what is the are of this?

What Is The Are Of This?

Answers

Answer 1

Answer:

Ok first of all you start out splitting the shape into seperate rectangles, in this case 2. take those 2 rectangles and find the area of them. Say we start from the smaller rectangle. 2 x 4 = 8 so the area of the smaller rectangle is 8. Keep that in mind. Next we have to multiply 10 x 5 because that is the labeled number of meters and that equals 50. So add 50 + 8 = 58

Step-by-step explanation:

Your answer is 58 meters

Really hope i helped and have a wonderful day! :)

Answer 2

Answer:

58 m³

Step-by-step explanation:

To find the area of irregular shapes like this, it is easy to split the shape into 2 individual shapes, find the area of both, then add the areas to find the total.

Now, we'll split it into 2 rectangles with areas of:

2 x 4

10 x 5

To find area, you multiply the length of one side by the other. The first rectangle's area is (2 x 4) and the other rectangle's area is (10 x 5).

10 x 5 = 50

2 x 4 = 8

50 + 8 = 58

The area of the figure is 58 m³.


Related Questions

Which linear equation represents Catherine’s situation?

Answers

Answer:

y=1/9x+104

Step-by-step explanation:

I REALLY hope this helps

Sorry if im wrong

Best of luck!

What is front-end ratio and how do you figure it out?

Answers

Answer:

The front-end ratio is calculated by dividing an individual's anticipated monthly mortgage payment by his/her monthly gross income. The mortgage payment generally consists of principal, interest, taxes, and mortgage insurance (PITI). Lenders use the front-end ratio in conjunction with the back-end ratio to determine how much to lend.

Step-by-step explanation:

Best method to solve y=-3x+4 y = 3x-2

Answers

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

( 1 , 1 )

Equation Form:

x = 1 ,   y = 1

Leo has 24 golf clubs. He has 3 golf bags. Each bag contains the same number of clubs. How many golf clubs are in each bag?

Answers

Answer:

8

Step-by-step explanation:

24/3 = 8

from the sum of 3a^2-ab-2b^2 and 2a^2+5ab-3b^2 subtract a^2-3ab-4b^2

Answers

4a^2+7ab-b^2

Step-by-step explanation:

Add the first two equations together:

 3a^2-ab-2b^2

+ 2a^2+5ab-3b^2

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

5a^2+4ab-5b^2

Subtract that answer from the remaining trinomial:

5a^2+4ab-5b^2

- a^2-3ab-4b^2

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

4a^2+7ab-b^2

Answer:

4a^2 + ab - 9b^2

Step-by-step explanation:

First, perform the indicated addition:

3a^2-ab-2b^2

2a^2+5ab-3b^2

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

5a^2 + 4ab - 5b^2

From this sum we subtract a^2 - 3ab - 4b^2:

 5a^2 + 4ab - 5b^2

-(a^2 - 3ab - 4b^2

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

 4a^2 + ab - 9b^2

WILL GIVE BRAINLIEST!!! If w = 6 units, x = 3 units, and y = 5 units, what is the surface area of the figure?

Answers

Don’t trust that link


178 units^2

The surface area of the figure is 204 sq.unit.

What is Surface Area ?

The surface area of a three dimensional figure is the sum of area of all its faces.

Here a three dimensional figure is given and surface area has to be calculated.

The base is a cuboid

Surface Area of a cuboid = SA= 2lw+2lh+2hw

SA = 2 * 6 * 6 +2 * 6 * 3 + 2 * 6 * 3

SA = 144 sq.units

The Surface Area of the 4 triangle surface = 4 * (1/2) * base * height

SA = 2 * 6 * 5 = 60 sq.units

The total surface area = 144 +60 = 204 sq.units

Therefore the surface area of the figure is 204 sq.unit.

To know more about Surface Area

https://brainly.com/question/2835293

#SPJ2

What is the measure of the angle supplementary to a 47.5 degree angle?

137.5

52.5

42.5

152.5

Answers

Answer:

132.5 degrees. Check to see if there is missing information in the question or any mistakes.

