Which led most directly to the Roman Republic's demise and its transition to an empire?

A) Consuls staying in power too long.

B) War with the Etruscans.

C) The growing divide between the rich and the poor.

D) The failure of direct democracy.

The slope of this graph is equal to 8/50 or 0.16.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (29.00 - 5.00)/(150 - 0)

Slope, m = 24/150

Slope, m = 8/50 or 0.16.

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Answer: 6

Step-by-step explanation:

Answer: 16 for number 1 and 15 for number 2

Step-by-step explanation: 24 divided by 8 is 3 meaning we have to multiply 8 by 2 to get the upper part if the fraction 2 times 8 is 16

24 divided by 8 is 3 so we multiply 5 by 3 to get 15

Answer:

(621.49 x  0.1) + 13.99 = x

Step-by-step explanation:

I hope this helps

A constant function is a function that returns the same output every time it is called, regardless of the input. In this case, we want to create a constant function that returns an infinite list of all the natural numbers starting at 0.

Here's an example of how you could implement the nats function in Haskell:

makefile

Copy code

nats :: [Integer]

nats = [0..]

The [0..] syntax creates an infinite list that starts with 0 and continues indefinitely. Every time the nats function is called, it returns this same infinite list, so it's considered a constant function.

Another way to write the nats function is to use the iterate function, which generates a list by repeatedly applying a function to an initial value.

makefile

Copy code

nats :: [Integer]

nats = iterate (+1) 0

In this case, iterate (+1) 0 generates a list by repeatedly adding 1 to 0. The first element of the list is 0, the second element is 0 + 1 = 1, the third element is 1 + 1 = 2, and so on. This generates an infinite list of all the natural numbers starting at 0, which is exactly what we want.

In either case, you can take any number of elements from the nats list by using the take function. For example, take 5 nats would return the first 5 elements of the nats list, which would be [0, 1, 2, 3, 4].

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Using the concept of PEDMAS, the simplified expression is equal to 12

Simplification of an algebraic expression involves transforming a given expression into a simpler equivalent expression while maintaining the same value. This can be done by combining like terms, applying the distributive property, using the properties of arithmetic operations, and combining constants. The goal is to write the expression in the most compact and understandable form.

In the question given, the expression is;

27^(1/3) * 16^(3/4) ÷ 8^(1/4) ÷ 2^(1/4)

simplifying the expression;

3 * 8 ÷ 4√8 ÷ 4√2

Applying the principle of PEDMAS here;

3 * 8 ÷ 4√8 ÷ 4√2 = 12

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The simplification of the given expression would be=225½

The simplification of equations involves the replacement of ambiguous values with a simple value through the used of the various arithmetic operations.

(27⅓ × 16¾) ÷ (8¼ ÷ 16¾)

The about equations in the bracket are solved differently by changing the mixed fraction to a simple fraction:

= (27⅓ × 16¾)

= 82/3 × 67/4

The second bracket;

= (8¼ ÷ 16¾)

= 33/4 ÷ 67/4

= 4/33 × 67/4

Solving the both bracket through the following:

82/3 × 67/4 ÷ 4/33 × 67/4

The fraction 67/4 will cancel out each other;

= 82/3 ÷ 4/33

= 82/3 × 33/2

= 41×11/2

= 451/2

= 2251/2

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The length of the side AB, /AB/ as determined using the cosine rule is  30.8 m

The length of the side AB, /AB/ is given below using the cosine rule:

c² = a² + b² - 2 * a* b * cosC

where;

c is the unknown side AB

C = (175°  - 035°)

C = 145°

a = 5 m

b = 30 m

c² = 5² + 30² - 2 * 5 * 30 * cos 145°

c = √( 5² + 30² - 2 * 5 * 30 * cos 145°)

c = 30.8 m

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Charlotte makes 500 pounds per week

30 % of 500 she has to pay to the commission per week

if she made 1575 one week how much would she get?

1575 divided by 30%=472.5

472.5 rounded = 473

x=473 or 472.5

Charlotte would make $972.50 in a week in which she made $1575 in sales and  if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.

percentage, a relative value indicating hundredth parts of any quantity.

To calculate how much Charlotte would make in a week in which she made $1575 in sales

we first need to calculate her commission:

Commission = 30% × $1575

= $472.50

Total earnings = Guaranteed salary + Commission

= $500 + $472.50

= $972.50

Therefore, Charlotte would make $972.50 in a week in which she made $1575 in sales.

To calculate how much Charlotte would make in a week if she made x dollars in sales, we can use the same method.

Her commission would be:

Commission = 30% ×x

And her total earnings would be:

Total earnings = Guaranteed salary + Commission

= $500 + 0.3x

So, if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.

