Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 34 meters ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 meter per second, and the adults hobbled after them at a rate of 2 meters per second. Soon they were side-by-side. How long did that take? How far did the adults go?

It took _ seconds for the adults to go _ meters and catch up to the kids.

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).

What is the distance between a and b? round your answer to the nearest tenth. a coordinate plane is shown. point a is located at negative 1, 5, and point b is located at 4, 1. a line segment connects the two points.

Which number can each term of the equation be multiplied by to eliminate the decimals before solving? 5.6j- 0.12=4+1.1j