함수와 그래프 전체 문제

In the following exercises, solve each equation.

$\frac{1}{x}+\frac{3}{4}=\frac{5}{8}$

In the following exercises, solve each equation.

$\frac{1}{z-5}+\frac{1}{z+5}=\frac{1}{{z}^{2}-25}$

In the following exercises, solve each equation.

$\frac{z}{2z+8}-\frac{3}{4z-8}=\frac{3{z}^{2}-16z-16}{8{z}^{2}+16z-64}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{6x}{x-6}\le 2$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{2x+3}{x-6}>1$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{1}{2}+\frac{12}{{x}^{2}}\ge \frac{5}{x}$

In the following exercises, find $R(x)$ given $f(x)=\frac{x-4}{{x}^{2}-3x-10}$ and $g(x)=\frac{x-5}{{x}^{2}-2x-8}.$

$R(x)=f(x)-g(x)$

In the following exercises, find $R(x)$ given $f(x)=\frac{x-4}{{x}^{2}-3x-10}$ and $g(x)=\frac{x-5}{{x}^{2}-2x-8}.$

$R(x)=f(x)\cdot g(x)$

In the following exercises, find $R(x)$ given $f(x)=\frac{x-4}{{x}^{2}-3x-10}$ and $g(x)=\frac{x-5}{{x}^{2}-2x-8}.$

$R(x)=f(x)\div g(x)$

Given the function, $R(x)=\frac{2}{2{x}^{2}+x-15},$ find the values of $x$ that make the function less than or equal to 0.

If $y$ varies directly with $x$, and $x=5$ when $y=30,$ find $x$ when $y=42.$

If $y$ varies inversely with the square of $x$ and $x=3$ when $y=9,$ find $y$ when $x=4.$

Matheus can ride his bike for 30 miles with the wind in the same amount of time that he can go 21 miles against the wind. If the wind’s speed is 6 mph, what is Matheus’ speed on his bike?

Oliver can split a truckload of logs in 8 hours, but working with his dad they can get it done in 3 hours. How long would it take Oliver’s dad working alone to split the logs?

The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of 29.5 liters with 2000 psi, what is the volume if the tank has a 14.7 psi rating? Round to the nearest whole number.

The cities of Dayton, Columbus, and Cincinnati form a triangle in southern Ohio. The diagram gives the map distances between these cities in inches.

The actual distance from Dayton to Cincinnati is 48 miles. What is the actual distance between Dayton and Columbus?

Simplify: ${(y-3)}^{2}.$

Solve: $2x-5=0.$

Solve ${n}^{2}-6n+8=0.$

Solve: $\sqrt{5n-4}-9=0.$