The Punic Wars led to demographic changes in Rome, with soldiers returning to find their lands claimed by others, resulting in their migration to the city and growth in the proletariat. This growth contributed to Rome's population reaching over one million by the first century BCE. The wars' aftermath also brought political upheaval that contributed to the fall of the Republic.
The Punic Wars significantly affected the demographic and social structure of Rome. Initially, Roman citizens were predominantly engaged in operating small family farms, with property ownership being a prerequisite for military service. Due to extended military campaigns during the Punic Wars, many soldiers found their lands neglected or in the hands of others upon their return. Consequently, this led to a mass migration of disenfranchised veterans and their families to Rome, swelling the ranks of the proletariat. The city's population ballooned, by some estimates reaching over one million by the first century BCE.
Additionally, the influx of wealth and resources from victories over Carthage markedly altered the political landscape. Disagreements on the distribution of wealth created political factions, primarily the Populares, who championed the cause of the common people, and the Optimates, who defended the interests of the elite. These developments precipitated deep social and political fractures, contributing to the eventual fall of the Roman Republic.
Let f(x) = - 4x - 1 and g(x) = x2 + 3.
Find (fog)(4)
Then (fog)(4) =
. (Simplify your answer)
Answer:
- 77
Step-by-step explanation:
To evaluate, substitute x = 4 into g(x) then substitute the value obtained into f(x).
g(4) = 4² + 3 = 16 + 3 = 19
f(19) = (- 4 × 19) - 1 = - 76 - 1 = - 77
The teacher tells the class the highest marks obtained by a student in her class is twice the lowest marks plus 7 . the highest score is 87. what is the lowest score? (pls tell with example and formula) thanks! (i am in grade 7)!
Answer:
40
Step-by-step explanation:
highest=2(lowest)+7
Replace the variables here:
87=2(lowest)+7
minus 7 on both sides
80=2(lowest)
divide both sides by 2
40=lowest
HELP! i'll give brianliest and lots of points, and if u will explain, explain it so a dumb person can understand, if u can't then just give me a straight answer
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325.
Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days.
Part B: Write the equation obtained in Part A using function notation.
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answer:
Step-by-step explanation:
There is a standard cost just for renting the car.
Let the daily cost = x
Let the addon be = z The add on is the amount they charge just to give you the keys and do the paper work. It might include insurance.
y = z + 4x
y = 180
z = ??
x = 4
y = 325
z = ??
x = 9
Equation 1: 180 = z + 4x
Equation 2:325 = z + 9x
Subtract (1) from (2)
325 = z + 9x
180 = z + 4x Subract
145 = 5x Divide by 5
145/5 = 5x/5
x = 29
What you have found is the daily cost. Now you have to find the fixed cost.
y = 29x + z
180 = 29*4 + z
180 = 116 + z Subtract 116 from both sides
180 - 116 = z
z = 64
Answer: Part A
y = 29x + 64
Part B
f(x) = 29x + 64
Part C
So what are the intervals?
Vertically each square is worth:
Horizontally: each square is worth.
How is the y axis labeled?
How is the x axis labeled? [e
Graph the points by letting
x = 2 days
x = 4 days
x = 6 days
I'm including the graph. You should be able to answer it just by looking at the graph. No single answer will be wrong. There are all sorts of ways of setting up the axis.
Lilly and Laura pooled their money to purchase
their brother, Liam, a video game for his birthday.
The video game cost a total of $45. If Laura was
only able to contribute of what Lilly did, how
much did Laura put toward the present?
Answer: $22.50
Step-by-step explanation: let x represent the amount Laura and Lilly contributed each. If Laura and Lilly contributed the same amount, x+x=2x=45. If 2x=45, divide both sides by 2 to find the value of x. 45/2= 22.5.
Laura contributed $15 toward the purchase of the video game.
