함수와 그래프 전체 문제

The number of hours it takes Jack to drive from Boston to Bangor is inversely proportional to his average driving speed. When he drives at an average speed of 40 miles per hour, it takes him 6 hours for the trip.

ⓐ Write the equation that relates the number of hours, $h,$ with the speed, $s.$ ⓑ How long would the trip take if his average speed was 75 miles per hour?

Marisol solves the proportion $\frac{144}{a}=\frac{9}{4}$ by ‘cross multiplying,’ so her first step looks like $4\cdot 144=9\cdot a.$ Explain how this differs from the method of solution shown in (see text).

Paula and Yuki are roommates. It takes Paula 3 hours to clean their apartment. It takes Yuki 4 hours to clean the apartment. The equation $\frac{1}{3}+\frac{1}{4}=\frac{1}{t}$ can be used to find t, the number of hours it would take both of them, working together, to clean their apartment. Explain how this equation models the situation.

In your own words, explain the difference between direct variation and inverse variation.

Make up an example from your life experience of inverse variation.

Determine the Values for Which a Rational Expression is Undefined

In the following exercises, determine the values for which the rational expression is undefined.

$\frac{5a+3}{3a-2}$

Determine the Values for Which a Rational Expression is Undefined

In the following exercises, determine the values for which the rational expression is undefined.

$\frac{b-7}{{b}^{2}-25}$

Determine the Values for Which a Rational Expression is Undefined

In the following exercises, determine the values for which the rational expression is undefined.

$\frac{5{x}^{2}{y}^{2}}{8y}$

Determine the Values for Which a Rational Expression is Undefined

In the following exercises, determine the values for which the rational expression is undefined.

$\frac{x-3}{{x}^{2}-x-30}$

Simplify Rational Expressions

In the following exercises, simplify.

$\frac{18}{24}$

Simplify Rational Expressions

In the following exercises, simplify.

$\frac{9{m}^{4}}{18m{n}^{3}}$

Simplify Rational Expressions

In the following exercises, simplify.

$\frac{{x}^{2}+7x+12}{{x}^{2}+8x+16}$

Simplify Rational Expressions

In the following exercises, simplify.

$\frac{7v-35}{25-{v}^{2}}$

Multiply Rational Expressions

In the following exercises, multiply.

$\frac{5}{8}\cdot \frac{4}{15}$

Multiply Rational Expressions

In the following exercises, multiply.

$\frac{3x{y}^{2}}{8{y}^{3}}\cdot \frac{16{y}^{2}}{24x}$

Multiply Rational Expressions

In the following exercises, multiply.

$\frac{72x-12{x}^{2}}{8x+32}\cdot \frac{{x}^{2}+10x+24}{{x}^{2}-36}$

Multiply Rational Expressions

In the following exercises, multiply.

$\frac{2{y}^{2}+y-3}{4-{y}^{2}}\cdot \frac{{y}^{2}-4y+4}{2{y}^{2}+11y+12}$

Divide Rational Expressions

In the following exercises, divide.

$\frac{{x}^{2}-4x-12}{{x}^{2}+8x+12}\div \frac{{x}^{2}-36}{3x}$

Divide Rational Expressions

In the following exercises, divide.

$\frac{{y}^{2}-16}{4}\div \frac{{y}^{3}-64}{2{y}^{2}+8y+32}$

Divide Rational Expressions

In the following exercises, divide.

$\frac{11+w}{w-9}\div \frac{121-{w}^{2}}{9-w}$