You plant an 8-inch-tall tomato plant that grows 5 inches taller each week. On the same day, you plant a 14-inch-tall tomato plant that grows 3.5 inches taller each week. Graph a system of equations that represents the heights y (in inches) of the plants after x weeks. Use the graph to solve the system.
UGHHH none of these help this poor 8th grader out heller
y = 5x + 8
y = 3.5x + 14
You need to graph each equation on the same graph paper and see where the two lines cross. That point is your answer.
I will give you a start.
The first graph has a point (0,8) and the second graph has a point (0, 14)
Find two more points for each graph and that will help you find your lines.
You have a total of 45 dimes and quarters. You have 3 more quarters than dimes. Which system of equations can you use to find the number x of quarters and number y of dimes you have? Use the system to determine how much money you have in quarters and dimes.
I'm really confused o how to do this.
Bruh can y’all just help… jus gimme the answer. You plant an 8-inch-tall tomato plant that grows 5 inches taller each week. On the same day, you plant a 14-inch-tall tomato plant that grows 3.5 inches taller each week. Graph a system of equations that represents the heights y (in inches) of the plants after x weeks. Use the graph to solve the system.
To graph a system of equations that represents the heights of the plants after x weeks, we need to write two equations based on the given information.
Let's consider the first plant:
- Initial height: 8 inches
- Growth rate: 5 inches taller each week
The equation representing the height of the first plant after x weeks would be: y = 8 + 5x.
Now, let's consider the second plant:
- Initial height: 14 inches
- Growth rate: 3.5 inches taller each week
The equation representing the height of the second plant after x weeks would be: y = 14 + 3.5x.
To solve the system, we need to find the point of intersection between the two equations. This point represents the week(s) when both plants have the same height.
To graph the system, plot the equations on a coordinate plane, with the x-axis representing the number of weeks (x) and the y-axis representing the height (y) in inches.
For example, if we consider x-values from 0 to 5, the graph would look like this:
Graph:
-------------------------------------
| | |
| * | * |
| | | | |
| | | | |
| | | | |
|--------|-------|--------|-------|
Week 0 Week 1 Week 2 Week 3
Explanation:
The asterisks (*) represent the intersection points of the two equations.
The first plant (y = 8 + 5x) grows faster than the second plant (y = 14 + 3.5x), so it will be taller after some weeks. The point of intersection represents the week when both plants have the same height.
To find this point, we can solve the system of equations by setting the two equations equal to each other:
8 + 5x = 14 + 3.5x
Simplifying the equation:
5x - 3.5x = 14 - 8
1.5x = 6
x = 4
So, after 4 weeks, both plants will have the same height.
To find their height at this point, substitute x=4 into one of the equations, let's use the first equation:
y = 8 + 5*4
y = 8 + 20
y = 28
Therefore, after 4 weeks, both plants will be 28 inches tall.