/*! 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 16 Evaluate each expression for ( \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 16

Evaluate each expression for ( \(\boldsymbol{a}\) ) \(x=4\) and \((\boldsymbol{b}) x=6\). \(5 x^{2}\)

Short Answer

Expert verified
For \(x=4\), the result is 80. For \(x=6\), the result is 180.

Step by step solution

01

Understand the expression

The given expression is a mathematical formula: \(5x^2\). This means we need to multiply 5 by the square of \(x\).
02

Step 1a: Substitute \(x = 4\)

First, substitute \(x = 4\) into the expression: \(5(4)^2\).
03

Step 1b: Calculate \(4^2\)

Next, calculate the square of 4: \(4^2 = 16\).
04

Step 1c: Multiply by 5

Finally, multiply 16 by 5: \(5 \times 16 = 80\). Thus, the expression evaluated for \(x = 4\) is 80.
05

Step 2a: Substitute \(x = 6\)

Now, substitute \(x = 6\) into the expression: \(5(6)^2\).
06

Step 2b: Calculate \(6^2\)

Next, calculate the square of 6: \(6^2 = 36\).
07

Step 2c: Multiply by 5

Finally, multiply 36 by 5: \(5 \times 36 = 180\). Thus, the expression evaluated for \(x = 6\) is 180.

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 most fundamental concepts in algebra. It involves replacing a variable with a given number or value. For example, in the expression \(5x^2\), if we are given \(x = 4\), we substitute 4 wherever there is an x in the expression. So, \(5x^2\) becomes \(5(4)^2\). This method helps us convert algebraic expressions into numerical computations, making it easier to evaluate them.

Here are some important points to consider for substitution:
  • Identify the variable in the expression.
  • Replace every occurrence of the variable with the given number.
  • Ensure that you maintain the structure of the expression while substituting.
Substitution simplifies the problem into something more manageable, allowing you to proceed to the next calculation steps such as squaring or multiplying.
Squaring a Number
Squaring a number means multiplying that number by itself. It is a basic operation in algebra. For instance, squaring 4 gives us \(4 \times 4 = 16\). In our expression \(5x^2\), once we substitute \(x\) with 4, we need to square the 4:

\( (4)^2 = 16 \).

This is because any number raised to the power of 2 is multiplied by itself. Another example is squaring 6:

\((6)^2 = 36\).

The squaring operation is crucial when dealing with quadratic expressions. Remember these key points about squaring:
  • Ensure you multiply the number by itself, not by any other number.
  • Squaring a negative number will result in a positive number, as multiplying two negative numbers yields a positive.
  • Double-check your calculations to avoid errors.
Understanding how to square numbers accurately is essential for correctly evaluating algebraic expressions.
Multiplication
Multiplication is the arithmetic operation of scaling one number by another. After substituting the variable and squaring the number in the expression \(5x^2\), the next step involves multiplication. For example, once we have \(4^2 = 16\), in the expression \(5(4)^2\), we need to multiply 5 by 16:

\(5 \times 16 = 80\).

This operation combines two quantities to produce a product. Let's see another example where \(x = 6\):

First, square the 6:

\(6^2 = 36\).

Then, multiply by 5:

\(5 \times 36 = 180\).

Key points about multiplication to keep in mind:
  • Ensure you are multiplying the correct numbers in sequence.
  • Understand that multiplication is associative, meaning \((a \times b) = (b \times a)\).
  • Use multiplication properties, such as distributive property, for more complex expressions.
Multiplication solidifies the final solution of the expression, making it possible to complete the evaluation.

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

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. (a) Is 2,287,321 divisible by \(9 ?\) (b) Is 4,114,107 divisible by \(9 ?\)

Write each expression without parentheses. $$ -(-5 c-4 d) $$

Solve each problem. Both Alabama and Ohio are projected to lose 1 seat in the U.S. House of Representatives in 2020 . The states projected to gain the most seats are Texas with 4 and Florida with \(2 .\) Write a signed number that represents the algebraic sum of these changes. (Data from Election Data Services.)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\left(\frac{5}{6} x+\frac{3}{2} y\right)\left(-\frac{1}{3} a\right)\)

Write each expression without parentheses. $$ -(-3 q+5 r-8 s) $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.