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The Aztec Empire was much larger than the state of Ohio, with an estimated area of around 80,000 square miles at its peak.

This vast empire encompassed much of central Mexico and included cities such as Tenochtitlan, the capital of the Aztec Empire. The area of Ohio is approximately 44,825 square miles, not 4,000 square miles. At its peak, the Aztec Empire covered an area of about 80,000 square miles. To compare the two:

1. Note the area of Ohio: 44,825 square miles
2. Note the area of the Aztec Empire at its peak: 80,000 square miles
3. Compare: The Aztec Empire was larger, covering nearly 1.78 times the area of Ohio.

In conclusion, the Aztec Empire was significantly larger than the state of Ohio at its peak, with an area estimate of around 80,000 square miles.

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In mathematics, two straight lines can mean a number of things depending on the context. In general, a straight line is a geometric object that has no curvature and extends infinitely in both directions.

When two straight lines are considered together, they can either be parallel, meaning they will never intersect, or they can be intersecting, meaning they will cross at exactly one point. If the two lines are parallel, they will have the same slope, and if they are intersecting, the lines will have different slopes.

The slope-intercept equations for the two straight lines in analytical geometry are written as y = mx + b, where m is the slope, x and y are the coordinates of a point on the line, and b is the y-intercept.

In conclusion, two straight lines can have different meanings in mathematics depending on the context, such as parallel or intersecting, which can be represented by their equations in slope-intercept form.

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Answer:

The left side of the equation is ignored

i is treated as -1, which it is not, it is instead the square root of negative 1.

To solve it properly we get:

(2 - 5i)(5 + 2i)

= 10 + 4i - 25i - 10i²

= 10 + 21i + 10

= 20 - 21i

Answer:

The error is that, the student replaced i with -1 which is wrong as i = √-1

And he has replaced i^2 with 1 while i^2 = -1

Step-by-step explanation:

Given two numbers that are being multiplied are:

(2-5i)(5+2i)

We will solve the question to get the right result so that the error can be detected.

So, multiplying both

\(= 2(5+2i)-5i(5+2i)\\=10+4i-25i-10i^2\\=10-21i-10(-1)\ \ \ as\ i^2 = -1\\=10-21i+10\)

The error is that, the student replaced i with -1 which is wrong as i = √-1

And he has replaced i^2 with 1 while i^2 = -1

Answer: sqrt216

Step-by-step explanation:

First, find line segment AD

6^2 + b^2 = 12^2

36 + b^2 = 144

b^2 = 108

b = sqrt108

Now, to find x

sqrt108^2 = x^2 = 18^2

108 + x^2 = 324

x^2 = 216

x = sqrt216

not sure if I should simplify?

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."

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Answer:

1) The volume of the model is 3159 in.³

2) The height of the real facility is 61.94 ft

Step-by-step explanation:

1) The parameters given are;

Volume of the Estabrook hall = 117 ft³

Scale of model = 1:4

For the scale factor of a volume, we have;

\(Volume \, scale \, factor =\left (\frac{a}{b} \right )^3 = \left (\frac{1}{4} \right )^3 = \frac{1}{64}\)

That is the volume of the model is 1/64 times the volume of the actual Estabrook hall restrooms or

\(\frac{1}{64} \times 117 \, ft^3= 1\tfrac{53}{64} \, ft^3\)

∴ The volume of the model = 1.83 ft.³

1 ft.³ = 1728 in.³

∴ 1.83 ft.³ = 1.83 ft.³ × 1728 in.³/ft.³ = 3159 in.³

2) Where the model of the floor has an area of 117 in.²

Therefore, since the volume of a rectangular prism shape = Floor area × Height, we have

The height, h = Volume/(floor area) = 3159/117 = 185.8 in.

From a scale of 1:4, we have that the height of the real facility = 4 × 185.8 in.

Hence, the height of the real facility = 743.3 in = 61.94 ft.

Answer:

$3.50

Step-by-step explanation:

4 2/3 x 0.75 = $3.50

Answer:$3.5

Step-by-step explanation:

The solution  in explanation given below.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

In this question, we are asked to give the reason why if we blend 2 scoops of chocolate ice cream with 1 cup of milk, we will have a milkshake with a stronger chocolate flavor than if 3 scoops are blended with 2 cup of milks.

