Combine similar terms and apply the operation. Do NOT evaluate or simplify.1) 2x + 4 + 3x
2) 12 + 5x -8
3) 2x^2 + 3x^2 + 4x
4) 5ax - 12 - ax
5) 4xy + 2x + 3xy + x

Answer:

HOPE IT HELPS! PLS mark branliest

Step-by-step explanation:

Creating a "factor rainbow" and listing the factors of a number by drawing rectangles are two visual methods used to understand and identify the factors of a given number.

Similarities:

Visual Representation: Both methods rely on visual aids to help understand and identify factors.

Systematic Approach: They both provide a structured way to identify factors. They guide you through a process to ensure you don't miss any factors.

Differences:

Nature of Representation:

Factor Rainbow:

A factor rainbow is typically a circular or semi-circular diagram. The number is placed at the top, and its factors are shown as radii (lines from the center to the edge) of the circle.

Each factor is represented as an arc.

It's a visual representation that helps to see the pairs of factors and how they relate to each other.

Rectangles:

Drawing rectangles involves creating a rectangular grid or array, with the number of rows and columns corresponding to the potential factors.

Each rectangle represents a possible combination of factors, and the number of rectangles gives a visual representation of how many factors there are.

It's a more structured and organized representation.

Space Utilization:

Factor Rainbow:

It might be more space-efficient compared to drawing rectangles because it uses a circular or semi-circular layout.

Rectangles:

Depending on the size of the number and the number of factors, drawing rectangles can require a larger space as it involves creating a grid.

Ease of Identification:

Factor Rainbow:

It's useful for visualizing relationships between factors. It's good for understanding how factors pair up.

However, it may not be as straightforward for identifying all factors, especially for larger numbers.

Rectangles:

It provides a systematic method for identifying all factors. You can easily count the number of rectangles to find the total number of factors.

Flexibility for Visualization:

Factor Rainbow:

It can be a bit more flexible in terms of visualization as it allows for curvature in its representation.

Rectangles:

It's a very structured method, which may not lend itself to certain numbers as well (e.g., prime numbers).

In summary, both methods serve the purpose of visualizing factors, but they do so in different ways. The factor rainbow emphasizes relationships between factors, while drawing rectangles provides a structured method for systematically identifying all factors. The choice of method may depend on personal preference and the specific number being analyzed.

Answer:

Both the factor rainbow and drawing rectangles are methods used to visually list all the factors of a given number.

Similarities:

Visual Representation: Both methods provide a visual representation of the factors of a number, making it easier to understand and identify the factors.

Systematic Organization: Both methods organize the factors in a systematic way, allowing for a clear and organized display of the factors.

Differences:

Representation Style:

A factor rainbow is a simple visual representation where factors are listed in an arched shape, starting from 1 and extending to the given number.

Drawing rectangles involves creating a grid or rectangles to represent the factors, where the dimensions of the rectangles correspond to the pairs of factors.

Geometric vs. Linear:

Drawing rectangles uses a geometric representation (rectangles) to display the factors.

Factor rainbow is a linear representation, showcasing the factors in an arched arrangement.

Flexibility and Versatility:

Drawing rectangles allows for the demonstration of the commutative property of multiplication (e.g., for factors 6 and 10, you can create a rectangle with dimensions 6x10 or 10x6).

Factor rainbow is a simpler method and may not easily demonstrate the commutative property.

In summary, both methods serve the purpose of visually representing the factors of a number, but they use different styles and structures for this representation. Drawing rectangles involves a geometric approach, while the factor rainbow uses a linear arrangement. Drawing rectangles also offers additional versatility in illustrating the commutative property of multiplication.

Hey!

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Prefect Pipes: 120 + 40 = $160 (y-intercept)

No Leaks Here: 50 + 60 = $110 (y-intercept)

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Hour #1:

Prefect Pipes: 160 + 40 = $200

No Leaks Here: 110 + 60 = $170

Hour #2:

Prefect Pipes: 200 + 40 = $240

No Leaks Here: 170 + 60 = $230

Hour #3:

Prefect Pipes: 240 + 40 = $280

No Leaks Here: 230 + 60 = $290

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$280 < $290

After 3 hours Perfect Pipes is less expensive than No Leaks Here!

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Hope This Helped! Good Luck!

Answer:  After 3.5 hours, Perfect pipes is less expensive than No leaks here.

Step-by-step explanation:

Let the number of hours be 'h'.

So, Perfect pipes charges $120 plus $40 per hour.

so, our equation becomes,

No leaks charges $50 plus $60 per hour.

So, our equation becomes,

According to question, Perfect pipes is less expensive than no leaks here after how many hours.

So, it becomes,

Hence, After 3.5 hours, Perfect pipes is less expensive than No leaks here.