Explanation:The question is asking to determine the amount contributed by Laura to buy a video game for their brother, Liam, if the entire cost of the game is $45 and Laura contributed half as much as Lilly. For simplicity, let's assume Lilly contributed x dollars. Then Laura, contributing half as much, would have contributed x/2 dollars. Given that their total contribution is $45, we set up the equation x + x/2 = 45. Solving for x, we find that Lilly contributed $30 and Laura, half of this, contributed $15.
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Please help me on this I’m so tired and I can’t sleep until my progress is at 80 and this is the end of my year it’s at 79%
Answer:
The answer is the bottom left
Find the area of this figure
Answer:
22.34 km²
Step-by-step explanation:
Here we have a circle whose diameter is 5 1/3 km. As an improper fraction, that's 16/3 km. Half that, or 8/3 km, is the radius.
The area of a circle is A = πr², where r is the radius.
In this case, the area is A = π(8/3 km)², or (64/9)π km², or 22.34 km² (same as first answer choice).
if f(x)=3x^2 and g(x)=x+2, find (f*g)(x)
Answer:
(f+g)(x) = 3x^2 + x + 1
What is 2^(4/3)
equal to?
Answer:
∛16
Step-by-step explanation:
First, remember that the denominator always goes outside the radical and the numerator inside. so with that, it looks like this.
∛2^4
simplify.
∛16
A grocery store donated 60 dozen hot dog rolls to the local Youth Baseball League for their Opening Day ceremonies. A total of 679 hotdogs were served. (Hint: a dozen contains 12 items) a) How many dozen rolls were used? (Express your answer in mixed number form)
Answer:
7 7/12
Step-by-step explanation:
Find the amount of rolls in all that were donated:
60 x 12 = 720.
The total amount used is 679. Subtract 679 from 720:
720 - 629 = 91.
Find the amount per dozen. Divide 91 with 12:
91/12 = 7 7/12
7 7/12 is your answer.
~
The local Youth Baseball League used 56 dozen rolls with 7 extra rolls for a total of 679 hot dogs, which is expressed as 56 7/12 dozen.
Explanation:The local Youth Baseball League served a total of 679 hot dogs using rolls from the grocery store.
If a dozen represents 12 items, we need to calculate how many dozens of rolls were used in this circumstance.
Since 679 hot dogs were served and each dozen contains 12 rolls, we can divide 679 by 12 to find the number of dozens.
Dividing 679 by 12, we get:
679 ÷ 12 = 56 dozens with a remainder of 7.
Therefore, 56 dozen rolls were fully used, with an additional 7 rolls from another dozen.
To express this in mixed number form, it would be 56 7⁄12 dozen rolls.
how would you solve x in this equation?
1.4(2x+3) = 0.9(3x-2)
Answer:
x = -60
Step-by-step explanation:
1.4(2x+3) = 0.9(3x-2)
(1.4)(2x) + (1.4)(3) = 0.9(3x) - 0.9(2)
2.8x + 4.2 = 2.7x - 1.8
2.8x - 2.7x = -1.8 -4.2
0.1x = -6
x = -60
Answer:
x = - 60
Step-by-step explanation:
1.4(2x+3) = 0.9(3x-2) Remove the brackets
2.8x + 4.2 = 2.7x - 1.8 Subtract 4.2 from both sides
2.8x +4.2-4.2 = 2.7x - 1.8- 4.2
2.8x = 2.7x - 6 Subtract 2.7x from both sides
2.8x-2.7x = - 6
0.1x = - 6 Divide by 0.1
0.1x/0.1 = - 6/0.1
x = - 60
Sanjay needs 90 meters of fence to go around a rectangular garden.
The length l of the garden is three times its width w.
Three of these equations give the correct value for w.
Which equation does NOT?
w+3w=90
w+3w+w+3w=90
2⋅w+2⋅3w=90
2⋅(3w+w)=90
To find the perimeter of a rectangle you can multiply the length by 2 and the width by 2, or you can add the four sides together.
The wrong equation is w + 3w = 90 because it only has one width and one length, which would be half the total perimeter.
Final answer:
The equation that does not correctly represent the width w of Sanjay's rectangular garden given the total fence length and length-width relationship is w + 3w = 90, as it simplifies to 4w = 90, which is not the correct equation for this context.