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The compound inequality for the graph shown above include the following:

x < -4.

x ≤ 5.

In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.

Since the first point is at -4 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.

Additionally, the second point is located at 5 and the arrow points to the left of the number line with a shaded circle, it represents the greater than (>) inequality symbol and should be written as x ≤ 5.

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the answer which equal to the 1 1/4 are 8 3/4 - 7 1/2 and 9 5/12 - 8 1/6.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

a) 5 2/8 - 4 1/4 = 42/8 - 17/4 = 42-34/8 = 8/8 =1

b) 8 3/4 - 7 1/2 = 35/4 - 15/2 = 35-30/4 = 1 1/4

c) 2 1/8 - 1 7/8 = 17/8 - 15/8 = 2/8

d) 9 5/12 - 8 1/6 = 113 - 98/ 12 = 15/12 = 1 3/12 =1 1/4

So the answer which equal the 1 1/4 is 8 3/4 - 7 1/2 and 9 5/12 - 8 1/6.

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Answer:

10 small bows; 8 large bows

Step-by-step explanation:

Let x = number of small bows.

Let y = number of large bows.

x + y = 18;

3x + 5y = 70

      -3x - 3y = -54

  +   3x + 5y = 70

  -----------------------

               2y = 16

y = 8

x + y = 18

x + 8 = 18

x = 10

Answer: 10 small bows; 8 large bows

The learning preference category that best describes a high school fine arts student who prefers a studio lesson that involves modeling with clay over a virtual field trip to the Louvre is a kinesthetic learner.

Kinesthetic learners are individuals who learn best through hands-on, physical experiences and activities. They tend to be active and enjoy engaging their bodies in learning, such as manipulating objects or performing movements. For this student, modeling with clay provides a hands-on, physical experience that allows them to learn through touch and movement. They can feel the texture and weight of the clay, and manipulate it to create their desired form. This type of learning experience is much more engaging and effective for a kinesthetic learner compared to a virtual field trip to the Louvre, which is primarily a visual learning experience.

In conclusion, a kinesthetic learning preference involves hands-on, physical activities and experiences, and this preference is evident in the student's preference for a studio lesson that involves modeling with clay over a virtual field trip to the Louvre.

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Space Explorer B travels 8600 miles per hour 4800 miles per hour Space Explorer A.

The slope, also known as gradient, in mathematics is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

Space Explorer B, flies 43000 miles in 5 hours. The speed will  be:

speed = 43000/5 = 8600 miles per hour

For Space Explorer A, we can find the speed from the slope of the graph. That is:

Speed = (38000-19000)/(10-5) = 19000/5 = 3800 miles per hour

Speed difference = 8600 - 3800 = 4800 miles per hour

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The parametric curve defined by x(t) = e^{-t} and y(t) = cos(t) for 0 ≤ t≤ π  is concave down in the interval (c) (0, π) .

The Concavity of a parametric curve is determined by the second derivative of the curve.

To find the second derivative of a parametric curve, we need to differentiate each component of the curve with respect to the parameter t, then differentiate those expressions with respect to t again.

For x(t) = e^{-t} and y(t) = cos(t),

the first derivative w.r.t "t" is x'(t) = -e^{-t} and y'(t) = -Sin(t) ;

the second derivative with respect to t of x''(t) = e^{-t} and  y''(t) = -Cos(t),

Since , y''(t) = -Cos(t) is negative over the interval (0, π), we can conclude that the curve is concave down over that interval.

Therefore, the curve is concave down over that interval (0, π).

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The expression (x - 10)(60 - 3x) represents Elliot's profit based on the price per key chain, where x is the price in dollars that Elliot charges for each key chain.

The expression can be interpreted as follows:

x - 10 represents the revenue Elliot makes from each key chain, as it's equal to the price per key chain minus the cost of materials for each key chain.

60 - 3x represents the number of key chains Elliot can make and sell, as it's equal to the maximum amount of money Elliot has minus the total cost of materials for all key chains.

So, (x - 10)(60 - 3x) represents Elliot's total profit, which is equal to the revenue from each key chain multiplied by the number of key chains Elliot can make and sell.

In other words, Elliot's profit is proportional to both the price he charges per key chain and the number of key chains he can sell at that price. The expression captures this relationship and can be used to determine Elliot's profit for different prices.

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The expression (x - 10)(60 - 3x) represents Elliot's profit based on the price per key chain, where x is the price in dollars that Elliot charges for each key chain.

The expression can be interpreted as follows:

x - 10 represents the revenue Elliot makes from each key chain, as it's equal to the price per key chain minus the cost of materials for each key chain.