This is a very interesting and relatable question.

To solve this question, we will have to use the aspect of mathematics that is referred to as rates or proportions.

In the first mix, what we have is that we are going to mix 2 scoops of chocolate ice cream with 1 cup of milk. What is noticeable here is that we have 2 scoops of chocolate per 1 cup of milk or there is a 2 to 1 ratio of chocolate ice cream to cup of milk.

Now in the second mix, we are mixing 3 scoops of chocolate with 2 scoops of milk. What we have here is a ratio of 3 to 2. This means that we are having a ratio of 1.5 to 1 of the number of scoops of chocolate ice cream to number of cups of milk.

Looking at this, we can deduce that a 2 to 1 ratio is a greater value compared to a 1.5 to 1 ratio. This is the reason why we are having a stronger chocolate flavor in the first mix than the chocolate flavor in the second mix.

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Okay, here we have this:

Considering the provided system of equations, we are going to graph the system, so we obtain the following:

Graphing the system we have:

We can see that the two functions do not intersect at any time, therefore the system of equations has no solution in the set of real numbers.

Answer: x= -1  y= -5

Step-by-step explanation: Multiply by 2 to eliminate the x

4x - 10y = 46

-4x + 5y  = -11

-5y = 35

 y= -5

Put -5 back in the equation for the letter y, and you will get x = -1

ANSWER :

139 feet

EXPLANATION :

The surveyor is 150 feet away from the base of the pole.

The transit is 4 feet tall and the angle of elevation to the top of the pole is 42 degrees.

The illustration will be :

We have a right triangle with an angle of 42 degrees.

The side opposite to the angle is x and the side adjacent to the angle is 150

Using Tangent function :

The height of the pole is x + 4

That will be 135 + 4 = 139 ft

The number of hours it would take Ganymede to complete a full rotation is 171.25 hours.

The first step is to convert days to hours. A day is equivalent to 24 hours. In order to convert days to hours, multiply 7 by 24.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

1 day = 24 hours

24 x 7 = 168 hours

The second step is to convert minutes to hours, In order to do this, divide 15 by 60. Division is the process that is used to determine the quotient of two or more numbers.

60 minutes = 1 hour

15 / 60 = 0.25 hours

Now, add all the converted hours together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.

Total hours = 168 hours + 3 hours + 0.25 hours = 171.25 hours

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Step-by-step explanation:

in an arithmetic sequence any new term is created by adding a defined constant to the previous term.

a1 = 2

the defined constant to be added = common difference = a2 - a1 = 11

so,

a2 = 2 + 11 = 13

a3 = a2 + 11 = a1 + 2×11 = 2 + 22 = 24

a4 = a3 + 11 = a1 + 3×11 = 2 + 33 = 35

Step-by-step explanation:

divide each side by 5 is the correct justification please give thanks

Answer:

x = 10.0

Step-by-step explanation:

Using the geometric mean formula:

       x                projection

-----------------  =  ---------------

entire base              x

Here, the projection is 5 and the entire base is (20 + 5). So:

       x                5

------------  =  ------------

      25              x

Cross multiply:

x² = 25 (5)

x² = 100

√x² = √100

x = 10

Answer:

x < 3

Step-by-step explanation:

Answer:

x<3

Step-by-step explanation:

    4x-7<5

+ 7               +7

     4x<12

÷4                  ÷4

   x<3

Answer:

what is this question asking for

Using the knowledge of angle pairs that are formed by transversal and parallel lines: <1 and <3 are supplementary, so also are <2 and <4, because they are same-side interior angles.

One of the angle pairs that are formed by parallel lines and transversal is called the same-side interior angles, or consecutive angles. They lie on the same side of the transversal that intersects the two parallel lines.

Based on the same-side interior angles theorem, these consecutive angles are proven to be equal or supplementary to each other. That is, their angle measure will be equal to 180 degrees if added.

