Write a polynomial equation of least degree for each set of roots. Does the equation have an odd or even degree? How many times does the graph of the related function cross the x-axis? -2, -0.5, 4

Four times the multiplicative inverse of a number is added to the number. The result is $10 \frac{2}{5} .$ What is the number?

Determine the binomial factors of each polynomial. $x^{3}+3 x^{2}+3 x+1$

Solve each inequality. $\sqrt{m+2} \leq \sqrt{3 m+4}$

The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by $P(x)=-0.78 x^{4}+133 x^{3}-7500 x^{2}+147,500 x+1,440,000,$ where P(x) represents the population and x represents the number of years since 1890. Do you think this model is valid for any time? Explain.

$$\begin{matrix} \text{Year} & \text{Population}\\ \text{1890} & \text{1,441,216}\\ \text{1910} & \text{2,331,542}\\ \text{1930} & \text{1,867,312}\\ \text{1950} & \text{1,960,101}\\ \text{1970} & \text{1,539,233}\\ \end{matrix}$$

The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by $P(x)=-0.78 x^{4}+133 x^{3}-7500 x^{2}+147,500 x+1,440,000,$ where P(x) represents the population and x represents the number of years since 1890. According to this model, what happens between 1970 and 1980?

$$\begin{matrix} \text{Year} & \text{Population}\\ \text{1890} & \text{1,441,216}\\ \text{1910} & \text{2,331,542}\\ \text{1930} & \text{1,867,312}\\ \text{1950} & \text{1,960,101}\\ \text{1970} & \text{1,539,233}\\ \end{matrix}$$

Explain the significance of popular sovereignty as a fundamental principle of the Constitution

The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by $P(x)=-0.78 x^{4}+133 x^{3}-7500 x^{2}+147,500 x+1,440,000,$ where P(x) represents the population and x represents the number of years since 1890. Use the model to predict the population in 1980

$$\begin{matrix} \text{Year} & \text{Population}\\ \text{1890} & \text{1,441,216}\\ \text{1910} & \text{2,331,542}\\ \text{1930} & \text{1,867,312}\\ \text{1950} & \text{1,960,101}\\ \text{1970} & \text{1,539,233}\\ \end{matrix}$$

The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by $P(x)=-0.78 x^{4}+133 x^{3}-7500 x^{2}+147,500 x+1,440,000,$ where P(x) represents the population and x represents the number of years since 1890. According to the data, how valid is the model?

$$\begin{matrix} \text{Year} & \text{Population}\\ \text{1890} & \text{1,441,216}\\ \text{1910} & \text{2,331,542}\\ \text{1930} & \text{1,867,312}\\ \text{1950} & \text{1,960,101}\\ \text{1970} & \text{1,539,233}\\ \end{matrix}$$

Determine whether each function is continuous at the given x-value(s). Justify using the continuity test. If discontinuous, identify the type discontinuity as infinite, jump, or removable. f(x) ={x2-1 if x> -2/x-5 if x< -2; at x=-2

Solve each inequality. $\sqrt[4]{5 y-9} \leq 2$

Write a polynomial equation of least degree for each set of roots. Does the equation have an odd or even degree? How many times does the graph of the related function cross the x-axis? -1, 1, 5

List the possible rational roots of each equation. Then determine the rational roots. $x^{4}+4 x^{2}-5=0$

Determine the binomial factors of each polynomial. $x^{3}+4 x^{2}-x-4$