Rome was able to gain its empire in large part by extending some form of citizenship to many of the people it conquered. Military expansion drove economic development, bringing enslaved people and loot back to Rome, which in turn transformed the city of Rome and Roman culture.

Answer:

(x - 5)(x - 7)

Step-by-step explanation:

Given

x² - 12x + 35

Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)

The factors are - 5 and - 7, since

- 5 × - 7 = 35 and - 5 - 7 = - 12, thus

x² - 12x + 35 = (x - 5)(x - 7) ← in factored form

They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas

Step-by-step explanation:

A Pizzeria sells pizza according to size:

We need to find how many of each size pizza they must sell to get $600

Assume that the number of small pizza is x, the number of medium pizza is y and the number of large pizza is z

∵ The Pizzeria sells x small pizzas, y medium pizzas and

   z large pizzas

∵ The small pizzas cost $10, medium pizzas cost $15, and

   large pizzas cost $40

∵ They get $600

∴ 10x + 15y + 40z = 600 ⇒ (1)

∵ They sell as many small pizzas as medium and large pizzas

   combined

∴ x = y + z ⇒ (2)

∵ The number of medium pizzas sold is twice as many as large ones

∴ y = 2z ⇒ (3)

Substitute equation (3) in equation (2) to find x in terms of z only

∵ x = (2z) + z

∴ x = 3z ⇒ (4)

Substitute x in equation (1) by equation (4), and substitute y in equation (1) by equation (3)

∵ 10(3z) + 15(2z) + 40z = 600

- Simplify the left hand side

∴ 30z + 30z + 40z = 600

- Add like terms

∴ 100z = 600

- Divide both sides by 100

∴ z = 6

Substitute the value of z in equations (3) and (4) to find y and x

∵ y = 2(6)

∴ y = 12

∵ x = 3(6)

∴ x = 18

They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas

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Answer:

6cd+10c

Step-by-step explanation:

(c+c)(3d+5)

2c(3d+5)=6cd+10c

-3x +8y = -48

Add 3x to both sides:

8y = 3x -48

Divide each term by 8:

y = 3x/8 - 6

Answer Y=-45/8

Step-by-step explanation:

-3+8y=-48

-3+8y+3=-48+3

8y=-45

8y/8=-45/8

y=-45/8

Answer:

Diameter is 11.14

Step-by-step explanation:

c=dπ

so... 35=dπ

 solve for d:

      35/π=d

11.14=d

Answer:

11.14

Step-by-step explanation:

/calculators/circumference-calculator/

Answer:

Votes received by Billy =15

Step-by-step explanation:

Given:

Total students in the class = 20

Billy receives 3 times more vote than Keeton.

To find the number of votes Billy receives.

Solution:

Let number of votes Keeton gets [tex]=x[/tex]

∴ Billy received [tex]=3x[/tex] votes

Expression for total votes can be given by ⇒ [tex]x+3x[/tex]

Total votes =20 as number of students is 20.

So, the equation to find [tex]x[/tex] is:

[tex]x+3x=20[/tex]

Solving for  [tex]x[/tex]

⇒ [tex]4x=20[/tex]

Dividing both sides by 4.

[tex]\frac{4x}{4}=\frac{20}{4}[/tex]

∴ [tex]x=5[/tex]

∴ Votes received by Keeton = 5

Votes received by Billy = [tex]3\times 5[/tex] = 15

Answer:

c 6 times that the answer

Final answer:

The second cube's side length is 6 times that of the first cube because the volume of a cube is a cubic function of its side length, and taking the cube root of 1/216 gives us 1/6.

Explanation:

The student's question is asking to determine how many times larger the side length of the second cube is compared to the first cube, given that the volume of the first cube is 1⁄216 times the volume of the second cube. The volume of a cube is calculated by raising the side length to the third power (V = s3). Therefore, if we denote the side length of the first cube as s and that of the second cube as S, we have s3 = 1⁄216S3. To find the side length ratio, we take the cube root on both sides of the equation, yielding s = 1⁄6S, which means the second cube's side length is 6 times that of the first cube.

The correct answer to the question is C, 6 times

The value of x in the equation is 11/15.

To find the value of x in the equation 5 1 10 x - 6 4 5 = 3 1 4, we need to isolate x on one side of the equation. Here's how you can solve it:

Step 1: Add 645 to both sides of the equation.

Step 2: Subtract 314 from both sides of the equation.

Step 3: Simplify the equation.