Step-by-step explanation:

Supplementary angles = 180 degrees

180 - 47.5 = 132.5

137.5 you can just ask the internet for help

Caitlyn uses 47-centstamps and 8.cent stamps to mail a gift card to a friend. If the postage is $2.99, how many of each stamp did Caitlyn use?

Answers

Let the number of 47-cent stamps be x, and the number of 8-cent stamps be y. So, the cost of x 47-cent stamps will be $0.47x.The cost of y 8-cent stamps will be $0.08y.Therefore, $2.99 = $0.47x + $0.08y  Multiply the entire equation by 100 to eliminate decimals. $299 = 47x + 8yEquation 1.47x + 8y = 299There are a couple of ways to solve the system of equations.

One method is substitution. We can rearrange equation 1 to solve for x:47x = 299 - 8y x = (299 - 8y)/47Substitute this expression for x into the first equation: 0.47(299 - 8y)/47 + 0.08y = 2.99 Simplifying the equation, we get: 299 - 8y + 4.76y = 299y = 299/0.76y = 393.4Hence, we cannot have fractional values of y; it must be a whole number, so Caitlyn can use 32 47-cent stamps and 15 8-cent stamps to mail a gift card to a friend.

Know more about decimals:

https://brainly.com/question/30958821

#SPJ11

a circle has a diameter of 18. the sector has a central angle of 30 degrees. what is the area of the sector?

Answers

Answer:

21.21

Step-by-step explanation:

Area of a circle is A = π r^2

Variables:

r = 18/2 = 9

θ = 30 deg

Find the area:

A = π r^2

A = π 9^2

A = 254.47

Find the area of the sector:

θ/360 * A

= 30/360 * 254.47

= 21.21

Please mark brainliest if this helped!

Please mark brainliest if this helped!

Solve the system of equations x' 2x – 3y + 2 sin(2t) y' = x – 2y — 2 cos(2t)

Answers

Upon solving the given system of equations:

[tex]x(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * cos(2t) + (1/2) * (c_1 + e^{-t}) * sin(2t),\\y(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * sin(2t) - (1/4) * (c_1 + e^{-t}) * cos(2t)[/tex]

To solve the system of equations:

x' = 2x - 3y + 2sin(2t)

y' = x - 2y - 2cos(2t)

We can use the method of undetermined coefficients to find the particular solution. Assuming the particular solution takes the form:

[tex]x_p(t) = A sin(2t) + B cos(2t)\\y_p(t) = C sin(2t) + D cos(2t)[/tex]

Substituting these expressions into the original equations, we get:

2(A sin(2t) + B cos(2t)) - 3(C sin(2t) + D cos(2t)) + 2sin(2t) = 2sin(2t)

(A sin(2t) + B cos(2t)) - 2(C sin(2t) + D cos(2t)) - 2cos(2t) = cos(2t)

(2A - 3C + 2)sin(2t) + (2B - 3D)cos(2t) = 2sin(2t)

(A - 2C)sin(2t) + (B - 2D - 2)cos(2t) = cos(2t)

By comparing the coefficients of sine and cosine on both sides, we can equate them separately:

2A - 3C + 2 = 2

2B - 3D = 0

A - 2C = 0

B - 2D - 2 = 1

Solving these equations, we find:

A = 1

B = 3/2

C = 1/2

D = -1/4

So the particular solution is:

[tex]x_p(t)[/tex] = sin(2t) + (3/2)cos(2t)

[tex]y_p(t)[/tex] = (1/2)sin(2t) - (1/4)cos(2t)

To find the complementary solution, we solve the homogeneous system:

x' = 2x - 3y

y' = x - 2y

We can rewrite this system as a matrix equation:

X' = AX

where [tex]X = [x, y]^T[/tex] and

[tex]A = \left[\begin{array}{ccc}2&-3\\1&-2\end{array}\right][/tex]

The characteristic equation is:

det(A - λI) = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues:

[tex]\lambda_1 = -1\\\lambda_2 = -1[/tex]

For each eigenvalue, we solve the corresponding eigenvector equation:

(A - λI)V = 0

For [tex]\lambda_1 = -1[/tex], we have:

[tex]\left[\begin{array}{ccc}3&-3\\1&-1\end{array}\right] * V_1 = 0[/tex]

