [tex]{}[/tex]                        2. Reflexive property

3. ΔMNP ≅ ΔNMO [tex]{}[/tex]               3. SAA congruency postulate

4. MP ≅ NO  [tex]{}[/tex]                         4. CPCTC

What are congruent segments?

Two segments are congruent if they have the same length

         

The known relationships between the measures of the angles are;

∠LMN ≅ ∠LNM

∠MPN ≅ ∠NOM

Required to prove that MP ≅ NO

The two column method can be used to prove the congruency of the sides MP and NO as follows;

Statement     [tex]{}[/tex]                                 Reasons

1. ∠LMN ≅ ∠LNM         [tex]{}[/tex]                1. Given            

∠MPN ≅ ∠NOM

2. MN ≅ MN     [tex]{}[/tex]                            2. Reflexive property of congruency

3. ΔMNP ≅ ΔNMO     [tex]{}[/tex]                  3. SAA congruency rule

4. MP ≅ NO     [tex]{}[/tex]                             4. CPCTC

Details of the above postulates and rules used to prove the congruency of the segments MP and NO are as follows;

SAA congruency postulate

The SAA (SAA is an acronym for Side-Angle-Angle) congruency postulate states that if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent. It indicates that if two triangles are congruent, then, their corresponding sides are also congruent.

Learn more on triangle congruency rules here: https://brainly.com/question/14818583

#SPJ1

Care dintre urmatoarele numar este prim 91,29,85,39

Answers

Answer:

29,

Step-by-step explanation:

What is quadratic inequalities Grade 9?

Answers

A quadratic inequality is an inequality that can be written in the form of "ax² + bx + c < or > 0" where a, b and c are real numbers and x is a variable.

The solutions to a quadratic inequality are the values of x that make the inequality true. To solve a quadratic inequality, we first set the expression equal to zero and then find the roots (also known as the zeroes or solutions) of the equation. We then use these roots to divide the number line into three regions: the region where the expression is less than zero, the region where the expression is greater than zero, and the region where the expression is equal to zero.

Learn more about quadratic inequality here: https://brainly.com/question/17810527

#SPJ4

What is the actual length of the bus?

Answers

Answer:

35feet

Step-by-step explanation:

Since it's a scale, we can take the backsides of both buses. They read 2in and 10ft

12 inches are in one foot, so 120 inches are in 10ft

Next we'll divide 120/2 and we get 60.

That's means we can multiply 7 * 60, getting 420inches

To get it back to feet, we divide by 12

420/12 = 35 feet

Hikers are traveling at 3.5 miles per hour. They leave camp and hike N72°W for 2 hours. They change course to S23°W for 4 hours. How many miles is the trip directly back to camp? What bearing should the hikers take to head back to camp?

Answers

Answer: To solve this problem, we can use the law of cosines. The law of cosines is a useful tool for solving problems involving distances and angles between points in two-dimensional space. We can use the law of cosines to find the distance between the starting and ending point of the hike, and the bearing to get back to camp.

The law of cosines states that:

c^2 = a^2 + b^2 - 2ab * cos C

where c is the distance between the two points, a and b are the distances of the two legs of the hike, and C is the angle between them.

Using the given information, we can set a as the distance traveled at 3.5 miles per hour for 2 hours, which is 3.5 * 2 = 7 miles,

b as the distance traveled at 3.5 miles per hour for 4 hours which is 3.5 * 4 = 14 miles,

C as the angle between the two legs of the hike which is (72 + 23) = 95 degrees.

Now we can substitute this values into the law of cosines formula:

c^2 = 7^2 + 14^2 - 2(7)(14) * cos 95

Solving this equation will give us the square of the distance between the starting and ending point of the hike. To find the actual distance, we'll have to take the square root of that.

The distance directly back to camp is √(196 - 98*(√2/2)) = √(196 - 98*(√2/2)) ≈ 8.14 miles

To find the bearing to head back to camp, we must know that the bearing of a line is defined as the angle between the line and the North direction, measured clockwise.

We can use the bearing of N72°W and S23°W to find the back bearing to camp.

The back bearing is (180 + 72 + 23) = 275 degrees. The hikers should take a bearing of 275 degrees to head back to camp.

Step-by-step explanation:

PLEASE HELP IM DESPERATE

Answers

[tex]\frac{sqrt{5} }{3}[/tex]

Step-by-step explanation:

Its root 5 over 3

Answer:

cos (90 - m)° = 2/3

--------------------------------------

If m° is one of the angles of a right triangle, the complementary angle is (90 - m)°.

We know that sine of the angle is same as the cosine of the complementary angle. It means:

sine m° = cos (90 - m)°

Therefore the value of cos (90 - m)° is 2/3.

An object is launched into the air at 60 feet per second from a platform 80 feet high given by the equation f(t) = -16t2+60t+80.
What is the maximum height?