Explanation:
The question asks to identify which equation does not correctly represent the width w of Sanjay's rectangular garden, given that the total length of the fence is 90 meters and that the length l of the garden is three times its width w. We know the perimeter P of a rectangle is given by P = 2l + 2w, where l is the length and w is the width.
We can substitute l = 3w into the perimeter formula to get P = 2(3w) + 2w, which simplifies to P = 6w + 2w or P = 8w. Given that P = 90, the correct equation is 8w = 90. Now, let's examine the provided equations:
w + 3w = 90 simplifies to 4w = 90.
w + 3w + w + 3w = 90 simplifies to 8w = 90, which is the correct equation.
2 · w + 2 · 3w = 90 simplifies to 2w + 6w = 90 which simplifies to 8w = 90, which is also correct.
2 · (3w + w) = 90 simplifies to 2 · 4w = 90 which simplifies to 8w = 90, which is again correct.
Thus, the equation that does not give the correct value for w is w + 3w = 90.
The temperature in Tampa Fonda is 15 degrees warmer than twice the temperature in Chicago, Illinois. The temperature in Tampa is 75 degrees. Write an equation to determine
the temperature in Chicago
The temp of Chicago is 30 degrees.
15 degree MORE than TWICE the temp of Chicago. 75-15=60/2. Hope this helps.
Answer:
2x + 15 = 75
Step-by-step explanation:
2 represents the twice, the x represents the unknown answer (Chicago), the + 15 is when it says florida is 15 degrees warmer
What is the slope of (0,32) and (100,212)
Answer:
( 212 - 0 )/ ( 100 - 32 ) = 212 / 68 = 3.11 ;
Step-by-step explanation:
Let m = slope
m = (delta y)/(delta x)
m = (212 - 32)/(0 - 100)
m = 180/(-100)
m = -180/100
You can reduce -180/100 to the lowest term. I'll let you do that.
Evaluate 2(x + 1) - 3 when x = 6.
ОА. 5
ов. 8
Ос. 11
OD. 10
Answer:
C. 11
Step-by-step explanation:
Evaluate 2(x + 1) - 3 when x = 6.
2(x + 1) - 3 <== substitute 6 for x
2(6 + 1) - 3 <== distribute 2
2(6) + 2(1) - 3
12 + 2 - 3 <== add and subtract
14 - 3
11 <== answer
Hope this helps!
Hey there!
2(x + 1) - 3
= 2(6 + 1) - 3
= 2(7) - 3
= 14 - 3
= 11
OR
2(x + 1) - 3
= 2(6 + 1) - 3
= 2(6) + 2(1) - 3
= 12 + 2 - 3
= 14 - 3
= 11
Therefore, your answer is: 11
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Julio bought 10 shares of Apex Co. for $50 each and later sold all of them at
$55 each. This transaction resulted in what type of event?
O
A. Capital profit
O
B. Capital gain
O
C. Capital win
O
D. Capital loss
Answer: B. Capital Gain
Step-by-step explanation:
A wave with a height of 5 feet and a wavelength of 10 feet has a wave base of
A. 20 feet
B. 10 feet
C. 5 feet
D. 2.5 feet
Answer:
A.
Step-by-step explanation:
Answer:
C. 5 feet
Step-by-step explanation:
If a wave with a height of 5 feet and a wavelength of 10 feet has a wave base of 5 feet.
B = x/2 = 10ft/2 = 5 feet
•••••Answer this question thanks •••••
2b < 10
b < 5
How to draw it:
1. Draw a hollow point on number "5"
2. Draw a small vertical line on the top of the point.
3. Draw a long honrizontal line from that vertical line to the left to the end, and add an arrow.
First divide 2 to both sides to isolate b. Since 2 is being multiplied by b, division (the opposite of multiplication) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.
2b ÷ 2 < 10 ÷ 2
1b < 5
b < 5
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
b < 5
aka b is less then five
This means that the graph will have an empty circle and the arrow will go to the left of 5.