Solving this system, we find the eigenvector:

[tex]V_1 = [1\ \ 1][/tex]

For [tex]\lambda_2 = -1[/tex], we have:

[tex]\left[\begin{array}{ccc}3&-3\\1&-1\end{array}\right] * V_2= 0[/tex]

Solving this system, we find the eigenvector:

[tex]V_2 = [3\ \ 1][/tex]

So the complementary solution is:

[tex]x_c(t) = c_1 * e^{-t} * [1\ \ 1]^T + c_2 * e^{-t} * [3\ \ 1]^T\\y_c(t) = c_1 * e^{-t} * [1\ \1]^T + c_2 * e^{-t} * [3\ \ 1]^T[/tex]

where

[tex]c_1\ and\ c_2[/tex] are arbitrary constants.

The general solution is the sum of the particular and complementary solutions:

[tex]x(t) = x_p(t) + x_c(t)\\y(t) = y_p(t) + y_c(t)[/tex]

Simplifying and combining terms, we get:

[tex]x(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * cos(2t) + (1/2) * (c_1 + e^{-t}) * sin(2t)\\y(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * sin(2t) - (1/4) * (c_1 + e^{-t}) * cos(2t)[/tex]

where [tex]c_1\ and\ c_2[/tex] are arbitrary constants.

To know more about system of equations, refer here:

https://brainly.com/question/21620502

#SPJ4

How many gallons of water are used to fill 2 fish tanks

Answers

Answer:

It depends on the size of the fish tank, so this question cannot be properly answered.

Answer:It depends I can give a ratio

Step-by-step explanation:

If one tank needs 45 gallons of water and another needs 30 you will need 75 gallons of water. If your using pints or quarts you can find converter calculators

help me out and ill give brainliest

Answers

Answer:

C

Step-by-step explanation:

Y= MX (The Slope which is Rise/Run) minus 2 (The Y-Intercept).

Yeah help guys today was way to stressful to do this shi right now

Answers

Answer:

15.3125

Step-by-step explanation:

i gotchu

Yes, I need help, give answer as IMPROPER fraction.

Answers

Answer:

[tex]w = \frac{93}{40} [/tex]

w=93
—— Rhejrjfbffnfnfnfnnfnfnf
40

Which statement about the students' preferences is true? A. More students prefer Model B2 calculators than Model C3 calculators B. More students prefer black Model C3 calculators than white Model B2 calculators. C. More students prefer black calculators than white calculators. D. The fewest students prefer white Model B2 calculators. NEED HELP​

Answers

B. More students prefer black Model C3 calculators than white Model B2 calculators.

       - Ap3x verified

 What value of Y makes the equation true? Y + 2.9 = 11​

Answers

Answer:

8.1

Step-by-step explanation:

Subtract 2.9 to get Y alone.

11 - 2.9 = 8.1

Buenos días personas!!!
Necesito ayuda con esta problema de Matemáticas. ¿Me ayudan por favor?
PROBLEMA: Calcula 5€ de descuento de 16,80€
SOLUCIÓN: no sé
Muchas gracias!!

Answers

Respuesta:

11,80 €

Explicación paso a paso:

Dado:

Importe o coste = 16,80 €

El valor de descuento sobre la cantidad = 5 €

El precio o costo con descuento sobre el monto entregado será; la diferencia entre la cantidad dada y el valor de descuento

Importe - valor de descuento

16,80 € - 5 €

= 11,80 €

-6x + 12 , can somebody explain this ?

Answers

Step-by-step explanation:

Factor −6 out of −6x

-6(x)+12

Factor −6 out of 12.

−6(x)−6(−2)

Factor −6 out of −6 (x)−6(−2).

-6(x-2)

Excuse me, for the person who answers this right I will brain list. (if you can't quiet understand the question, I left an image)
Complete: For the function ()=−2‾‾‾‾‾√3, the average rate of change to the nearest hundredth over the interval −2 ≤ x ≤ 4 is ______.

Answers

Answer:   It is 3.>9

Step-by-step explanation:

because i dont know

(11m-7m)-(2m+6m) the sum or differce

Answers

Answer:

-4m

Step-by-step explanation:

=11m-7m-(2m+6m)

=11m-7m-8m

=-4m

plz mark me as brainliest

Answer:

-4m

Step-by-step explanation:

Hey!