Answers

Answer:

Below

Step-by-step explanation:

For the Quadratic Equation   - 16t^2+ 60t + 80

   the max value will occur at   t = - b/2a =  -60 / (2 * -16) = 1.875 s

     use this value f t in the equation to find max height = 136.25 ft

Pls help with this rounding

Answers

Answer:

0.36

0.0068

0.043

0.00048

Step-by-step explanation:

trust me bro

Alicia paid $1.32 for a bag of pinto beans. The beans cost $.55 per lb. How much did the bag of pinto beans weigh?

Answers

The weight of the bag of pinto beans she bought is; 2.4 lbs

How to solve Algebra Word problems?

Algebraic word problems are defined as questions that require translating sentences to equations, after which we then solve those equations.

Now, we are told that;

Amount paid by Alicia for a bag of pinto = $1.32

Cost of beans = $0.55 per lb

Now, the weight of the bag of pinto beans that Alicia bought will be;

Weight = Amount paid/cost per lb

Weight = 1.32/0.55

Weight = 2.4 lbs

Read more about Algebra Word Problems at; https://brainly.com/question/21405634

#SPJ1

y = 5x + 22
y - 4 = 10x
please help need a solution

Answers

Answer:

x=18/5, y=40. (18/5, 40).

Step-by-step explanation:

y=5x+22

y-4=10x

---------------

y=10x+4

10x+4=5x+22

10x-5x=22-4

5x=18

x=18/5

y-4=10(18/5)

y-4=36

y=36+4

y=40

Maryellen opened a aving account with an initial depoit of $1500 and will not make any additional depoit or withdrawal. The account earn 5% interet compounded annually. What i the balance in dollar and cent that Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. )

Answers

Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. ) is 1578.93 dollar of 5% interest

Why is it called compound interest?

Compound interest is the interest on a deposit calculated based on both the initial principal and the accumulated interest from previous periods. Or, more simply put, compound interest is interest you earn on interest

What are simultaneous equations?

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

deposit = 1500

interest = 5%

after one year = 1500+75= 1575

second year = 78.75+1500 = 1578.75

third year = 78.93+1500= 1578.93

Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. ) is 1578.93 dollar of 5% interest

learn more about of interest here

https://brainly.com/question/30116771

#SPJ4

Use the drop-down menus to compare −5.25 and −6.

A number line. Points are plotted at negative 5 and 25 hundredths and at negative 6.
CLEAR CHECK
−5.25
−6 because −5.25 is ...
−6 on the number line.

Answers

−5.25  > −6.

There are two of them.

These two numbers need to be compared.

A number's square root is always less than?

A number's square root is never greater than the number itself.

According to the question, we have -

A = −5.25

B =  −6.

Clearly, A > B

Hence,−5.25  > −6.

To learn more about comparing numbers refer to:

brainly.com/question/30221120

#SPJ1

Hi, hope you have a great day

Answers

hope you rest well and stay hydrated

7/6 u = 42
how do i solve u

Answers

Answer:

36

Step-by-step explanation:

7/6 u=42

7u =42×6

u=252/7

u=36

What is the solution to this system of equations 2x y 40 x − 2y − 20?

Answers

The system of equations 2x + y = 40 and x - 2y = -20 has a solution of x = 12 and y = 16. We can solve this system by using the method of substitution or elimination.

One way to solve the system is to use the method of substitution. We can first solve one of the equations for one of the variables and substitute that expression into the other equation.

For example, we can solve the first equation for y by isolating y on one side: y = 40 - 2x. Then we can substitute that expression into the second equation and solve for x:

x - 2(40 - 2x) = -20

x - 80 + 4x = -20

5x = 60

x = 12

Then we can substitute x = 12 into the first equation, or either equation to find the value of y:

2(12) + y = 40

y = 16

So the solution to the system of equations is x = 12 and y = 16.

Another way to solve the system of equations is to use the method of elimination. This involves adding or subtracting the equations to eliminate one of the variables. For example, we can add the equations and get:

3x - y = 20

Then we can solve for x or y and substitute it back into either of the equation to find the other variable.

Learn more about system of equations at

https://brainly.com/question/21620502

The complete question is:

What is the solution to this system of equations 2x + y = 40 and x - 2y = -20?

#SPJ4

2/3 (n - 6) = 5n - 43
please help me i cant get the right answer you will get 30 points please help

Answers

[tex]\dfrac{2}{3} (n-6)=5n-43[/tex]

Distribute:

[tex](\dfrac{2}{3} )(n)+(\dfrac{2}{3} )(-6)=5n-43[/tex]

[tex]\dfrac{2}{3} n-4=5n-43[/tex]

Subtract 5n from both sides:

[tex]\dfrac{2}{3} n-4-5n=5n-43-5n[/tex]

[tex]-\dfrac{13}{3} n-4=-43[/tex]

Add 4 to both sides:

[tex]-\dfrac{13}{3} n-4+4=-43+4[/tex]

[tex]-\dfrac{13}{3} n=-39[/tex]

Multiply both sides by -3/13:

[tex]-\dfrac{3}{13} \times(-\dfrac{13}{3} n)=-\dfrac{3}{13} \times(-39)[/tex]

[tex]\fbox{n = 9}[/tex]

Simplify.

