/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 96 Use a calculator to evaluate eac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 96

Use a calculator to evaluate each expression for \(x=23\) and \(y=72\). \(16 y-20 x+x^{3}\)

Short Answer

Expert verified
The expression evaluates to 12859.

Step by step solution

01

Substitute Values

Begin by substituting the given values of the variables into the expression. Replace \(x\) with 23 and \(y\) with 72 in the expression. The expression becomes: \[16(72) - 20(23) + 23^3\]
02

Compute Each Term

Calculate each term separately. First, compute \(16(72)\): \(16 imes 72 = 1152\).Next, compute \(20(23)\): \(20 imes 23 = 460\). Finally, compute \(23^3\): \(23 imes 23 imes 23 = 12167\).
03

Perform the Operations

Now substitute the values found back into the expression and perform the arithmetic operations: \[1152 - 460 + 12167\] First, subtract 460 from 1152: \[1152 - 460 = 692\]. Then add 12167 to the result: \[692 + 12167 = 12859\].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution is one of the foundational concepts in prealgebra that allows you to replace variables in an expression with known values. When you substitute, you simplify the problem into actual numbers you can work with. To substitute correctly:
  • Identify the variables in your expression. Here, they are \(x\) and \(y\).
  • Insert the given values for these variables. In this case, replace \(x\) with 23 and \(y\) with 72.
  • Rewrite the entire expression with these values in place of the variables, turning it from a problem involving variables to a purely numerical expression.
The original expression, \(16y - 20x + x^3\), becomes \(16(72) - 20(23) + 23^3\) after substitution. This step sets the stage for performing calculations with actual numbers. By following these steps, you ensure accuracy and clarity in solving the problem.
Arithmetic Operations
Arithmetic operations involve basic mathematical tasks like addition, subtraction, multiplication, and division. In this problem, we focused on multiplication, addition, and subtraction:
  • Multiplication: This is the process of finding the product of numbers. For instance, to calculate \(16 \times 72\), you perform multiplication to find the product, which is 1152.
  • Subtraction: Here, you calculate the difference between two numbers. For example, subtracting 460 from 1152 gives you 692.
  • Addition: Finally, you add numbers together to find their sum, as when you add 692 and 12167 to reach the final answer, 12859.
Each operation must be performed according to the precedence rules, meaning multiplication and division take priority over addition and subtraction. Ensuring the order is correct is crucial to reaching the right answer.
Exponents
Exponents represent repeated multiplication of the same number. In the expression \(x^3\), it means multiplying the number \(x\) by itself three times. Here's how you approach exponents:
  • Understand that \(23^3\) means \(23 \times 23 \times 23\).
  • Calculate the exponentiation step-by-step. First, find \(23 \times 23 = 529\), then multiply by 23 again to get 12167.
  • Pay close attention during calculations to avoid errors, as exponentiation can lead to large numbers quickly.
Mastering exponents is critical because they show up frequently in algebra and beyond. Handling them correctly paves the way for more advanced topics in mathematics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Without computing it, tell whether the average of \(38,27,58,\) and 43 is \(17 .\) Explain why it is possible or why it is not.

Identify each answer as correct or incorrect. Use addition to check. If the answer is incorrect, write the correct answer. $$ \begin{array}{r} 741 \\ -56 \\ \hline 675 \end{array} $$

The state of Delaware has 2029 miles of urban highways and 3865 miles of rural highways. Find the total highway mileage in Delaware.

Perform each indicated operation. Find the product of 19 and 4

Write each whole number in expanded form. $$47,703,029$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.