Step 4: Divide both sides of the equation by 510.

Step 5: Simplify the fraction.

Therefore, the value of x in the equation is 11/15, which is option B) 11/15.

Answer:  4!

Step-by-step explanation:

You can turn 4 2/3 into improper fraction as 14/3. Then you have 14/3 and 6/7. You multiply both tops, then both bottoms. 6x14 is 84 and 3x7 is 21. You get 84/21 or 4. -viridiancat4, an 8th grader.

Answer: 16/7

Step-by-step explanation:

6/7 times 4 2/3 equals 16/7

Answer:

2.1 x 10^8

Step-by-step explanation:

2.1*10^8

The first number can not exceed ten so just count how many decimal place it would be and that should be the power.

Answer:

750:90

Step-by-step explanation:

12% of 750 is 90

8t+12s=180 and t=3s is the system of equations that represents the given scenario.

Step-by-step explanation:

Given,

Cost of a t-shirt = $8

Cost of a shorts = $12

t-shirt = t

shorts = s

Revenue earned = $180

According to given statement;

8t+12s=180

The store sold three times as many T- shirts as shorts.

t = 3s

8t+12s=180 and t=3s is the system of equations that represents the given scenario.

Keywords: linear equation, revenue

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Answer: 8t+12s=180;t=3s APEX

Answer:

y-6=-4(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

Where m=slope and (x1, y1) is a point on the line.

m=-4

y-6=-4(x-(-1))

y-6=-4(x+1)

Answer:

y-6=-4(x+1)

Step-by-step explanation:

Plato

Answer:

6/55 = x/44

55x = 6(44)

55x = 264

x = 264/55 = 4.8 miles

hope this helps<3

Step-by-step explanation:

Answer:

2060

Step-by-step explanation:

x=5*15

b=11*189

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

x=75

b=2079

b-x+56=2079-75+56=2060

Answer:

i just want points

Step-by-step explanation:

Answer:

2nd graph on edge 2020

Step-by-step explanation:

the line will cross the y-axis at y = 1.5 and the line will be a broken line

Inequality graphs

The inequality functions are not separated by an equal sign.

For the inequality 4x + 2y < 3, the lower portion of the graph will be shaded

Determine the y-intercept. If x = 0

4(0) + 2y < 3
2y < 3

y < 1.5

This shows that the line will cross the y-axis at y = 1.5 and the line will be a broken line as shown:

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W=L+2

A=48=L*W

48=L*(L+2)

48=L^2+L*2

0=L^2+L*2-48

L1=6

L2=-8 (can't be used since it's negative)

Lenght=6

Width=8

The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17

Step-by-step explanation:

Let us revise how to differentiate an equation with respect to x

If the equation is [tex]y = ax^{n}+b[/tex] , where a , b are constant

∵ P = 0.2x² - 17x - 10

- Let us differentiate each term

∵ The differentiation of 0.2x² is [tex]0.2(2)x^{2-1}=0.4x^{1}=0.4x[/tex]

∵ The differentiation of -17x is [tex]-17(1)x^{1-1}=-17x^{0}=-17(1)=-17[/tex]

∵ The differentiation of -10 is zero because the differentiation

    of the numerical term is 0

∴ The differentiation of P is P' = 0.4x - 17

The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17

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Answer:

13.  b.  4 + 5x = 29; $5.

14.  c.  74 + w = 3w + 6; 34 pounds.

15.  b.  $42.5.

Step-by-step explanation:

13. 4 + 5x = 29

5x = 29-4 = 25

x = 5.

14. 74 + w = 3w + 6

68 = 2w

w = 34.

15. Let x be the money he got last year. Then:

2x + 5 = 90

2x = 85

x = $42.5.

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{2})\implies y+4=\cfrac{3}{5}x-\cfrac{6}{5}[/tex]

[tex]\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y+4)=5\left( \cfrac{3}{5}x-\cfrac{6}{5} \right)}\implies 5y+20=3x-6\implies 5y=3x-26 \\\\\\ -3x+5y=-26\implies 3x-5y=26[/tex]

Answer:

y=4x+23

Step-by-step explanation:

The slope-intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10 is y = 4x + 23.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Slope-intercept form:

y = mx + b, where m is the slope and b is the y-intercept.

And we have the given equation:

12x - 3y = 10

Arranging the equation as slope-intercept form.

3y = 12x - 10

Divide by 3,

y = 4x - 10/3.

And this line is parallel to the required line.

