함수와 그래프 전체 문제

A 2-foot-tall dog casts a 3-foot shadow at the same time a cat casts a one foot shadow. How tall is the cat ?

If $y$ varies directly as $x$ and $y=14,$ when $x=3.$ find the equation that relates $x$ and $y.$

If $a$ varies directly as $b$ and $a=16,$ when $b=4.$ find the equation that relates $a$ and $b.$

If $p$ varies directly as $q$ and $p=9.6,$ when $q=3.$ find the equation that relates $p$ and $q.$

If $v$ varies directly as $w$ and $v=8,$ when $w=\frac{1}{2}.$ find the equation that relates $v$ and $w.$

The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10-pound watermelon on a hanging scale, the spring stretched 5 inches.

ⓐ Write the equation that relates the length of the spring to the weight. ⓑ What weight of watermelon would stretch the spring 6 inches?

The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds.

ⓐ Write the equation that relates the load to the diagonal of the cross-section. ⓑ What load will a beam with a 10-inch diagonal support?

If $y$ varies inversely with $x$ and $y=5$ when $x=4,$ find the equation that relates $x$ and $y.$

If $p$ varies inversely with $q$ and $p=2$ when $q=1$, find the equation that relates $p$ and $q.$

If $v$ varies inversely with $w$ and $v=6$ when $w=\frac{1}{2},$ find the equation that relates $v$ and $w.$

If $a$ varies inversely with $b$ and $a=12$ when $b=\frac{1}{3},$ find the equation that relates $a$ and $b.$

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds getting 33 mpg on the highway.

ⓐ Write the equation that relates the mpg to the car’s weight. ⓑ What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?

A car’s value varies inversely with its age. Jackie bought a 10-year-old car for $2,400.

ⓐ Write the equation that relates the car’s value to its age. ⓑ What will be the value of Jackie’s car when it is 15 years old?

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).

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.

$\frac{18}{24}$