(-3ab3)4 please

Answers

Answer: -12ab^3

Step-by-step explanation: (-3ab^3) 4 -12ab^3

Other Questions
1815 - your patient was exposed to an unknown chemical that has soaked their clothing. you should immediately 100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, the period, phase shift, and vertical shift of the function. Then graph the function. Thank you! a pendulum is made of a rod mass mr=3.7kg and length l=4.8m whose moment of inertia about its center of mass is 1/12M L^2 and a thin cylindrical disk of mass 1.3 kg and radius 1.2 m whose moment of inertia about its center of mass is 1/2 M R^2. What is the moment of inertia of the pendulum about the pivot point? Answer in units of kg define the linear transformation t by t (x) = ax. find (a) ker(t ), (b) nullity(t ), (c) range(t ), and (d) rank(t ). a = 1 2 3 1 5 3 1 1 0 4 1 1 3 1 2 why do we refer to the letters to timothy and titus as the pastoral letters? how are they dierent from the other letters weve studied so far a corporation must be incorporated in each state in which it does business. group of answer choices true false if we have a 8-pole generator, what is its synchronous speed in europe? how many grams of magnesium are needed to completely react with 54.5 ml of oxygen gas at stp? be sure to balance the equation. Major crises in Eastern Europe and the Middle East create severe challenges for Eisenhower's foreign policy. An American plane over the Soviet Union, disrupting a summit and retiling the Cold War. Eisenhower refuses to use American troops to prevent a communist victory over a colonial power in Asia. t/f Read this passage from chapter 5 of The Prince.There are, for example, the Spartans and theRomans. The Spartans held Athens and Thebes,establishing there an oligarchy: nevertheless they lostthem. The Romans, in order to hold Capua, Carthage,and Numantia, dismantled them, and did not losethem. They wished to hold Greece as the Spartansheld it, making it free and permitting its laws, and didnot succeed. So to hold it they were compelled todismantle many cities in the country, for in truth thereis no safe way to retain them otherwise than byruining them. And he who becomes master of a cityaccustomed to freedom and does not destroy it, mayexpect to be destroyed by it, for in rebellion it hasalways the watchword of liberty and its ancientprivileges as a rallying point, which neither time norbenefits will ever cause it to forget. And whatever youmay do or provide against, they never forget thatame or their privileges unless they are disunited orWhat text evidence supports Machiavelli's primarypurpose to persuade readers that a conquering princemust destroy a former republic if he hopes to holdit? Select three options.the list of cities Rome and Sparta conqueredthe portrayal of Greece as being held by Spartathe explanation of how Rome held Capua,Carthage, and Numantiathe description of liberty as a rallying cry forrebellion in former republics53:48the example of the Florentines losing control overPisaNextSubmit a square pyramid sitting on its base. The sides are 8cm, 14cm, and 14cm. whats the surface area of the pyramid in square centimeters? TRUE/FALSE. The process by which a majority opinion becomes exaggerated because my minorities do not feel comfortable speaking out in opposition is called the spiral of silence. a root widget's destroy method can be used as a callback function for a quit button.T/F The average tire pressure for an automobile is 38.5 psi which is how many atmospheres of pressure? a) 1.77 x 10-3 atm. b) 566 atm. c) 2.62 atm. While comparing 'Notes and Mortgages', which one of the following statements is False about 'Notes'?1.You can borrow money only if you pledge something2. The legal instrument is not recorded in the County Office/ Recording Office.3. It is more personal and mostly an 'I.O.U' to an individual.4. Mortgages use 'property' as a collateral. A trapezoidal weir has a length of 19ft with side slope 1 horizontal to 2 vertical. What is the head over the weir for a flow of 100 cfs? Which of these conditions does not share significant overlap with overtraining syndrome?A. DOMSB. chronic fatigue syndromeC. clinical depressionD. fibromyalgia Triangle ABC, A (1,7), B (3, 4), and C (6,5) is reflected across the y-axis then translated left five units to form Triangle A'B'C'Select true or false for each statement Side A'B' is the same length as side AB __ Triangle ABC and Triangle A'B'C' are similar but not congruent ___ Triangle ABC and Triangle A'B'C' are similar and congruent ___ determine the mathematical equation for volume (v) in units of liters, and of a piston filled with an ideal gas subjected to increasing pressure (p) in units of atmospheres What trinomial can be added to x^2+5x-8 to give me a sum of 2x-5