Step-by-step explanation:
6x - 15 = 75, 6x = 90, x = 15.
2(2x - 1) = 46, 2x - 1 = 23, x = 12.
x + (x - 10) = 26, 2x = 36, x = 18.
5x - 3x = 10, 2x = 10, x = 5.
Hence the equations
in increasing order of x-values are:
5x - 3x = 10,
2(2x - 1) = 46,
6x - 15 = 75, and
x + (x - 10) = 26.
Answer:
27/20
Step-by-step explanation:
The absolute value of any expression is always positive or zero
3/5 + 3/4
Add the fractions
27/20
Solution
27/20
Alternate form
1 7/20, 1.35
Answer:
x = 0/2
x = 0
Step-by-step explanation:
4(x+8)-2(x-7) = 46
Expanding the brackets
4x +32 - 2x +14 = 46
2x + 46 = 46
2x = 46-46
2x = 0
x = 0/2
x = 0
<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 ratio would be
45/100
45 to 100
45:100
Hope this helps!
