SLC-S22W1/Variables and Expressions
Hello steemians,
Algebra is an essential discipline of mathematics that finds its use in many areas of daily and academic life, ranging from elementary levels to advanced applications, due to its importance, this algebra course particularly captivated me, and I chose to actively participate in it to deepen my knowledge.
Explain two types of variables and expressions other than those explained in this course.
When we talk about variables in algebra, these are symbols, generally represented by letters like x, y, or z, which can take different values in formulas or equations, these variables make it possible to model changing phenomena, among others. The many types of variables, two distinct examples are discrete variables and continuous variables.
Discrete variables are variables that take on specific and distinct values, often used to count elements, for example, if we are looking to count the number of students present in a class, this value could be 0 , 25 or 30, but it could never be a fraction like 25.5, let's take another practical case: if a family counts the number of shoes in a closet, they may have 8, 10 or 12 shoes, but not 8.3, a discrete variable therefore represents integer quantities, and its specific character facilitates its use in situations where fractions have no meaning.
In contrast, continuous variables are those that can take an infinite number of values in a given interval, which makes them an essential tool for measuring physical quantities or fluid phenomena, for example, the outside temperature at a given moment could be measured as 23.4 °C, or even more precisely as 23.456 °C, and so on, the measurement of the speed of a car is another example: a car can drive at 50 km/h, but also at 50.7 km/h or 50.76 km/h, depending on the precision required, continuous variables therefore allow to capture progressive variations or nuances that would be impossible to describe with discrete variables.
As for expressions, they are made up of combinations of variables, constants and mathematical operations such as addition, subtraction, multiplication and division, among the many types of algebraic expressions, two notable examples are fractional expressions and radical expressions.
A fractional expression is an expression that includes a fraction involving variables or constants. For example, if a person wants to divide x candies among y children, the amount of candies per child would be given by the expression x/y. Another fractional expression could be 12/x + 8/7, where x is a variable that could represent a changing quantity, these expressions are widely used in scenarios that involve ratios or proportional sharing.
A radical expression, on the other hand, is characterized by the presence of a root symbol, such as a square root or a cube root, for example, the square root of an area can be expressed as √16, which gives a result of 4, a more complex expression could be √(15x 3 ) + 7/9 , where the root includes a variable, these expressions are commonly used in physics or geometry to model relationships between different measurements.
Show how to evaluate an algebraic expression if the values of the variables are given.
The given expression is Exp = 2X² + 3XY - Y², and it is specified that X = 4 and Y = 2 .
The values X = 4 and Y = 2 are inserted directly into the expression, which gives: Exp = 2(4)² + 3(4)(2) - (2)², this step is essential because it makes it possible to transform the algebraic expression into a numerical form ready to be simplified.
We begin by evaluating the terms with exponents: (4)² = 16 and (2)² = 4, by replacing these results in the expression, it becomes Exp = 2(16) + 3(4) (2) - 4, at this stage, all the powers have been calculated and all that remains is the multiplications to perform.
We first multiply 2 * 16, which gives 32, then 3 * 4 * 2, which gives 24, by substituting these results, the expression then becomes Exp = 32 + 24 - 4, the multiplications are thus performed, and the expression is simplified for the final step.
We start by adding the first two terms: 32 + 24 = 56, then we subtract 4, which gives Exp = 52, The final result of the evaluation of the expression is therefore 52.
Simplify this expression: 3(2x - 1) + 2(x + 4) - 5
The first step is to expand the terms in parentheses by applying the distributive property: 3(2x - 1) gives 6x - 3 and 2(x + 4) gives 2x + 8, after this expansion the expression becomes 6x - 3 + 2x + 8 - 5, then, in the second step, the similar terms are combined, the terms containing x are added, i.e. 6x + 2x = 8x, while the constants -3 + 8 - 5 cancel to give zero, The simplified expression is therefore E = 8x.
Evaluate this expression: (x^2 + 2x - 3) / (x + 1) when x = 2
The first step is to substitute x with 2 in the expression, which gives E = 2^2 + 2(2) - 3/2 + 1. The second step is to calculate the numerator, by performing the operations we obtain 2^2 = 4, then 2(2) = 4, which leads to 4 + 4 - 3 = 5, the numerator is therefore 5, then the denominator is calculated by adding 2 + 1, which gives 3. The expression then becomes E = 5/3, which can also be written in decimal form as 1.66.
Solve the following equation: 2x + 5 = 3(x - 2) + 1
The first step is to expand the term 3(x - 2), which gives 3x - 6, adding 1 the equation becomes 2x + 5 = 3x - 5, in the second step the equation is rearranged to isolate terms containing x on one side and constants on the other, subtracting 3x from both sides gives 2x - 3x = -5 - 5, which simplifies to -x = -10, finally, in the last step, we divide both sides by -1 to get 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.
To solve the problem and write an expression representing the total daily profit of the bakery, we start by analyzing the data, The number of loaves of white bread sold is indicated by the variable (x), while the number of loaves of bread of whole wheat is 30 more than the number of loaves of white bread, which means that the number of loaves of whole wheat bread is (x + 30), the bakery's profit per loaf of white bread is 0.50 $, while the profit per loaf of whole wheat is $0.75, the goal is to find an expression for total daily profit.
To calculate the profit on white bread, we multiply the number of loaves x by $0.50 to get 0.50x, for the profit on whole wheat bread, we multiply the number of loaves x + 30 by 0.75 $, which gives us 0.75(x + 30), therefore the total daily profit of the bakery becomes the sum of the profits of the two types of bread.
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.
To solve this problem and write an expression for the total cost of renting a car for x hours, you first need to analyze the available data, the cost of renting a car for one day is given by the expression ** 2x + 15**, where x represents the number of hours, if the rental period is more than 4 hours, the rental company offers a package of 3x - 2 dollars.
In this case, the total cost depends on the number of hours x and the rental duration required, if x > 4 (i.e. more than 4 hours), the package expression **3x - 2 ** is used instead of base cost 2x + 15, so the general expression for total cost can be written as follows:
Costo total = (2x + 15) + (3x - 2)
To simplify the expression, we start by removing the parentheses and write all the terms together: 2x + 15 + 3x - 2, then we group like terms together, where terms with x are combined together and constant terms are grouped separately , combining 2x and 3x gives 5x, and adding 15 and subtracting 2 gives 13, therefore the simplified expression for total cost is 5x+13.
Thank you very much for reading, it's time to invite my friends @graceleon, @adrianagl, @karianaporras to participate in this contest.
Best Regards,
@kouba01
