1. Simplify x(3x+2) - (2x-4) 2. f(x)= (x+2) (2x-1) Evaluate f(5.5)3. (a) 4872 correct to 1 significant figure is.....? (b) 4872 correct to...

We'll simplify by removing the
brackets:

x(3x+2) - (2x-4) = x*3x + 2*x - 2x +
4

We'll eliminate like
terms:

3x^2 + 4

The simplified
expresion is:

x(3x+2) - (2x-4) = 3x^2 +
4

We'll evaluate
f(5.5):

f(5.5) = 3(5.5)^2 +
4

f(5.5) = 3*30.25 + 4

f(5.5)
= 90.75 + 4

f(5.5) =
94.75

4. Let's note the price
of the painting as x.

The profit she made is
calculated as a difference between the price she sold the painting and the price she
bought it.

800 - x 

But the
profit is 25% on the price she bought the painting.

800-x =
25*x/100

800 - x =
0.25*x

We'll add x both
sides:

800 = 1.25*x

We'll
divide by 1.25 both sides:

x =
800/1.25

Price of aquisition = x = 640 monetary
units

So, the pinting was sold at the price
of 800 monetary units and the aquisition price was 640 monetary
units.

5. We'll solve the
system of equations:

3x= 7y
(1)

12y= 5x-1 (2)

We'll solve
the system using the substitution method.

We'll divide the
first equation by 3:

x = 7y/3
(3)

We'll substitute (3) in
(2):

12y= 5x-1

12y= 5*7*y/3 -
1

12y = 35y/3 - 1

We'll
multiply -1 by 3:

12y = (35y -
3)/3

We'll cross multiply:

36y
= 35y - 3

We'll subtract 35y both
isdes:

y =
-3

We'll substitute y in (3), to find out
the value of x:

x = 7y/3

x =
7*(-3)/3

We'll reduce like
terms:

x =
7*(-1)

x =
-7

The solution of the system
of equations is {(-7 , -3)}.