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 .......... significant figure is 4870. 4. A dealer...

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 .......... significant figure is 4870.

4. A dealer sold a painting for \$800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.

5. Solve the simultaneous equation:

3x= 7y

12y= 5x-1

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1. Simplify x(3x+2) - (2x-4)

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

First let us expand brackets:

==> x*3x + x*2 - 2x + 4

==> 3x^2 + 2x- 2x + 4

==> 3x^2 + 4

2. f(x)= (x+2) (2x-1)

Evaluate f(5.5)

f(5.5) = (5.5 + 2)(2*5.5 - 1)

= (7.5)(11-1)

= (7.5)*(10)

= 75

3. (a) 4872 correct to 1 significant figure is ... 4870

(b) 4872 correct to .....1..... significant figure is 4870.

4. A dealer sold a painting for \$800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.

Let us assume that the cost = x

Then the porofit is 25% of the cost = (25/100) * x

But she sold it for 800,

Then the sale price = cost price + profit

==> 800 = x + (25/100)x

==> 800 = x + 0.25*x

==> 800 = 1.25*x

==> x= 800/1.25

==> x= 640

Then the paintng cost = \$640

5. Solve the simultaneous equation:

3x= 7y...... (1)

12y= 5x-1..........(2)

From (1) , divide by 3:

==> x= (7/3)y

Now substitute in (2),

12y = 5(7/3)y - 1

12y = (35/3)y - 1

12y - (35/3)y = 1

(36-35)/12 *y = 1

1/12 * y = 1

==> y= 12

x= (7/3)*12 = 7*4 = 28

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Simplify

1.

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

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

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

=3x^2+4 is the simplified form.

2.

f(x)= (x+2) (2x-1)

=x*2x -x*1+2*2x-2*1

=2x^2-x+4x-2

=2x^2-3x-2 is the simplified form.

Evaluate f(5.5).

f(x) is only a very geneal way of naming a function. Unless the  function is known we cannot evaluate f(x).We say substitute 5.5 in place of x and we get f(5.5).

Examples:

If f(x) = 2^x, then f(5.5) = 2^5*5 = 32 sqrt2. Iff(x) = x^2+3x+1, then f(5.5) evaluted gives (5.)^2+3(5.5)+1 = 30.25+16.5+1 = 47.75.

3. (a) 4872 correct to 1 significant figure is 4000

(b) 4872 correct to  3  significant figure is 4870.

4. A dealer sold a painting for \$800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.

So the price paid by her  = {Sold price /(100+25)}100 = 800*100/125 = 640

5. Solve the simultaneous equation:

3x= 7y...............(1)

12y= 5x-1.........(2)

Eq(1)*5+(2)*3 gives:

15x +36y = 35y +15x-3.

15x on both sides gets cancelled.So the equation becomes:

36y = 35y-3

36y-35y = -3

y = -3.

Substitute y = -3 in (1):

3x= 7(-3)

x= 7(-3)/3 = -7.

x= = -7 and y = -3 are the solutions.

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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

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)}.