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Learning Task 3:
Solve.
1. What is the area of the rectangle whose length is (x + 5) and width (x - 5)?
2. What is the area of the square whose sides measure (3x + 4)?
3. The area of the rectangle is 3x2 + 7x - 6, what is the length if the width is
(x + 3)
4. What is the average speed of the car that covers a distance of
(2y3-7y2 + 5y - 1) km in (2y-1) hour?
5. Multiply (m2 + 2m-2) by the sum of (m + 3 ) and (2m - 3)​

Sagot :

MrRoyal

Answer:

[tex]Area = x^2- 25[/tex]

[tex]Area =9x^2 +24x + 16[/tex]

[tex]Length = (3x -2)[/tex]

[tex]Speed = \left(y^2-3y+1\right)[/tex]

[tex]Product = 3m^3 + 6m^2 - 6m[/tex]

Step-by-step explanation:

Solving (1):

[tex]Length = (x + 5)[/tex]

[tex]Width = (x - 5)[/tex]

Required

Calculate Area

[tex]Area = Length * Width[/tex]

[tex]Area = (x + 5) * (x - 5)[/tex]

[tex]Area = x^2 + 5x - 5x - 25[/tex]

[tex]Area = x^2- 25[/tex]

Solving (2):

Given

[tex]Length = (3x + 4)[/tex]

Required: Calculate Area

[tex]Area =Length * Length[/tex]

[tex]Area =(3x + 4) * (3x + 4)[/tex]

[tex]Area =9x^2 + 12x + 12x + 16[/tex]

[tex]Area =9x^2 +24x + 16[/tex]

Solving (3):

[tex]Area = 3x^2 + 7x - 6[/tex]

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

Required: Calculate Length

[tex]Area = Length * Width[/tex]

[tex]Length = \frac{Area}{Width}[/tex]

[tex]Length = \frac{3x^2 + 7x - 6}{x + 3}[/tex]

Factorize the numerator

[tex]Length = \frac{3x^2 + 9x -2x - 6}{x + 3}[/tex]

[tex]Length = \frac{3x(x + 3) -2(x + 3)}{x + 3}[/tex]

[tex]Length = \frac{(3x -2) (x + 3)}{x + 3}[/tex]

Divide by x + 3

[tex]Length = (3x -2)[/tex]

Solving (4):

[tex]Distance = (2y^3 - 7y^2 + 5y -1)[/tex]

[tex]Time = 2y - 1[/tex]

Required: Determine the average speed

This is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{2y^3 - 7y^2 + 5y -1}{2y - 1}[/tex]

Factorize the numerator

[tex]Speed = \frac{\left(2y-1\right)\left(y^2-3y+1\right)}{2y - 1}[/tex]

[tex]Speed = \left(y^2-3y+1\right)[/tex]

Solving (5):

Multiply [tex](m^2 + 2m - 2)[/tex] by sum of [tex](m + 3)[/tex] and [tex](2m - 3)[/tex]

First, calculate the sum:

[tex]Sum = m + 3 + 2m - 3[/tex]

[tex]Sum = m + 2m+3 - 3[/tex]

[tex]Sum = 3m[/tex]

Then, the product

[tex]Product = (m^2 + 2m - 2)(3m)[/tex]

[tex]Product = 3m^3 + 6m^2 - 6m[/tex]

younglargeamount

Answer:

Step-by-step explanation:

Solving (1):

Required

Calculate Area

Solving (2):

Given

Required: Calculate Area

Solving (3):

Required: Calculate Length

Factorize the numerator

Divide by x + 3

Solving (4):

Required: Determine the average speed

This is calculated as:

Factorize the numerator

Solving (5):

Multiply  by sum of  and  

First, calculate the sum:

Then, the product

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