<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
The student is incorrect, the actual x-intercept is (5, 0).
<h3>Is the student correct or incorrect?</h3>
Here we have the equation:
x + 2y = 5
The student says that the x-intercept is the point (0, 5).
So if you look at the point you already can see that the student is incorrect, this is because the x-intercept always must have a y-value of 0. (the graph only intercepts the x-axis when y = 0).
So the point (0, 5) can't be an x-intercept.
For the given function:
x +2y = 5
The x-intercept is given by:
x + 2*0 = 5
x = 5
So it is (5 , 0).
If you want to learn more about x-intercepts:
brainly.com/question/3951754
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Answer:
£ 2.8
Step-by-step explanation:
4 kg = 1.60
1 kg= 1.6/4 = £0.4
7 kg = 0.4*7 = £2.8
Answer:
1/2, 1/3, 1/4, 1/5, 1/6
Step-by-step explanation:
You would have to evaluate the problem so it would be 940
