"SLC-S22W1/Variables and Expressions" by @rossnenye
| Explain any two variables and expressions types other than that which are explained in this course.(Practical and algebric examples are required!) |
|---|
| What is a Variables? |
|---|
This is a Symbol which is mostly letters example X, Y, C that represents an unknown number or Value.
| Types of Variables |
|---|
- Discrete variables
This is a type of variable that has a specific separate values. They're no values like decimals or fraction between them. They're mostly whole numbers
Example
They're 50 Apples in the Basket.
They're 4 Standing fans in the House.
Continuous Variables
These are Variables that can take an Infinite number of Values in a given Interval and because of these, it's an important tool used for measuring Physical quantities. It can be divided into smaller Values.
Example
The height of a room after measurement is 165.2cm.
The weight of this phone is 55.1kg
Her first semester GPA is 3.8
| What is an Expression? |
|---|
This is the combination of numbers, variables, constants and mathematical operations like multiplication, addition, subtraction. In Mathematics, they help to indicate the relationship between variables and numbers.
| Types of Expression |
|---|
- Fractional expression
This is a type of expression that contains variables or numbers inform of fractions. It contains Numerator(The polynomial on top) and Denominator(The Polynomial on the bottom) This two Polynomials is separated with a fraction bar
Example
(4x² +3x +1)/ (x +1)
- Radical expression
It has a radical symbol which represents a square or cube root.
Example
√(y + 2) -1)/(y -3)
Show your way of evaluating of an algebraic expression if values of variables are given? Step by step explanation required!
So from Elementary School, we were taught by our Teacher how to use BOBMAS, to solve Mathematical problems. BODMAS is an acronym which stands for BRACKET, ORDER, DIVISION, MULTIPLICATION, ADDITION and SUBTRACTION
- Brackets
This is the first thing to solve in any given problems. For example, in the expression (8 + 2) × 2, we would first calculate what is inside the brackets, after the calculation, the answer is 10.
- Orders
This refers to powers or exponents, so after opening the Bracket, then we would solve for powers or exponentials next. For instance, in the expression 4², it means 4 x4 = 16
- Division
The next thing to do is here is division, which is division of numbers. So if I have an equation like 16 ÷ 4 X 2 =
16 divided by 4
= 4 X 2
=8
- Multiplication
After division, the next rule is multiplication so if given this equation 9 ÷ 3 x 3 =
Then the first thing to do is to divide 9 by 3 to get 3
Then
3 x 3 = 9
- Addition
This is the adding of numbers, so in an equation after you're done with the multiplication then you add any figure with the addition sign (+)
Example 3 × 8 ÷ 2+ 2
So first of all we divide 8 by 2 to get 4
So 3 x 4 +2
Then we multiply 3 x 4 to get 12 +2
Then addition =
12+2 = 14
- Substraction:
It's the same process as addition, the only difference is that we're removing
Example: 3 × 8 ÷ 2+ 2
So first of all we divide 8 by 2 to get 4
So 3 x 4 +2
Then we multiply 3 x 4 to get 12 +2
Then subtracting=
12 - 2 =14
| Simplify this expression: 3(2x - 1) + 2(x + 4) - 5 |
|---|
Step 1
Opening brackets....
To open this bracket, in 3(2x-1) use 3 to multiply what is inside the bracket to get 6 x -3....equ 1
Use 2 to multiply what is inside the second bracket
= 2(X+4)-5
=2 x+ 8 - 5....equ 2
Substituting the values we have
6x-3+2x +8 -5...equ 3
So we can't solve this equation like this because they are unlike terms. So moving over to the next step.
Step 3
Collecting like terms
6x +2x -3 + 8 - 5
8 x = 0
The final answer= 8x because 0 can't divide 8x.
| Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2 |
|---|
The first thing to do here is to substitute x with 2 in the equation.
Equation= 2^2 +2(2) -3/2 +1.
Step 2
The next thing is to find the Numerator = 2^2 +2(2) -3 =
2 X 2 + 2 x2 -3 =
4 +4 -3 = 5
The Numerator= 5
The next step is finding the Denominator=
2+1 =3
So to find the final result = Numerator/Denominator= 5/3 = 1.66
| Solve the following equation: 2x + 5 = 3(x - 2) + 1 |
|---|
2x+5 =3(x-2) -1
First of all remove bracket
2x + 5=3(x-2) + 1=
2x + 5 = 3x- 6+1=
2x +5 =3x -5
Second step is collecting like terms=
2x -3x = -5 - 5
-x = -10
Then divide both sides by -1 to get 10
Therefore x =10
| Suppose there's a bakery selling a total of 250 loaves of bread per day. They are selling whole wheat and white bread loaves with numbers of whole wheat loaves sold being 30 more than the number of white bread loaves. If x is representing number of white bread loaves sold out and bakery is making a profit of $0.50 for each white bread loaf and $0.75 for each whole wheat loaf then please write an expression for representing bakery total daily profit. |
|---|
The expression for the bakery's total daily profit
Based on the question, x is = the number of white bread loves sold.
x + 30 is the number of whole wheat loaves of bread that are sold.
250 is the total loaves of bread sold per day.
x + (x + 30) = 250
Simplify;
2x + 30 = 250
2x = 220 implies x = 110
However, according to the question,
110 = The white bread loaves sold
Then, 110 + 30 = 140 which is the whole wheat loves sold.
The expression for the profit =
Profit per white bread loaf = $0.50
Profit per whole wheat loaf = $0.75
Total profit = (0.50x) + (0.75(x + 30)
Here, we would simplify the expression by substituting the values thus.
Total profit = 0.50x + 0.75x + 0.75(30)
Total profit = 1.25x + 22.5 answer.
| Suppose that cost of renting a car for a day is re-presented by the expression 2x + 15 and here x is the number of hours in which car is rented. If the rental company offers a package of 3x - 2 dollars for customers who take car at rent for more than 4 hours then write an expression for the total cost of renting the car for x hours and show how you simplify it. |
|---|
Total Cost of Renting the Car:
According to the questions, The first thing to do is writing the expression of the cost of renting the car for x hours which will be expressed as
2x + 15
Additional package cost for more than 4 hours of renting will be 3x - 2
Total Cost = (2x + 15) + (3x - 2)
At this point, we will have to simplify the expression by combining the like terms which will be expressed it in the following ways.
To simplify the expression, we would start by removing the Brackets
(2x +15) (3x -2)=
2x + 15 + 3x - 2
The next step is collecting like terms=
2 x +3 x + 15 - 2
5 x + 13 answer.
It was an amazing exercising my brain and solving this Mathematical problems. I invite @chommygift, @ukpono and @blessedbee to participate in this contest.
Cc:
@khursheedanwar