Diagram 2 shows a piece of rectangular card in grey colour The white region is a ribbon with width y cm. The area of the card which is not covered by the ribbon is 96 cm.

Form an equation, in terms of x and y, based on the statements above.

Solution:

we have given the length of the rectangular card-

and, width-

now, the area of the card will be- length×width.

so, we have-

we also have given the length of ribbon-

and, width-

so, area of the ribbon is-

length×width

now the area of shaded gray region will be-

Hence, the required expression would the above expression.

the balance is found at the link

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for