Math 8_Q1 Week 1

Designing a Window

Designing a rectangular window involves balancing aesthetics, functionality and sustainability through optimal dimensions. The process begins with determining the ideal width and height, considering wall space, architectural style and functional needs. The width-to-height aspect ratio is crucial, ensuring visual appeal and functionality while considering orientation (north, south, east, west) for natural light and ventilation. Dimensional constraints, such as minimum/maximum sizes, building codes, safety standards and structural limitations, must also be considered.

Architect Ana is designing rectangular windows, and one of them has an area represented by the trinomial 6x²+11x+4. She needs to factor the trinomial completely to determine the dimensions of the window.

To factor the trinomial 6x2+11x+4, Ana first needs to find two numbers whose product is a • c = 24 and whose sum is b = 11. What are these two numbers?

• 4 and 6

• 2 and 12

• 8 and 3

• 7 and 4

Designing a Window

Designing a rectangular window involves balancing aesthetics, functionality and sustainability through optimal dimensions. The process begins with determining the ideal width and height, considering wall space, architectural style and functional needs. The width-to-height aspect ratio is crucial, ensuring visual appeal and functionality while considering orientation (north, south, east, west) for natural light and ventilation. Dimensional constraints, such as minimum/maximum sizes, building codes, safety standards and structural limitations, must also be considered.

Architect Ana is designing rectangular windows, and one of them has an area represented by the trinomial 6x²+11x+4. She needs to factor the trinomial completely to determine the dimensions of the window.

Ana splits the middle term 11x using the two numbers 8 and 3. What is the trinomial rewritten with the middle term split?

• 6x2 + 8x + 3x + 4

• 6x2 - 3x + 8x + 4

• 6x2 - 8x - 3x + 4

• 6x2 + 3x- 8x + 4

Designing a Window

Designing a rectangular window involves balancing aesthetics, functionality and sustainability through optimal dimensions. The process begins with determining the ideal width and height, considering wall space, architectural style and functional needs. The width-to-height aspect ratio is crucial, ensuring visual appeal and functionality while considering orientation (north, south, east, west) for natural light and ventilation. Dimensional constraints, such as minimum/maximum sizes, building codes, safety standards and structural limitations, must also be considered.

Architect Ana is designing rectangular windows, and one of them has an area represented by the trinomial 6x²+11x+4. She needs to factor the trinomial completely to determine the dimensions of the window.

After grouping the terms and factoring out the common factors, Ana finds the dimensions of the window are represented by (2x+1) and (3x+4). How does this relate to the original polynomial 6x2+11x+4?

• The product of (2x+1) and (3x+4) equals the original trinomial, representing the area of the window.

• The sum of (2x+1) and (3x+4) equals the original trinomial.

• The dimensions (2x+1) and (3x+4) are unrelated to the trinomial.

• The product of (2x+1) and (3x+4) is the perimeter of the window.

Painting a Wall with a Design

A decorator is designing a rectangular wall mural with a patterned border. The total area of the wall, including the border, is represented by the polynomial x²+10x+21, where x is the width of the border in meters. The mural itself (without the border) is a rectangle with an area of 21 m². The decorator needs to factor the polynomial to determine the dimensions of the entire wall, including the border.

What is the factored form of the polynomial x^2 + 10x +21?

• (x+7)(x+3)

• (x+21)(x+1)

• (x+5)(x+5)

• (x+10)(x+2)

Painting a Wall with a Design

A decorator is designing a rectangular wall mural with a patterned border. The total area of the wall, including the border, is represented by the polynomial x²+10x+21, where x is the width of the border in meters. The mural itself (without the border) is a rectangle with an area of 21 m². The decorator needs to factor the polynomial to determine the dimensions of the entire wall, including the border.

If the border width is x=2, what are the total dimensions of the wall, including the border?

• 9meters by 5 meters

• 7meters by 6 meters

• 10meters by 7 meters

• 8meters by 4 meters

Painting a Wall with a Design

A decorator is designing a rectangular wall mural with a patterned border. The total area of the wall, including the border, is represented by the polynomial x²+10x+21, where x is the width of the border in meters. The mural itself (without the border) is a rectangle with an area of 21 m². The decorator needs to factor the polynomial to determine the dimensions of the entire wall, including the border.

How does the factored form (x+7)(x+3) help in solving the problem?

• It represents only the area of the border around the mural.

• It is used to calculate the perimeter of the wall.

• It shows how the mural's area can be divided into equal parts.

• It provides the total area of the wall, including the border, by multiplying the wall's length and width.

Sharing Study Expenses

Three friends are preparing for an exam and decide to share the cost of a subscription to an online study platform. The total cost paid by one friend is represented by the rational algebraic expression:

s1/(s1 + s2 + s3),

Where , s1, s2, and s3 are the hours each friend spends using the platform. To ensure fairness, they need to analyze and simplify the expression to determine each person's contribution to the total subscription cost.

If the first friend uses the platform for 10 hours (s1= 10), the second friend for 15 hours (s2 = 15), and the third friend for 5 hours (s3 = 5), what is the proportion of the cost paid by the first friend?

• 1030

• 13

• 12

• 14

Sharing Study Expenses

Three friends are preparing for an exam and decide to share the cost of a subscription to an online study platform. The total cost paid by one friend is represented by the rational algebraic expression:

s1/(s1 + s2 + s3),

Where , s1, s2, and s3 are the hours each friend spends using the platform. To ensure fairness, they need to analyze and simplify the expression to determine each person's contribution to the total subscription cost.

How does the rational algebraic expression s1/(s1+s2+s3) help ensure fairness in sharing the subscription cost?

• It calculates the total hours spent on the platform by all friends.

• It determines the percentage of the cost each friend should pay based on their usage.

• It reduces the total subscription cost for all friends.

• It ensures each friend gets the same amount of platform usage time.

Fuel Efficiency of a Car

A car's fuel efficiency, in kilometers per liter (km/L), is represented by the rational algebraic expression:

d/(t+2),

where d is the distance traveled (in kilometers), and t is the time taken (in hours). The additional +2 accounts for traffic delays. The driver wants to analyze the fuel efficiency under different driving conditions to plan a long journey effectively.

If the car travels a distance of 240 km in 4 hours, what is the fuel efficiency based on the expression dt+2?

• 30km/L

• 40km/L

• 60km/L

• 20km/L

Fuel Efficiency of a Car

A car's fuel efficiency, in kilometers per liter (km/L), is represented by the rational algebraic expression:

d/(t+2),

where d is the distance traveled (in kilometers), and t is the time taken (in hours). The additional +2 accounts for traffic delays. The driver wants to analyze the fuel efficiency under different driving conditions to plan a long journey effectively.

If the car's fuel efficiency is 25km/L, what is the total time taken to travel a distance of 300 km?

• 12 hours

• 10 hours

• 8 hours

• 6 hours