The graph is in the image below:
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the product of (3a + 2)(4a2 - 2a + 9)?
12a3 - 2a + 18
12a + 6a +9
1203 - 6a2 + 23a + 18
12a3 + 2a + 23a + 18
To find the product of two expressions, we use the distributive property and multiply each term from the first expression with each term from the second expression, then combine the like terms.
The product of[tex](3a + 2)(4a^2 - 2a + 9) is 12a^3 - 6a^2 + 23a + 18.[/tex]
To find the product of two binomials, you can use the distributive property. In this case, you multiply each term in the first binomial, 3a and 2, by each term in the second binomial, 4a^2, -2a, and 9, and then combine like terms.
[tex](3a + 2)(4a^2 - 2a + 9) = 3a * 4a^2 + 3a * (-2a) + 3a * 9 + 2 * 4a^2 + 2 * (-2a) + 2 * 9[/tex]
Now, perform the multiplications:
[tex]12a^3 - 6a^2 + 27a + 8a^2 - 4a + 18[/tex]
Combine like terms:
[tex](12a^3 - 6a^2) + (27a - 4a) + 1812a^3 - 6a^2 + 23a + 18[/tex]
So, the product of[tex](3a + 2)(4a^2 - 2a + 9)[/tex]is indeed[tex]12a^3 - 6a^2 + 23a + 18.[/tex]
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Which of the following choices gives you a slope of 3?
Answer: Could you list the choices?
EASY QUESTION PLEASE HELP
Answer:
Yea its table 1
Step-by-step explanation:
Answer:
The answer is the first table, or Table 1.
Step-by-step explanation:
Happy to help! c:
20 POINTS!!! NEED HELP ASAP!!!
Which exponential function is represented by the table?
f(x) = 0.2(0.5x)
f(x) = 0.5(5x)
f(x) = 0.5(0.2x)
f(x) = 0.2(0.2x)
Answer:
c
Step-by-step explanation:
Two cylinders. The smaller cylinder has height labeled as 1 cm. The larger cylinder has height labeled as 3 cm.
The cylinders are similar. The volume of the larger cylinder is 2106 cubic centimeters. What is the volume of the smaller cylinder?
93 cm3
81 cm3
78 cm3
65 cm3
Answer: third option.
Step-by-step explanation:
You know that the height of the smaller cylinder is 1 cm and the height of the larger cylinder is 3 cm, then you can find the volume ratio. This is:
[tex]Volume\ ratio=(\frac{1\ cm}{3\ cm})^3\\\\Volume\ ratio=\frac{1}{27}[/tex]
Knowing that the volume of the larger cylinder is 2,106 cubic centimeters, you need to multiply it by the volume ratio to find the volume of the smaller cylinder.
Therefore:
[tex]V_{smaller}=\frac{1}{27}(2,106\ cm^3)\\\\V_{smaller}=78\ cm^3[/tex]
ANSWER
The correct answer is C
EXPLANATION
We have that, the smaller cylinder has height 1 cm and the larger cylinder has height 3cm.
The scale factor of similarity is
[tex]k = \frac{1}{3} [/tex]
That's if the smaller cylinder is the image.
The volume of the larger cylinder is 2106 cm³.
To find the volume of the smaller cylinder, we multiply the volume of the larger cylinder by k³
[tex]( { \frac{1}{3} })^{3} \times 2106 {cm}^{3} [/tex]
[tex]{ \frac{1}{27} } \times 2106 = 78 {cm}^{3} [/tex]
Can someone help me with this
Hello There!
Your answer is the last option r*n^2
I plugged in the values for each of these dilations.
Rebecca has 45 coins, all nickels and dimes. The total value of the coins is $3.60. How many
of each type of coin does Rebecca have?
Answer:
Rebecca has 18 nickels and 27 dimes
Step-by-step explanation:
Let x be the number of nickels Rebecca has, then 45-x is the number of dimes she has.
The total value of Rebecca's coins is $3.60.
