SOLVE FOR x:
4x^2+6x=10

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

The federal reserve controls certain interest rates in the united states. investors often try to speculate as to whether the federal reserve will raise or lower rates and by how much. suppose a company conducts extensive interviews with financial analysts, and as a result, predicts that "thefed" will increase rates by an average of 0.25 percentage points every six months for the forseeable future. which type of equation could be used to model the predicted interest rates over the next several years, assuming no other significant changes? a) a linear equation b) a quadratic equation c) a polynomial equation d) an exponential equation

(50 points) drag each description to the correct location on the table. each description can be used more than once. some systems of equations and their graphs are given in the table. for each system, place the description(s) in the box that correctly describe the type of system shown. :