<u>Question 8</u>
a^2 + 7a + 12
= (a+3)(a+4)
When factorising a quadratic, the product of the two factors should equal the constant term (12), and the sum of the two factors should equal the linear term (7). To find the two factors, list out the factors of 12 (1x12, 2x6, 3x4) and identify the pair that adds up to 7 (3+4).
An alternative method if you get stuck during your exam would be to solve it algebraically using the quadratic formula and then write it in the factorised form.
a = (-7 +or- sqrt(7^2 - 4(1)(12)) / 2(1)
= (-7 +or- sqrt(1))/2
= -3 or -4
These factors are the negative of the values that would go in the brackets when written in factorised form, as when a = -3 the factor (a+3) would equal 0. (If it were positive 3 instead, then in the factorised form it would be a-3).
<u>Question 10</u>
-3(x - y)/9 + (4x - 7y)/2 - (x + y)/18
Rewrite each fraction with a common denominator so you can combine the fractions into one.
= -6(x - y)/18 + 9(4x - 7y)/18 - (x + y)/18
= (-6(x - y) + 9(4x - 7y) - (x + y)) /18
Expand the brackets and collect like terms.
= (-6x + 6y + 36x - 63y - x - y)/18
= (29x - 58y)/18
= 29/18 x - 29/9 y
Answer:
a) -10 b) 7
Step-by-step explanation:
a) 2(x+ 3) = x - 4
2x + 6 = x - 4
2x - x = -6 - 4
x = -10
b) 4(5x - 2) = 2(9x + 3)
20x - 8 = 18x + 6
20x - 18x = 6 + 8
2x = 14
x = 14/2
x = 7
Answer:
#1. X=3 and #2. Y=9
Step-by-step explanation:
Glad i could help, give me a follow, so if you need help with any other question, im here.
Answer:
2bm + 7an
Step-by-step explanation:
Multiply.
8bm - 6an - bm + 5an - 5bm + 8an
Combined like terms:
8bm - <em>6an</em> - bm + <em>5an</em> - 5bm + <em>8an</em>
= 2bm + 7an
Answer:
Step-by-step explanation:
The mode is the number of most repeated data in the set.
Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).
If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.
There is no change in mode, so the mode decrease is zero.
