"SLC-S22W1/Variables and Expressions"

Hello friends,
Welcome to my blog! Let's get this task done with the required simplicity and steps.

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Task 1

• Explain any two variables and expressions types other than that which are explained in this course.(Practical and algebric examples are required!)

Constant Variable

Just like the name, a constant variable remains unchanged all through the use in a mathematical process or calculation.

Practical example of a constant variable is that of a gravitational force with a (g) with value 9.81m/s². This is a constant variable that is applied all through a calculation process without changing its value.

For example, if we are to calculate the weight (W) of an object thrown up with mass (m) of 15kg...
Then, Weight (W) = Mass (m) x Force of gravity (g)
Therefore, W = 15 x 9.81
W = 147.15

For an Algebric example: wenhaveba scenario where a single number is a constant.
In an equation where X = 4y+10.
10 is rhe constant variable and remains unchange until the final equation is achieved.
For instance, if y = 2:
Then, X = 4(2)+10 = 8+10
X = 18

Rational Expressions

These are situations where quantities are represented between each other. Both quantities are polynomials. Quantities here are the denominator and numerator.

For example could be a typical scenario of the speed of a car covered over a distance and time.
Speed = s
Distance = d
Time = t
Therefore, S =d/t

For instance, if a car covers 200 km in 4 hours, the speed can be determined as;

S = 200km/4hr = 50 km/hr

For an Algebric example where both quantities are represented well, lets take a look here;
If Y = x²-1/x-1
Therefore, Y = (x-1)(x+1)/x-1
Then, Y = x+1

Task 2

Show your way of evaluating of an algebraic expression if values of variables are given? Step by step explanation required!
(The more you will be detailed and accurate,the more your task will be perfect!)

Let's get to evaluate this algebraic expression;

E (y, z) = 6y² + 8z - 10
Where y = 4, z = 6

Let's start by inputing the given values of y and z into the algebraic expression.

E (4, 6) = 6(4)² + 8(6) - 10

Expanding the exponent, (4)² = 16
E (4, 6) = 6(16) + 8(6) - 10

Now, let's remove the brackets by multipling with the corresponding values with them.

E (4, 6) = 6×16 + 8×6 - 10
E (4, 6) = 96 + 48 - 10

Let's firstly add up the values and then subtract from the constant value of 10.

E (4, 6) = 144 - 10
E (4, 6) = 134

Therefore our evaluated algebraic expression with E(y, z) when y and z are 4 and 6 respectively is 134.

Therefore E(4,6) = 134.

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Task 3

• Simplify this expression: 3(2x - 1) + 2(x + 4) - 5
• Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2
• Solve the following equation: 2x + 5 = 3(x - 2) + 1
(You are required to solve these problems at paper and these share clear photographs for adding a touch of your creativity and personal effort which should be marked with your username)

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Task 4

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.

Number of white bread sold = x
Number of whole wheat bread sold = x + 30
(We already know that whole wheat is selling 30 more pieces than the white bread)

However, total bread sold is 250.
Therefore; white bread + (whole wheat bread + 30) = 250

Representing this; x + (x+30) = 250

FOR PROFIT MARGINS:
Profit from white bread = $0.50
Profit from whole wheat bread = $0.75

Therefore profit from white bread would be 0.50x
And profit from whole wheat bread would be 0.75 (x+30)

Representing this;
Profit = 0.50x + 0.75 (x+30)
Profit = 0.50x + 0.75x + 22.5
Profit = 1.25x + 22.5

• 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.
(Solve the above scenerio based questions and share step by step that how you reach to your final outcome)

Cost of renting a car for the day = 2x + 15
(Therefore, this also represents the same value if hours of usuage is less than 4 hours)
So, when x < 4 hrs = 2x+15

Secondly when x > 4hrs = 3x -2

So we have different costs;
When x < 4hrs, Cost = 2x +15
When x > 4 hrs, Cost = 3x - 2

These cost values can be applied given the number of hours car is used.

Thank you.

I am inviting, @missyleo, @ngoenyi, and @chant.