Den URA - Add/sub/monomials Practice
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Rectangle ABCD has a length represented by the expression 2x - 3, and a width
represented by the expression 4x + 5. Rectangle PQRS has a length represented by
the expression x - 1, and a width represented by the expression 3x + 2. Which are used to represent the difference in the perimeters of
Rectangle ABCD and Rectangle PQRS

Perimeter of ABCD - Perimeter of PQRS = 4x + 2

Step-by-step explanation:

i. For rectangle ABCD;

length, l = 2x -3

width, w = 4x + 5

Perimeter of a rectangle = 2(l + w)

Perimeter of ABCD = 2((2x -3) + (4x + 5))

                                = 2(2x -3 + 4x + 5)

                                = 2(6x + 2)

Perimeter of ABCD = 12x + 4

ii. For rectangle PQRS;

length, l = x - 1

width, w = 3x + 2

Perimeter of a rectangle = 2(l + w)

Perimeter of PQRS = 2((x - 1) + (3x + 2))

                                = 2(x - 1 + 3x + 2)

                                = 2(4x + 1)

Perimeter of PQRS = 8x + 2

So that,

Perimeter of ABCD - Perimeter of PQRS = (12x + 4) - (8x + 2)

                                          = 12x + 4 - 8x - 2

                                          = 4x + 2

Perimeter of ABCD - Perimeter of PQRS = 4x + 2

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.