60 - 3x represents the number of key chains Elliot can make and sell, as it's equal to the maximum amount of money Elliot has minus the total cost of materials for all key chains.

So, (x - 10)(60 - 3x) represents Elliot's total profit, which is equal to the revenue from each key chain multiplied by the number of key chains Elliot can make and sell.

In other words, Elliot's profit is proportional to both the price he charges per key chain and the number of key chains he can sell at that price. The expression captures this relationship and can be used to determine Elliot's profit for different prices.

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The sum of the two solutions is equal to 17/5.

Here we want to solve the quadratic equation:

5x^2 - 16x + 3 = 0

Using the quadratric formula, we will get the solutions:

[tex]x = \frac{16 \pm \sqrt{(-16)^2 - 4*3*5} }{2*5} \\\\x = \frac{16 \pm14 }{10}[/tex]

Then the two solutions of the quadratic equation are:

x = (16 + 14)/10 = 30/10 = 3

x = (16 - 14)/10 = 2/10 = 2/5

The sum is: 3 + 2/5 = 3 + 2/5 = 15/5 + 2/5 = 17/5

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Answer: To find the roots of a polynomial equation, we can use various methods, such as factoring, synthetic division, or the quadratic formula. One common method to find the roots of a quartic polynomial (degree 4) is to use the factor theorem, which states that if a polynomial equation has a root "r", then "r" is a factor of the polynomial.

In this case, we can factor 2x^4-26x^2-28 as:

2x^4 - 26x^2 - 28 = 2(x^2 - 7)(x^2 + 4)

So, the roots of 2x^4-26x^2-28 are x = ±√7 and x = ±i√2.

These are the solutions to the equation 2x^4-26x^2-28 = 0.

Step-by-step explanation:

Yes it's linear because the rate of change between x and y remain the same. Every increase of 5 in x results in a decrease of 4 in y, as example from x0 to x5, y goes from 18 to 14, from x5 to 10, y goes from 14 to 10. They decide to double the jump and go from x10 to x20, but as proof of it being linear, y also double the amount it decreases going from 4 to 8.

(A) The number of doughnuts that were jelly = 6

(B) The number of doughnuts that were glazed = 14

As per the data given in the question,

We have,

Total number of doughnuts sold = 40

Percentage of jelly doughnuts = 15%

Percentage of doughnuts that's were glazed = 35%

A) The number of doughnuts that were jelly can be found by multiplying the total number of doughnuts by the percentage that was jelly:

40 x 15% = 6 donuts

So there were 6 doughnuts that were jelly.

B) The number of doughnuts that were glazed can be found by multiplying the total number of doughnuts by the percentage that was glazed:

40 x 35% = 14 donuts

So there were 14 doughnuts that were glazed.

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The Intermediate Value Theorem tell us that there is a c in the interval [0,1] such that f(c) = k is lies between f(0) and f(1).

The Intermediate Value Theorem is a fundamental concept in calculus that states that given a continuous function f and two real numbers a and b, if k is a real number between f(a) and f(b), then there exists a real number c in the interval [a, b] such that f(c) = k.

In the specific case of [0,1], the Intermediate Value Theorem tells us that if k is a real number between f(0) and f(1), then there exists a real number c in the interval [0,1] such that f(c) = k. This means that for any value of k that falls between the values of the function at 0 and 1, there is a point in the interval [0,1] where the function takes on that value.

So, for what values of k does the Intermediate Value Theorem tell us that there is a c in the interval [0,1] such that f(c) = k? The Intermediate Value Theorem tells us that there is a c in the interval [0,1] such that f(c) = k for any real number k that falls between the values of f(0) and f(1).

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The difference between the given statements is that opposite sides are congruent means that all four sides of the quadrilateral are equal in length.

While one pair of parallel sides means that two sides of the quadrilateral are parallel and have the same length, the other two sides may or may not have the same length.

These two conditions define different types of quadrilaterals like a rectangle and a parallelogram, respectively.

So the answer is "construct a quadrilateral with one pair of opposite sides congruent and parallel."

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Answer:

40% is bigger

Step-by-step explanation:

40% ⇒ 40/100

1/4 ⇒ 25/100

40>25

∴ 40% is bigger

Therefore, the AAA test of congruency demonstrated that ABE is Congruence to CDE.

Something that is "exactly equal" in terms of size and shape is referred to as congruent. No matter which way we spin, flip, or rotate the shapes, they remain accurate. For instance, you may draw two circles with the same radius, cut them out, and stack them.

In this case, we are aware that AB ll DC - GIVEN

In light of the characteristic of parallel lines,

Let's recall the property of parallel lines:-

"When the pair of alternating angles equals one another, two straight lines become parallel."

