Select The Correct Answer.Find The Value Of $h(-67)$ For The Function Below:$h(x) = -49x - 125$A. -1.18 B. 3,283 C. \$-3,408$[/tex\] D. 3,158

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Introduction

In mathematics, solving linear equations is a fundamental concept that is used extensively in various fields, including algebra, geometry, and calculus. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear equations of the form h(x) = -49x - 125, where h(x) is a function that takes an input x and returns an output.

Understanding the Function

The given function is h(x) = -49x - 125. This function takes an input x and returns an output that is calculated by multiplying x by -49 and then subtracting 125. To find the value of h(-67), we need to substitute -67 for x in the function.

Substituting x = -67

To find the value of h(-67), we need to substitute -67 for x in the function h(x) = -49x - 125. This means we need to multiply -67 by -49 and then subtract 125.

Calculating h(-67)

h(-67) = -49(-67) - 125

To calculate this, we need to follow the order of operations (PEMDAS):

  1. Multiply -67 by -49: -67 × -49 = 3293
  2. Subtract 125 from 3293: 3293 - 125 = 3168

Conclusion

Therefore, the value of h(-67) is 3168. This means that when x = -67, the function h(x) = -49x - 125 returns an output of 3168.

Answer

The correct answer is D. 3,168.

Discussion

This problem requires the application of linear equations and the order of operations (PEMDAS). The function h(x) = -49x - 125 is a linear equation, and to find the value of h(-67), we need to substitute -67 for x and follow the order of operations. This problem is a good example of how linear equations can be used to model real-world situations and how the order of operations is essential in solving mathematical problems.

Tips and Tricks

  • When solving linear equations, always follow the order of operations (PEMDAS).
  • When substituting values into a function, make sure to replace the variable with the correct value.
  • When calculating the value of a function, make sure to follow the order of operations and perform the calculations correctly.

Related Topics

  • Linear equations
  • Functions
  • Order of operations (PEMDAS)
  • Algebra
  • Geometry
  • Calculus

Practice Problems

  1. Find the value of h(50) for the function h(x) = 2x + 5.
  2. Find the value of f(-3) for the function f(x) = -x + 2.
  3. Find the value of g(10) for the function g(x) = x - 3.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations of the form h(x) = -49x - 125. In this article, we will provide a Q&A guide to help you understand and apply the concepts of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. For example, the equation 2x + 5 = 11 is a linear equation.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I apply the order of operations to solve a linear equation?

A: When solving a linear equation, you need to apply the order of operations to evaluate any expressions inside parentheses, exponents, multiplication and division, and addition and subtraction.

Q: What is a function?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A function takes an input and returns an output.

Q: How do I find the value of a function?

A: To find the value of a function, you need to substitute the input value into the function and evaluate the expression.

Q: What is the difference between a linear equation and a function?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. A function is a relation between a set of inputs and a set of possible outputs.

Q: How do I determine if an equation is a linear equation?

A: To determine if an equation is a linear equation, you need to check if the highest power of the variable(s) is 1.

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

  • Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
  • Standard form: Ax + By = C, where A, B, and C are constants.
  • Point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to plot two points on the graph and draw a line through them.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that is used extensively in various fields. By understanding and applying the concepts of linear equations, you can solve a wide range of problems and model real-world situations. We hope this Q&A guide has been helpful in understanding and applying the concepts of linear equations.

Practice Problems

  1. Find the value of h(50) for the function h(x) = 2x + 5.
  2. Find the value of f(-3) for the function f(x) = -x + 2.
  3. Find the value of g(10) for the function g(x) = x - 3.

Related Topics

  • Linear equations
  • Functions
  • Order of operations (PEMDAS)
  • Algebra
  • Geometry
  • Calculus

Tips and Tricks

  • When solving linear equations, always follow the order of operations (PEMDAS).
  • When substituting values into a function, make sure to replace the variable with the correct value.
  • When calculating the value of a function, make sure to follow the order of operations and perform the calculations correctly.