7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is:

. With this consideration, we can continue.
(i) Let E the expression that we are analyzing:

Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.
(ii) Manipulating the expression:

So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.
8) Let E the expression that we want to calculate:

Multiplying by (2-1) in the both sides:

Repeating the process, we obtain:
Answer:

Step-by-step explanation:
To factor the expression, remove the greatest common factor or GCF from each term. Both terms share in common xy. The expression becomes:

What remains in the parenthesis is a different of perfect squares. Factor the difference of perfect squares into two binomials of the form (x+a)(x-a) where a is the square root of
.
So the expression becomes:

553,000 is the answer for rounding up
Answer:
30 miles
Step-by-step explanation:
The rate is distance /time
50 /15 =10/3 miles per hour
To find the distance traveled in 9 minutes, multiply the rate by the time
distance = 10/3 *9 = 30
30 miles