Alternate angles are angle ABE and angle CDB.

angle BAE ≅ angle DCE -{alternate angles}

E is a midway, given that.

According to the midpoint theorem, opposite angles are congruent when angle AES and angle CED are compared.

Here, we may see the congruency test from AAA.

Hence its proved that ∆ABE ≅ ∆CDE by AAA test of congruency.

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The company that has a better value is: company A.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the total fee that is being charged by company A is denoted by C(x) and it charges $14 per delivery fee and $8 per hour, an equation that models this situation is given by;

C(x) = 8x + 14

When hours, x = 8 hours, the total fee is given by:

C(8) = 8(8) + 14

C(8) = $78.

For company B, the total fee is given by:

C(x) = 10x + 10

C(8) = 10(8) + 10

C(8) = $90.

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Press second, then CALC (above the TRACE key). Select option 2: 0You'll be required to enter an x-intercept guess, a left bound, and a right bound into the calculator.

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The answer is Quantitative because quantitative data mainly deals with the statistic and figures.

As given, Comparing data collected on individuals’ sales and individuals’ attendance records would be an example of what type of data analysis?

Quantitative data analysis involves the use of numerical data to discover patterns and relationships. In the example of comparing individuals' sales and attendance records, the data collected would be numerical and would be analyzed to determine the relationship between sales and attendance. This type of analysis often involves statistical techniques such as regression analysis, correlation analysis, and hypothesis testing. The goal is to gain insights and make informed decisions based on the numerical data, rather than just describing or summarizing it.

Answer is Quantitative.

Reason- Quantitative data mainly deals with the statistic and figures.

Thus, the answer is Quantitative because quantitative data mainly deals with the statistic and figures.

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The answer is Quantitative because quantitative data mainly deals with statistic and figures.

As given, Comparing data collected on individuals’ sales and individuals’ attendance records would be an example of what type of data analysis?

Quantitative data analysis involves the use of numerical data to discover patterns and relationships. In the example of comparing individuals' sales and attendance records, the data collected would be numerical and would be analyzed to determine the relationship between sales and attendance. This type of analysis often involves statistical techniques such as regression analysis, correlation analysis, and hypothesis testing. The goal is to gain insights and make informed decisions based on the numerical data, rather than just describing or summarizing it.

Answer is Quantitative.

Reason- Quantitative data mainly deals with statistic and figures.

Thus, the answer is Quantitative because quantitative data mainly deals with statistic and figures.

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Answer:

62.2 m

Step-by-step explanation:

From 148m away at ground level, the angel of elevation to the tower base is 18 degrees. Imagining this as a right angled triangle, if considering the angle of 18 degrees, 148m is the adjacent and the opposite is the height of the hill:

tanA=opposite/adjacent

tan18=opposite/148

opposite = 57.8357059295m

From 148m away at ground level, the angel of elevation to the tower top is 34 degrees. Imagining this as a right angled triangle, if considering the angle of 34 degrees, 148m is the adjacent and the opposite is the height of the hill+the tower:

tanA=opposite/adjacent

tan34=opposite/148

opposite = 120.062515998m

Knowing the height of the hill and tower is 120.062515998m and the height of the hill is 57.8357059295m, we can say the height of the tower is the difference:

120.062515998 - 57.8357059295 = 62.2268100685 m

The function (f - g)(x) is given as follows:

C. (f - g)(x) = |7x + 1| - 6.

The functions for this problem are defined as follows:

To obtain the subtraction of f(x) by g(x), we merely subtract the definitions, as follows:

(f - g)(x) = f(x) - g(x).

Hence:

(f - g)(x) = |7x + 1| - 8 - (-2)

(f - g)(x) = |7x + 1| - 8 + 2.

The like terms in the expression are given as follows:

-8 + 2 = -6.

Hence the subtraction function for this problem is defined as follows:

(f - g)(x) = |7x + 1| - 6.

Meaning that option C is the correct option.

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The bicycle that has a diameter of 26 inches has a circumference of 81.64 inches

The perimeter is the total length of the edge of a geometric figure.

To solve this geometry exercise the equation and procedure we will use is:

P = 2*pi*r

Where:

Information about the problem:

Applying the perimeter equation of a circumference, we have:

P = 2*pi*r

P = 2*3.14*(26 inches/2)

P = 3.14*26 inches

P = 81.64 inches

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-12X -- 66y + 10
_____________
           45

Answer:

A 28°

Step-by-step explanation:

we see that the sum of angle 1 and 62° must be 90° (right angle).

90 = 62 + angle 1

28° = angle 1