/*! 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 56 If \(g(x)=10 x\), evaluate \(g(5... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 56

If \(g(x)=10 x\), evaluate \(g(50)\).

Short Answer

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Step by step solution

01

Understand the Function

The given function is defined as \( g(x) = 10x \). This means that for any input \( x \), you multiply it by 10 to find the value of \( g(x) \).
02

Substitute the Input Value

To evaluate \( g(50) \), substitute 50 for \( x \) in the function definition. Therefore, \( g(50) = 10 \times 50 \).
03

Calculate the Result

Perform the multiplication: \( 10 \times 50 = 500 \). Thus, \( g(50) = 500 \).

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that helps us solve problems with unknown values. It's like a puzzle where we find missing pieces. One common element in algebra is the use of variables. Variables are symbols, usually letters like x or y, that represent unknown numbers. In algebra, you're often asked to solve for these variables using various operations such as addition, subtraction, multiplication, or division.

In this exercise, we work with a function given by the expression \( g(x) = 10x \). Here, x is the variable. When we evaluate this function for a specific value of x, we substitute that value into the expression and solve it.
Functions
Functions are mathematical entities that show a relationship between two sets of numbers. In simpler terms, a function is like a machine: you put some value (input) into it, and it gives you a result (output).

In this exercise, the function is defined as \( g(x) = 10x \). The input value is the number you choose for x, and the output is the result after performing the operation defined by the function. So, if you put 50 as the input for x, the function tells us to multiply this value by 10 to get the output.

Let's break down the function step-by-step:
  • Identify the function: \( g(x) = 10x \)
  • Input value: 50
  • Substitute 50 for x in the function
  • Perform the calculation: \( 10 \times 50 = 500 \)
Having these steps in place makes it easier to understand how to go from an input to an output in a function.
Substitution
Substitution is an essential technique in algebra that allows us to simplify expressions and solve equations. To substitute means to replace a variable with a given value.

In the function \( g(x) = 10x \), we are asked to evaluate it for x = 50. To do this, follow these steps:
  • Write down the function: \( g(x) = 10x \)
  • Identify the value of the variable to be substituted: x = 50
  • Replace x in the function with 50: \( g(50) = 10 \times 50 \)
  • Calculate the result: \( 10 \times 50 = 500 \)
Substitution is thus the method we used to find the value of g(50) in this problem. It's a straightforward process, but very powerful when solving more complex problems.

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Most popular questions from this chapter

(a) find three solutions of the equation. (b) graph the equation. \(y=\frac{2}{3} x-4\)

For exercises 95-98, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Find the \(y\)-intercept of \(6 x+5 y=30\). Incorrect Answer: \(9 x+2 y=36\) $$ \begin{aligned} 9(0)+2 y &=36 \\ 2 y &=36 \\ \frac{2 y}{2} &=\frac{36}{2} \\ y &=18 \end{aligned} $$ The \(x\)-intercept is \((0,18)\).

Use the slope formula to find the slope of the line that passes through the points. \(\left(-6, \frac{1}{2}\right) ;\left(10, \frac{3}{4}\right)\)

Use the slope formula to find the slope of the line that passes through the points. \(\left(\frac{1}{8}, 7\right) ;\left(\frac{7}{8}, 9\right)\)

(a) write the equation of the vertical line that passes through the point. (b) graph the equation. \((6,3)\)
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