In the same vein, if we apply this to how the interior angles of a trapezoid relate, we can deduce the following:

Angle 1 and angle 3 are supplementary, and Angle 2 and angle 4 are supplementary because they are consecutive angles or same-side interior angles.

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Answer: $29.78

Step-By-Step:

You take 42.54 and multiply it by 0.3 and you will get around 12.762. Then you will take 12.762 and subtract it from 42.54 and get 29.778. You will then round it to 29.78.

Answer:

45 (1+2)

Step-by-step explanation:

Answer:5,5,4

Step-by-step explanation:5+4=9

9*5=45

Answer:

D.

Step-by-step explanation:

Not for sure sorry but i think its D or A so so sorry

To minimize the penalty cost, the linear programming problem is formulated as a goal programming problem by introducing deviation variables (d₁, d₂, d₃) and surplus variables (s₁, s₂), with the objective function Z = 100d₁ + 50d₂ + 10d₃ and the corresponding constraints.

To formulate the given linear programming problem as a goal programming problem to minimize the penalty cost, we can introduce deviation variables on each constraint and assign penalty weights to these variables. The goal is to minimize the total penalty cost:

d₁: Deviation variable for the first constraint (3x₁ + 2x₂ ≥ 30)

d₂: Deviation variable for the second constraint (2x₁ + x₂ ≥ 40)

d₃: Deviation variable for the third constraint (5x₁ + 3x₂ ≤ 50)

We also need to introduce positive surplus variables to ensure the original constraints are not violated:

s₁: Surplus variable for the first constraint (3x₁ + 2x₂ ≥ 30)

s₂: Surplus variable for the second constraint (2x₁ + x₂ ≥ 40)

Now, let's formulate the linear programming model with penalty costs and deviation variables:

Minimize:

Z = 100d₁ + 50d₂ + 10d₃

Subject to:

3x₁ + 2x₂ - d₁ + s₁ = 30

2x₁ + x₂ - d₂ + s₂ = 40

5x₁ + 3x₂ + d₃ ≤ 50

x₁, x₂, d₁, d₂, d₃, s₁, s₂ ≥ 0

The objective function minimizes the penalty cost by summing the products of deviation variables and their respective penalty weights.

The first constraint includes the deviation variable d₁ to measure the deviation from the minimum requirement of 30. The surplus variable s₁ ensures that the original constraint is not violated.

Similarly, the second constraint includes the deviation variable d₂ and the surplus variable s₂.

The third constraint includes the deviation variable d₃ to penalize any excess beyond the upper limit of 50.

All decision variables (x₁, x₂, d₁, d₂, d₃, s₁, s₂) are non-negative.

Solving this goal programming problem will minimize the penalty cost associated with failing to satisfy the original constraints.

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Answer:

Step-by-step explanation:

You want to know which functions have 5 in their domain, and what the function value is at x=5.

It is more convenient to do the second part first, as that tells you the answer to the first part:

f(5) = 5² -3·5 = 25 -15 = 10 . . . . 5 is in the domain

g(5) = (5 -5)/5 = 0/5 = 0 . . . . 5 is in the domain

h(5) = √(5 -10) = √(-5) . . . . UNDEFINED; 5 is not in the domain

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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Answer:

y=-3+15

Step-by-step explanation:

Answer: $6.75

Step-by-step explanation:

25 hours times $9= $225/week

3% increase from $9.00= $0.27

$9.27 times 25 hours= $231.75

$231.75-$225= $6.75 more per week

There would be around \(2,714 mm3\) of material required for each cylindrical cracker.

What is the Volume of a Cylinder ?

Volume of a cylinder = π r² h

The volume of the material used for each cylindrical cracker = Volume of entire cylindrical cracker - volume of cylindrical hole

Radius of entire cracker \((r) = 16/2 = 8 mm\)

Height (h) = 18 mm

Volume of the entire cracker = π(8²)(18) ≈ 3,619 mm³

Radius of hole \((r) = 8/2 = 4 mm\)

Height \((h) = 18 mm\)

Volume of the entire cracker = π(4²)(18) ≈ 905 mm³

The volume of the material used for each cylindrical cracker \(= 3,619 - 905 = 2,714 mm³\)

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