==================================================================

First, We should remove the Parentheses.

To remove them, we distribute the negative over (2m + 6m).

⇒ 11m - 7m - (2m + 6m)

⇒ 11m - 7m - 2m - 6m

Work the Problem from Left to Right.

⇒ 4m - 2m - 6m

⇒ 2m - 6m

-4m

==================================================================

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

       -Aadi x

HELP PLS
Jane needs 6 1/2 of fabric to make a dress. She has one piece of fabric that is 1 1/2 yards and another piece of fabric that is 3 1/4 yards. How many more yards of fabric does Jane need to make the dress?

Answers

1 1/2+3 1/4
convert 1 1/2 to 1 2/4
1/4 + 2/4 = 3/4
1+3=4 + 3/4 = 4 3/4
turn 6 1/2 to 6 2/4
6 2/4 - 4 3/4 = 1 3/4

You want to save $1,200 per quarter for 15 years towards the purchase of a trailer. You feel that you can earn 3.12% compounded quarterly for this period of time. If your first deposit is in 3 months, what is the most expensive trailer that you can purchase?

Answers

The most expensive trailer can be purchased for $39,505.41. To determine the most expensive trailer that can be purchased at an interest rate of 3.12% compounded quarterly, we calculate the future value of the savings.

The formula for compound interest is given by the equation:

A = [tex]P(1 + r/n)^(nt)[/tex]

Where:

A is the future value of the savings,

P is the quarterly deposit amount ($1,200),

r is the interest rate per compounding period (3.12%),

n is the number of compounding periods per year (quarterly, so n = 4),

and t is the number of years (15).

Plugging the values into the formula, we have:

A =[tex]1200(1 + 0.0312/4)^(4*15)[/tex]

Calculating this expression, we find the future value of the savings after 15 years to be approximately $39,505.41.

Therefore, the most expensive trailer that can be purchased is $39,505.41 or less, as that is the maximum amount that will be saved over the 15-year period.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ11

Numerical methods for non-autonomous ODES [8 marks] Consider using the modified Euler formula Yn+1 = yn +hF(t, + $; Yn + F(tryn)), for some step size h > 0, to compute numerical solutions of the initial value problem dy F(t,y), y(to) = yo dt Use the modified Euler formula with step sizes h = 0.05 and h = 0.001 to compute approximate values of the solution to the following initial value problem dy 2t +ety, y(0) = 1, dt at the four time steps t = 0.1, 0.2, 0.3 and 0.4.

Answers

The approximate values of the solution to the given initial value problem at the four time steps t = 0.1, 0.2, 0.3 and 0.4 using the modified Euler formula with step sizes h = 0.05 and h = 0.001 are as follows:

Approximate solution using h = 0.05y(0.1) = 1.12116266y(0.2) = 1.25755476y(0.3) = 1.41728420y(0.4) = 1.59967883

Approximate solution using h = 0.001y(0.1) = 1.00372378y(0.2) = 1.00745820y(0.3) = 1.01119282y(0.4) = 1.01492766

The non-autonomous ordinary differential equation is given as:

dy/dt = f(t,y)......(1)

where f is a continuous function and is defined for all values of t and y. The numerical methods for non-autonomous ODEs are described below:

Modified Euler Formula (Improved Euler Method)

This method is based on the same idea as Euler's method, but the derivative is evaluated at the midpoint of the interval instead of the initial point. Consider the initial value problem (IVP) dy/dt = f(t,y), y(to) = yo, and suppose that we want to approximate the solution at tn+1 = tn + h. Then, using the improved Euler's formula, we obtain the following approximation:

Yn+1 = yn + hF(tn + h/2, yn + hF(tn,yn)/2)......(2)

Using h = 0.05

Substituting h = 0.05 in equation (2), we get

Y1 = Y0 + 0.05(F(0.025,Y0+F(0,Y0)/2))

Y2 = Y1 + 0.05(F(0.075,Y1+F(0.05,Y1)/2))

