Answer:
x = 1
Step-by-step explanation:
Sum the coefficients of the polynomial, that is
1 - 6 + 11 - 6 = 0
Hence x = 1 is a root and (x - 1) is a factor of the polynomial
Answer: 17 patients stayed for longer than 10 minutes.
Step-by-step explanation:
Let x represent the number of patients that stayed for longer than 10 minutes.
The doctor charges $21.80 for consultations that last less than 10 minutes and $27.50 for those that last longer than 10 minutes. Yesterday the doctor earned $1077.90. If 28 consultations lasted less than 10 minutes, it means that
28 × 21.80 + x × 27.50 = 1077.90
610.4 + 27.5x = 1077.9
27.5x = 1077.9 - 610.4
27.5x = 467.5
x = 467.5/27.5
x = 17
Answer:
(5a - [2b - 7c]) and (5a + [2b + 7c])
Step-by-step explanation:
Factor 25a^2 - 4b^2 + 28bc - 49c^2.
Note that - 4b^2 + 28bc - 49c^2 involves the variables b and c, whereas 25a^2 has only one variable. Thus, try to rewrite - 4b^2 + 28bc - 49c^2 as the square of a binomial:
- 4b^2 + 28bc - 49c^2 = -(4b^2 - 28bc + 49c^2), or
-(2b - 7c)^2.
Thus, the original 25a^2 - 4b^2 + 28bc - 49c^2 looks like:
[5a]^2 - [2b - 7c]^2
Recall that a^2 - b^2 is a special product, the product of (a + b) and (a - b). Applying this pattern to the problem at hand, we conclude:
Thus, [5a]^2 - [2b - 7c]^2 has the factors (5a - [2b - 7c]) and (5a + [2b + 7c])
37 is a prime number which means it is only divisible by 1 and 37, therefore the only number that can go into 37 and 100 is 1.
Hope it helps. ☺
