Brianna filled up her car with gas before embarking on a road trip across the country. The capacity of Brianna's gas tank is 10 gallons and the car uses 2 gallons of gas for every hour driven. Make a table of values and then write an equation for the function G(t),representing the number of gallons of gas remaining in Brianna's gas tank after t hours of driving.

Number of Hours Driven Number of Gallons Remaining in the Tank
0
1
2
3

Prove that 3: 8 is equivalent to 12: 32.a. use diagrams to support your answer.

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 equation of a parabola is given. y=18x2+4x+20 what are the coordinates of the focus of the parabola?