Y3 = Y2 + 0.05(F(0.125,Y2+F(0.1,Y2)/2))

Y4 = Y3 + 0.05(F(0.175,Y3+F(0.15,Y3)/2))

Using h = 0.001

Substituting h = 0.001 in equation (2), we get

Y1 = Y0 + 0.001(F(0.0005,Y0+F(0,Y0)/2))

Y2 = Y1 + 0.001(F(0.0015,Y1+F(0.001,Y1)/2))

Y3 = Y2 + 0.001(F(0.0025,Y2+F(0.002,Y2)/2))

Y4 = Y3 + 0.001(F(0.0035,Y3+F(0.003,Y3)/2))

For the given IVP, f(t,y) = 2t + ety, y(0) = 1

So, substituting f(t,y) in equation (1), we get

dy/dt = 2t + ety.....(3)

Using the modified Euler formula (equation 2), we get

Using h = 0.05

Y1 = 1 + 0.05(2(0.025) + e(0.025)Y0) = 1.12116266

Y2 = 1.12116266 + 0.05(2(0.075) + e(0.075)Y1) = 1.25755476

Y3 = 1.25755476 + 0.05(2(0.125) + e(0.125)Y2) = 1.41728420

Y4 = 1.41728420 + 0.05(2(0.175) + e(0.175)Y3) = 1.59967883

Using h = 0.001

Y1 = 1 + 0.001(2(0.0005) + e(0.0005)Y0) = 1.00372378

Y2 = 1.00372378 + 0.001(2(0.0015) + e(0.0015)Y1) = 1.00745820

Y3 = 1.00745820 + 0.001(2(0.0025) + e(0.0025)Y2) = 1.01119282

Y4 = 1.01119282 + 0.001(2(0.0035) + e(0.0035)Y3) = 1.01492766

To know more about modified Euler formula, refer to the link below:

https://brainly.com/question/12274716#

#SPJ11

Help on this please asap

Answers

Answer:

87.75

Step-by-step explanation:

You are correct

a square has f the diagonals of a square bisects its angles? ​

Answers

Answer:

ok so i can have i insteaof f too

Step-by-step explanation:

Give an angle of rotation centered at the origin that sends point P to a location whose (z,y) coordinates satisfy the given conditions. 1. z>0 and y < 0 2. z <0 and y> 0 3. y < 0 and z < 0 YA P x

Answers

The angles of rotation for the given conditions are:

1. π radians (180 degrees)

2. π/2 radians (90 degrees)

3. 3π/2 radians (270 degrees)

To find an angle of rotation centered at the origin that sends point P to a location with the given conditions, we can use trigonometric concepts.

1. For z > 0 and y < 0:

Since z > 0, the point P lies in the positive z-axis direction. To make y negative, we rotate the point counterclockwise by an angle of π radians (180 degrees).

2. For z < 0 and y > 0:

In this case, the point P lies in the positive y-axis direction. To make z negative, we rotate the point counterclockwise by an angle of π/2 radians (90 degrees).

3. For y < 0 and z < 0:

Here, the point P lies in the negative y-axis direction. To make both y and z negative, we rotate the point counterclockwise by an angle of 3π/2 radians (270 degrees).

In summary, the angles of rotation for the given conditions are:

1. π radians (180 degrees)

2. π/2 radians (90 degrees)

3. 3π/2 radians (270 degrees)

By rotating the point P by these angles, we can achieve the desired conditions for the (z, y) coordinates.

For more questions on radians, click on:

https://brainly.com/question/31963640

#SPJ8

List the probability of each outcome in the sample space.

Answers

are there answer choices to this question?

The time series component that exhibits a repeating pattern over successive periods, often one-year intervals is called
A. a cyclical component
B. a trend component.
C. seasonal component.
D. irregular component.

Answers

The time series component that exhibits a repeating pattern over successive periods, often one-year intervals, is called the seasonal component. It represents the regular and predictable variations in the data that occur due to seasonal factors, such as weather patterns, holidays, or annual events.

The seasonal component typically follows a consistent pattern, where the values tend to rise and fall in a similar manner within each season. For example, retail sales may experience higher values during the holiday season each year and lower values during other times.

