Joelle currently has 18 rocks in her collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Set up a system of equations to show how many rocks each has in their collection.(6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) Joelle has y = Response areax + Response area b) Lewis has y = Response areax + Response area c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeks d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeks: Let's set the two equations equal to each other and solve for x: 18 + 4x = 30 + 3x
Subtract 3x from both sides: 18 + x = 30
Subtract 18 from both sides: x = 12
Therefore, they will have the same number of rocks in their collections after 12 weeks.
d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection: To find the number of rocks they will have when equal, substitute x = 12 into either equation:
Joelle: y = 18 + 4(12) = 18 + 48 = 66 rocks
Lewis: y = 30 + 3(12) = 30 + 36 = 66 rocks
Therefore, they will each have 66 rocks in their collection when the amount is equal.
a) Joelle has y = 18 + 4x
b) Lewis has y = 30 + 3x
c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? They will have the same number of rocks in their collections after Response area weeks.
d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
a) Joelle has y = 18 + 4x, where x is the number of weeks.
b) Lewis has y = 30 + 3x, where x is the number of weeks.
c) To find the number of weeks until Joelle and Lewis have the same number of rocks, we need to set their equations equal to each other:
18 + 4x = 30 + 3x
Simplifying the equation, we get:
x = 12
Therefore, it will take 12 weeks for Joelle and Lewis to have the same number of rocks in their collections.
d) To find out how many rocks they will each have when the amount is equal, we substitute x=12 into either of the equations:
Joelle: y = 18 + 4(12) = 18 + 48 = 66 rocks.
Lewis: y = 30 + 3(12) = 30 + 36 = 66 rocks.
Therefore, when the amount of rocks in their collections is equal, Joelle and Lewis will each have 66 rocks.
what would a graph representing the solution −5/2x−1=4x+2 look like?
To graph the equation −5/2x−1=4x+2, we need to rearrange it in slope-intercept form (y = mx + b).
Start by isolating the x-term on one side of the equation:
-5/2x - 1 = 4x + 2
-5/2x - 4x = 2 + 1
-13/2x = 3
x = -6/13
Now that we have the x-intercept, we can find the y-intercept by substituting x = 0 into the equation:
y = -5/2(0) -1 = 4(0) + 2
y = -1
So, the y-intercept is -1.
Now we can plot these two points on the graph:
x-intercept: (-6/13, 0)
y-intercept: (0, -1)
The line representing the equation −5/2x−1=4x+2 will pass through these two points. Since the slope is -5/2, it means that for every 2 units moved horizontally (to the right), the line goes down 5 units vertically. The line will have a negative slope and will be decreasing as it moves from left to right.
Now we can draw a line through these two points and extend it to the right and left to represent the graph of the equation. The line will be sloping downwards and intersecting the y-axis at -1.