So, the slope of the required line;

m = 4

Hence, the slope-intercept form,

y = 4x+b  equation 1

To find y-intercept:

We substitute the value of x and y from the point (-5,3) to the slope-intercept form,

y = 4x + b

(3) = 4(-5) + b

b = 20 +3

b = 23

Now, the equation 1

y = 4x + 23

Therefore, y = 4x + 23 is the required slope-intercept form.

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Answer:

420 cars were tested

Step-by-step explanation:

55/100=231/x

55x= 23100

x=420

Final answer:

The total number of cars tested can be calculated by dividing the number of cars that failed (231) by the percentage that failed (55%), resulting in 420 cars tested.

Explanation:

The question asks about the total number of cars tested based on the percentage that failed the safety test. To find the total, we can set up a proportion: if 55% of cars, or 0.55 of the total, failed the safety test and that number is 231, we can represent the total number of cars tested as 'X'. Using the proportion 0.55 = 231/X, we can solve for X, which represents the total number of cars tested.

Step by step, we can start by multiplying both sides of the equation by X to get 0.55X = 231, then we divide both sides by 0.55 to isolate X and find the total:

X = 231 / 0.55
X = 420

Therefore, 420 cars were tested.

Answer:

[tex]86\frac{2}{3}[/tex] yards²

Step-by-step explanation:

19 feet = [tex]\frac{19}{3}[/tex] yards

42 feet = 14 yards

14 × [tex]\frac{19}{3}[/tex] = [tex]\frac{266}{3}[/tex] = [tex]86\frac{2}{3}[/tex]

Answer:

18

Step-by-step explanation:

The lower base will 18units.

quadrilatral whose one opposite sides are parallel.

The tangent of an angle is the ratio between the opposite side of the angle and the adjacent side of the angle.

tanθ=opposite side/adjacent side

So according to asked question

in the trpezoid VWXZ,

VW || XZ

Height of trapezoid= VZ =WY=8√3

VW=10

∠YWX=30°

∠WXY=60°

In triangle ΔWYX,

∠WYX=90°

ΔWYX is a right angle triangle

so, tan∠YWX= XY/WY

⇒tan30°=XY/8√3

⇒1/√3=XY/8√3

⇒XY=8√3/√3

⇒XY=8 units

the length of the lower base ZX= ZY+XY = VW+XY = 10+8=18units

Therefore the lower base will 18units.

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Answer:

x=-5, 3

Step-by-step explanation:

(x+5)(x-3)=0

Apply the zero property,

set x+5=0 and x-3=0.

x=0-5=-5

x=0+3=3

x=-5, 3

Answer:

b&e

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation: In this problem, we're tossing a coin and we want to find the probability of tossing a heads.

Now, let's find the probability of tossing a heads.

Remember that a coin has two sides which are heads and tails. When you flip a coin, each side is as likely to come up as the other. This means that the probability of flipping heads is the fraction 1/2.

Since the probability of flipping a heads is 1/2, we can also say that the probability of flipping a heads is 50%.

Therefore, the probability of flipping a heads on a fair coin is 1/2.

Answer:

f(3)=7

Step-by-step explanation:

f(x)=7

f(3)=7

Answer:

10/31

Step-by-step explanation:

I'm pretty certain this is the answer, since 10/31 cannot be simplified any further; 31 being the total days in the month of May

A 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.

To find the fraction of the month that 10 days represent, we can divide the number of days represented by 10 by the total number of days in the month, which is 31.

Fraction = (Number of days represented) / (Total number of days in the month)

Fraction = 10 / 31

Therefore, 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.

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The manager should sale the bookshelf for $235.20

Step-by-step explanation:

Wholesale price of book shelf = $147.00

Mark up = 60% of original price

[tex]Mark\ up=\frac{60}{100}*147.00\\\\ Mark\ up=\frac{8820}{100}\\Mark\ up=\$88.20[/tex]

Total = Wholesale price + Mark up

[tex]Total= 147.00+88.20\\Total=\$235.20[/tex]

The manager should sale the bookshelf for $235.20

Keywords: mark up, percentage

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Answer:

45.64

Step-by-step explanation:

thats the answer

To round 45.6379 to the nearest hundred, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros.

To round 45.6379 to the nearest hundred, we look at the digit in the hundredth place, which is 5. Since 5 is greater than or equal to 5, we round up. Therefore, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros. The rounded number to the nearest hundred is 45.6400.

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