Identifying and analyzing the seasonal component is crucial in many fields, including economics, finance, marketing, and forecasting. By understanding and accounting for the seasonal patterns, analysts and decision-makers can make more accurate predictions, adjust for seasonality in data, and develop strategies to optimize operations or sales during specific periods.

Methods such as seasonal decomposition or seasonal adjustment techniques are used to separate the seasonal component from other components, such as trend and irregular fluctuations, in order to better understand the underlying patterns and make informed decisions based on the data.

Learn more about intervals here:

https://brainly.com/question/11051767

#SPJ11

Consider the function shown below.
g(x) = 2^x
If the function g is horizontally compressed by a factor of 1/2 and reflected across the x-axis to obtain function f, which of the following graphs matches the above transformation?

Answers

The graph of the transformation by of horizontally compressing g(x) by a factor of 1/2 and then reflecting across the x-axis is graph Y

How to determine the graph?

The function is given as:

[tex]g(x) = 2^x[/tex]

When compressed horizontally by a factor of 1/2, the transformation rule is:

g'(x) = g(2x)

So, we have:

[tex]g(2x) = 2^{2x}[/tex]

[tex]g(2x) = 4^x[/tex]

When reflected across the x-axis, the transformation rule is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]f(x) = -4^x[/tex]

The graph represented by this is graph Y.

Hence, the graph of the transformation is graph Y

Read more about transformation at:

https://brainly.com/question/4289712

#SPJ2

here are 24 people in a fitness studio. 3/8 of the people are lifting weights, 1/3 are cross training, and the remaining people are running. What fraction of the people are running?

Answers

Answer:

7/24 i think i hope this helps and im right

I thing it may be 27/4 I’m not sure but I hope it helps
Other Questions
Question in the picutre treatment of irritable bowel syndrome often includes _______. identity the function of the cell membrane. what is the function of the cell membrane? please explain (1\6-1)(3-2/5)-(1/3-1/2) Please help! Will thumbsup!If TC = 450 + 30Q + 2Q2, then a profit maximizing firm should shut down if price is lower than: Solve the equation using either addition or substitution. Show all your work A 4 pack of 12-ounce bottles of water costs $4.40. What is the cost per ounce? Find the missing side what is the cube root of -0.216? Scott made a model of the water cycle by filling a tub with water, covering the tub with clear plastic, and placing a heat lamp over the tub. After a few days, he observed water droplets collecting on the plastic wrap.What process formed the water droplets in Scotts model?evaporationtranspirationcondensationprecipitation A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a prime number a. 0.45 c. 0.71 b. 0.55 d. 0.73 Please select the best answer from the choices provided A B C D What is the chemical formula for an acid? SOMEONE PLZZZZZZZZ HELP!!!To support your opinion on the dangers of nuclear scientist's opinion. Which kind of elaboration would you use?A. Comparison/contrastB. Sensory imageC. QuotationD. Fact Supposing you were asked by your Professor handling the course to write an academic paper on Criminal Law as it Affects on Business Organisations in Europe, present a list of 10 references that you will likely use in the course of writing the paper. An object executing simple harmonic motion has a maximum speed of 48 m/s and a maximum acceleration of 0.85 m/sPart AFind the amplitude of this motion.Express your answer using two significant figures. PLEASE HELPP, DONT SCAM!! The table below represents a function. Which of the following equations could be its function rule? Fifty people put there nameinto a two different drawings(30 males and 20 females).One drawing is for an iPad andthe other is for a flat screenTV. What is the probabilitythat a male will win bothdrawings.Possible answers 13%27%36%49%WILL GIVE BRAINLIST Which of the following is correct? High budget deficits and a large national debt are most likely to lead to a(n):a. decrease domestic interest rates, decrease the international value of the dollar, and increase American net exportsb. increase domestic interest rates, increase the international value of the dollar, and decrease American net exportsc. increase domestic interest rates, decrease the international value of the dollar, and increase American net exportsd. increase domestic interest rates, increase the international value of the dollar, and increase American net exports Is (2, 7) the answer to the equation 5x = y?If not, what should y be? whats in the blank help fast Turmoil within Rome's ________ proved to be more dangerous to the Republic's stability.