<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
4/10 × 1/6 = 2/30
You can cross cancel 4 and six...then multiply 2/10 × 1/3 which equals 2/30
If you want you can simplify 2/30 to 1/15
<span>The tortoise is runing one mile per hour the entire race.
The hare is runing 3/4 only the first half.
If we multiply by 2 totis =2 miles and hare =1.50 the hare need to run 1/2 or .50 faster to beat the tortis.</span>
Answer:
D
Step-by-step explanation:
If you look at the right side of each piecewise function, you will see the x-values. That is what we will be focusing on in this explanation. All four equations have x <u>></u> 4, and we know that to be true. If you look at the equation on the graph going South West, you will see that the endpoint is at x=1. Only 1 equation, D, has this in the piecewise function. To confirm it is D, you can see that 1<x<4 is also in the piecewise function, and all the values line up with their corresponding y-values.
Hope this helps! :)
Answer:C
Step-by-step explanation:
180-(60+40)=80°
C=80°
20/sin80. =a/sin40
a=(20sin40)÷sin80
=13.1
