a) Factorise 3x²-x-4.
b) Make D the subject of the given formula B=(c-a on 4)D
c) Solve the simultaneous equations. Give your
answer in the simplest fraction.
2x+2y =1
-X+4y=2
a) To factorise 3x²-x-4, we need to find two numbers that multiply to 3(-4)=-12 and add up to -1. These numbers are -4 and 3. Therefore, we can write the expression as:
3x² - x - 4 = 3x² - 4x + 3x - 4
= x(3x - 4) + 1(3x - 4)
= (3x - 4)(x + 1)
Therefore, the factorised form of 3x²-x-4 is (3x - 4)(x + 1).
b) To make D the subject in the formula B=(c-a) on 4)D, we need to isolate D on one side of the equation.
B = (c-a)/4)D
B = (c-a)/4 * D
D = 4B/(c-a)
Therefore, D = 4B/(c-a)
c) To solve the simultaneous equations:
2x + 2y = 1
-x + 4y = 2
From the first equation, we have:
y = (1 - 2x) / 2
Now we substitute y into the second equation:
-x + 4((1 - 2x) / 2) = 2
-x + 2 - 4x = 2
3x = 0
x = 0
Now, substitute x back into the first equation to solve for y:
2(0) + 2y = 1
2y = 1
y = 1/2
Therefore, the solution to the simultaneous equations is x = 0 and y = 1/2.