How are equations and inequalities used in the real world?
Inequalities are arguably used more often in “real life” than equalities. Businesses use inequalities to control inventory, plan production lines, produce pricing models, and for shipping/warehousing goods and materials. Look up linear programming or the Simplex method.
What are some examples of real life inequalities used with math?
| Situation | Mathematical Inequality |
|---|---|
| Speed limit | Legal speed on the highway ≤ 65 miles per hour |
| Credit card | Monthly payment ≥ 10% of your balance in that billing cycle |
| Text messaging | Allowable number of text messages per month ≤ 250 |
| Travel time | Time needed to walk from home to school ≥ 18 minutes |
How is solving a system of equations algebraically similar to solving the system by graphing?
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
How can systems of linear equations with two variables be solved using algebraic methods?
Algebraic Methods for Solving Systems
- Use the substitution method. Solve a system of equations using the substitution method.
- Use the elimination method without multiplication. Solve a system of equations when no multiplication is necessary to eliminate a variable.
- Use the elimination method with multiplication.
What are some real life examples of equations?
Real life examples include:
- Calculating wages based on an hourly pay rate.
- Calculating medicine doses based on patients’ weights.
- Calculating the perimeters of squares.
- Hiring a car if a deposit is paid and there is an hourly charge.
What are examples of exponential functions in real life?
Exponential functions are often used to represent real-world applications, such as bacterial growth/decay, population growth/decline, and compound interest. Suppose you are studying the effects of an antibiotic on a certain bacteria.
What is an exponential situation?
Exponential growth is the increase in number or size at a constantly growing rate. In exponential growth, a population’s per capita (per individual) growth rate stays the same regardless of the population size, making it grow faster and faster until it becomes large and the resources get limited.
Why Exponential is used?
Exponential functions can be used to model growth and decay. Exponential functions are ever-increasing so saying that an exponential function models population growth exactly means that the human population will grow without bound.
What are the two types of exponential functions?
The two types of exponential functions are exponential growth and exponential decay.
Why do we use E in math?
The number e is an important mathematical constant, approximately equal to 2.71828 . When used as the base for a logarithm, we call that logarithm the natural logarithm and write it as lnx .
Why is it called linear equation?
Why is it Called a Linear Equation? It is called a linear equation, because if you try to plot the graph of the given equation with variables x and y on a graph with axes as x and y, you would get a line as your result. Hence, it is called a linear equation.
What is K in a linear equation?
yx=k. Where k is a constant. Rewriting this equation by multiplying both sides by x yields: y=kx. Notice that this is a linear equation in slope-intercept form, where the y -intercept b is equal to 0 .
Is X Y 0 a linear equation?
Hint: The equations x=0 represents y -axis and y=0 represents x –axis. Complete step-by-step answer: The equations given are x=0, y=0. Similarly for the equation y=0, the graph would be XOX’ (since the value of y is fixed as zero and the value of x can be anything).
How do you find the value of k in linear equations in two variables?
Then, by substituting all the values of constants in the condition of inconsistency and by using the first two equality relation, we get the value of k. Complete step by step answer: In this question, we are supposed to find the value of k for the pair of linear equations 4x-5y=5 and kx+3y=3 is inconsistent.
What is the value of K that will make the given system of linear equation inconsistent?
k=2