/*! 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 46 Solve each equation for \(k\) ... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 46

Solve each equation for \(k\) $$ 25=9 k $$

Short Answer

Expert verified
k = \( \frac{25}{9} \)

Step by step solution

01

Understand the equation

The given equation is a simple linear equation: \[ 25 = 9k \]
02

Isolate the variable

To solve for the variable \(k\), divide both sides of the equation by 9:\[ k = \frac{25}{9} \]
03

Simplify the fraction

The fraction \( \frac{25}{9} \) is already in its simplest form. Therefore, \(k = \frac{25}{9}\).

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Key Concepts

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

linear equations
Linear equations are one of the first types of equations you will encounter in algebra. They are called 'linear' because their graph is a straight line. A typical linear equation looks like this: \[(Ax + B = C)\], where A, B, and C are constants, and x is the variable. In our example, it is set up as:\[25 = 9k\]. Here, 25 is the constant, 9 is the coefficient of the variable k.
isolate the variable
To solve a linear equation, the main goal is to isolate the variable. This means getting the variable on one side of the equation and everything else on the other side. In our exercise, we isolate k by dividing both sides of the equation by 9. When we do this, we perform the same operation (division) on both sides, maintaining the equation's balance. Here鈥檚 how it looks:\[ 25 = 9k \]
Dividing both sides by 9: \[ k = \frac{25}{9} \]. This gives us the value of k.
fractions
Fractions are a way of expressing numbers that aren't whole. They are represented as ratios of two integers: a numerator (the top part) and a denominator (the bottom part). In the solution, the variable k is expressed as a fraction: \[ k = \frac{25}{9} \]. To simplify a fraction, you divide the numerator and the denominator by their greatest common divisor (GCD). In this case, 25 and 9 are already relatively prime, so the fraction \[ \frac{25}{9} \] is already in its simplest form. Simplifying fractions makes them easier to understand and work with in future calculations.

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Most popular questions from this chapter

The average number of vehicles waiting in line to enter a sports arena parking area is approximated by the rational expression $$\frac{x^{2}}{2(1-x)}$$ where \(x\) is a quantity between 0 and 1 known as the traffic intensity. (Source: Mannering, E., and W. Kilareski, Principles of Highway Engineering and Traffic Control, John Wiley and Sons.) To the nearest tenth, find the average number of vehicles waiting if the traffic intensity is the given number. (a) 0.1 (b) 0.8 (c) 0.9 (d) What happens to waiting time as traffic intensity increases?

Simplify each fraction. $$ \frac{1+t^{-1}-56 t^{-2}}{1-t^{-1}-72 t^{-2}} $$

Solve each problem involving direct or inverse variation. If \(m\) varies inversely as \(r,\) and \(m=12\) when \(r=8,\) find \(m\) when \(r=16\)

Find each power. $$ 3.5^{2} $$

The percent of deaths caused by smoking is modeled by the rational expression $$\frac{x-1}{x}$$ where \(x\) is the number of times a smoker is more likely than a nonsmoker to die of lung cancer. This is called the incidence rate. (Source: Walker, A., Observation and lnference: An Introduction to the Methods of Epidemiology, Epidemiology 91影视 Inc.) For example, \(x=10\) means that a smoker is 10 times more likely than a nonsmoker to die of lung cancer. Find the percent of deaths if the incidence rate is the given number. (a) 5 (b) 10 (c) 20 (d) Can the incidence rate equal \(0 ?\) Explain.
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