Answer:
m + m = 36
18 + 18 = 36
Step-by-step explanation:
<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:
$22.50....................
Answer:
Rachel
Step-by-step explanation:
We need to measure how far (towards the left) are the students from the mean in<em> “standard deviations units”</em>.
That is to say, if t is the time the student ran the mile and s is the standard deviation of the class, we must find an x such that
mean - x*s = t
For Rachel we have
11 - x*3 = 8, so x = 1.
Rachel is <em>1 standard deviation far (to the left) from the mean</em> of her class
For Kenji we have
9 - x*2 = 8.5, so x = 0.25
Kenji is <em>0.25 standard deviations far (to the left) from the mean</em> of his class
For Nedda we have
7 - x*4 = 8, so x = 0.25
Nedda is also 0.25 standard deviations far (to the left) from the mean of his class.
As Rachel is the farthest from the mean of her class in term of standard deviations, Rachel is the fastest runner with respect to her class.
