The table lists three points on the graph of a proportional relationship.
The equation for the relationship is y = 12 x
Answer:
x = 2 is the solution of the given equation
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given equation

squaring on both sides , we get

⇒ x + 2 = x²
⇒x² - x -2 =0
<u><em>Step(ii)</em></u>:-
Given x² - x -2 =0
⇒ x² - 2x + x - 2 =0
⇒ x ( x-2) + 1(x - 2) =0
⇒ (x + 1) ( x-2) =0
⇒ x = -1 and x =2
x = 2 is the solution of the given equation
<u><em>Verification</em></u>:-

Put x= 2


2 = 2
Answer:
The number of ways to select 2 cards from 52 cards without replacement is 1326.
The number of ways to select 2 cards from 52 cards in case the order is important is 2652.
Step-by-step explanation:
Combinations is a mathematical procedure to compute the number of ways in which <em>k</em> items can be selected from <em>n</em> different items without replacement and irrespective of the order.

Permutation is a mathematical procedure to determine the number of arrangements of <em>k</em> items from <em>n</em> different items respective of the order of arrangement.

In this case we need to select two different cards from a pack of 52 cards.
- Two cards are selected without replacement:
Compute the number of ways to select 2 cards from 52 cards without replacement as follows:



Thus, the number of ways to select 2 cards from 52 cards without replacement is 1326.
- Two cards are selected and the order matters.
Compute the number of ways to select 2 cards from 52 cards in case the order is important as follows:




Thus, the number of ways to select 2 cards from 52 cards in case the order is important is 2652.