# 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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### 3 Answers

**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 paint ng 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 **

** 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.**

** **

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)}.**