1 nickel - 5 cents
x nickels - 5x cents
1 dime - 10 cents
45-x dimes - 10(45-x) cents
Total x nickels and 45-x dimes is 5x+10(45-x) cents that is $3.60=360 cents. So,
5x+10(45-x)=360
5x+450-10x=360
5x-10x=360-450
-5x=-90
5x=90
x=18
45-x=45-18=27
What type of scan tool is shown in the above photograph?
A. Laptop computer adapter
B. Factory scan tool
C. Bluetooth interface
D. Generic scan tool
The scan tool shown in the photograph is a factory scan tool, which is designed for use with a specific brand or model of vehicle. It provides advanced diagnostics and requires a separate adapter to connect to a device. Generic scan tools are more affordable but have limited functionality.
Explanation:The scan tool shown in the photograph is a factory scan tool. Factory scan tools are specifically designed for use with a particular brand or model of vehicle.
They provide access to advanced diagnostics, including reading and clearing fault codes, monitoring live data, and performing special functions.
Factory scan tools are usually more expensive than generic scan tools, but they offer more comprehensive and accurate information for troubleshooting specific vehicle systems.
They often require a separate adapter or cable to connect to a laptop or other device.
In contrast, generic scan tools are more affordable and can work with multiple vehicle brands.
They typically have limited functionality and may not be able to access all the features and functions of a factory scan tool.
The type of scan tool that is shown in the above photograph is Bluetooth interface. Option C
Bluetooth interfaces are commonly used as scan tools for connecting to onboard diagnostics (OBD) systems in vehicles wirelessly.
They can be paired with compatible software on devices like smartphones or tablets, allowing users to retrieve diagnostic information from the vehicle's computer system.
This technology provides convenience and flexibility for automotive diagnostics.
Help me please with this
Answer:
(b) 240
Step-by-step explanation:
First, we use the Pythagorean formula using the given side lengths to find x. Then we use x to find the side lengths. Then we add the side lengths to find the perimeter.
Pythagorean theorem formula:
a^2 + b^2 = c^2
(x - 20)^2 + (x - 40)^2 = x^2
x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2
x^2 -120x + 2000 = 0
(x - 100)(x - 20) = 0
x - 100 = 0 or x - 20 = 0
x = 100 or x = 20
We see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. The only valid solution is x = 100.
perimeter = sum of the lengths of the sides
perimeter = x + x - 20 + x - 40
perimeter = 3x - 60
Replace x with 100.
perimeter = 3(100) - 60
perimeter = 300 - 60
perimeter = 240
What is the product of (2x-1)(x+4)
Answer:
[tex]\large\boxed{(2x-1)(x+4)=2x^2+7x-4}[/tex]
Step-by-step explanation:
[tex](2x-1)(x+4)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(2x)(x)+(2x)(4)+(-1)(x)+(-1)(4)\\\\=2x^2+8x-x-4\qquad\text{combine like terms}\\\\=2x^2+(8x-x)-4\\\\=2x^2+7x-4[/tex]
What is the base of the exponential expression of 4 to the power of 5
The base of the exponential expression 4^5 is 4.
Explanation:The base of an exponential expression refers to the number being raised to a power.
In the exponential expression 4 to the power of 5, the base is 4 because it is the number being multiplied by itself 5 times.
Therefore, the base of the exponential expression 45 is 4.
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Solve the equation for x.
3(6x - 1) = 12 Please help I've tried doing the math and I can't find out what I'm doing wrong
Answer:
edg 2021 answer is A
Step-by-step explanation:
Multiply and simplify the product. –12i × 3i Select the product. 36 -36 36i -36i
Answer:
36
Step-by-step explanation:
–12i × 3i
Multiply the numbers
-12*3 = -36
Multiply the imaginary number
i*i= i^2
We know i^2 = -1
-36 * -1 = 36
Answer:
36Step-by-step explanation:
[tex]i=\sqrt{-1}\to i^2=(\sqrt{-1})^2=-1\\\\-12i\times3i=(-12)(3)i^2=(-36)(-1)=36[/tex]