<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:259
Step-by-step explanation:
Its summation of 6^i-1 for values of I = 1,2,3 and 4
= 6^0 + 6^1 +6^2 +6^3
=259
1.) 3.5% * 500 = 17.5
2.) 70.0% * 50 = 35.0
3.) 25.0% * 440 = 110.0
4.) 10.0% * 46 = 4.6
Answer:
Part a) The expression is 
Part b) Customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00
Step-by-step explanation:
<u><em>The complete question is</em></u>
A spice store charged 2.75 for 25 grams of paprika. It also charges 5% of the purchase price for shipping any order.
Part a) Write and simplify an expression to determine the cost of buying and shipping x ounces of paprika. Use 1 ounce = 28 grams
Part b) Can a customer buy 2.5 ounces of paprika and have it shipped for less than 8.00? Explain
step 1
Convert grams to ounces
Remember that

To convert grams to ounces divide by 28

The unit price is

Let
x ----> the number of ounces of paprika
y ----> the cost of buying and shipping x ounces of paprika
5%=5/100=0.05
![y=3.09x+(3.09x)0.05\\y=3.09x[1+0.05]\\y=3.2445x](https://tex.z-dn.net/?f=y%3D3.09x%2B%283.09x%290.05%5C%5Cy%3D3.09x%5B1%2B0.05%5D%5C%5Cy%3D3.2445x)
Part b) For x=2.5 oz
substitute in the equation


therefore
Customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00