Algebraically determine the values of that satisfy the system of equations shown below:
Algebraically determine the values of that satisfy the system of equations.
Perry invested in property that cost him \ 1500$ 3000$ 6000$. Assuming the growth rate remains the same, which type of function could he create to find the value of his investment 30 years from his original purchase?
The initial push of a child on a swing causes the swing to travel a total of 6 feet. Each successive swing travels of the distance of the previous swing. Determine the total distance, to the nearest hundredth of a foot, a child travels in the first five swings.
Determine the total distance, to the nearest hundredth of a foot, a child travels in the first five swings.
In the quadratic formula, is called the discriminant. The function has a discriminant value of 8 , and has a discriminant value of -16 . The quadratic graphs, and , are shown below.
Which quadratic functions have imaginary roots?
The roots of the equation are and .
The solution to the equation is
The directrix of the parabola has the equation . Find the coordinates of the focus of the parabola.
Find the coordinates of the focus of the parabola.
Consider the function . Is an even function? Justify your answer.
Write an equation for , the function that results after is shifted up 5 units.
Write an equation for , the inverse of .
Is an even function? Justify your answer.
Write an equation for , the function that results after is shifted up 5 units.
Write an equation for , the inverse of .
Taylor wants to open an investment account with the \ 12006.4 %6.35 %$ annual interest compounded continuously.
Write functions for and to represent the value of her investment with America's Bank and Barnyard Bank as a function of time, , in years.
Taylor would like to invest the \ 1200$ into one bank for ten years making no additional deposits and no withdrawals. With which bank will Taylor earn the most money? Justify your answer.
Taylor chooses to invest her money in Barnyard Bank. Algebraically determine how long, to the nearest tenth of a year, it will take her initial investment to triple assuming she makes no deposits or withdrawals.
Write functions for and to represent the value of her investment with America's Bank and Barnyard Bank as a function of time, , in years.
Determine with which bank Taylor will earn the most money after ten years and justify your answer.
Algebraically determine how long, to the nearest tenth of a year, it will take her initial investment to triple assuming she makes no deposits or withdrawals.
A cup of coffee is left out on a countertop to cool. The table below represents the temperature, , in degrees Fahrenheit, of the coffee after it is left out for minutes.
Based on these data, write an exponential regression equation, , to model the temperature of the coffee. Round all values to the nearest thousandth.