Find the mean median of each data set.
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Answer: For the system given, there is no solution.
The slopes are the same for both equations, so the lines are parallel. With no intersection, there is no solution.
It may be easier to graph the system if you change the equations to slope intercept form y = mx + b
That locates the y-intercept, <em><u>b</u></em> and you can use the slope, <em><u>m</u></em> to plot additional points to draw the lines.
The attachment shows the graph of this system of equations.
Step-by-step explanation: Isolate y on the left
<u>First equation:</u>
4x + 6y = -12 Subtract 4x from both sides
6y = -4x -12 Divide both sides by 6
y = -4x/6 -12/6 Simplify
y = -2x/3 - 2 The y-intercept is -2, <u>the slope is -2/3</u>
<u>Second equation:</u>
2x + 3y = 6 Subtract 2x from both sides
3y = –2x + 6 . Divide both sides by 3
y = –2x/3 + 6/3 Simplify
y = –2x/3 +2 The y-intercept is -2, <u>the slope is -2/3 </u>
At this point we see that the slopes are the same, so the lines are parallel.
It will take exactly 4 years for these trees to be the same height
Step-by-step explanation:
A gardener is planting two types of trees:
- Type A is 3 feet tall and grows at a rate of 7 inches per year
- Type B is 5 feet tall and grows at a rate of 1 inches per year
We need to find in how many years it will take for these trees to be the
same height
Assume that it will take x years for these trees to be the same height
The height of a tree = initial height + rate of grow × number of years
Type A:
∵ The initial height = 3 feet
∵ 1 foot = 12 inches
∴ The initial height = 3 × 12 = 36 inches
∵ The rate of grows = 7 inches per year
∵ The number of year = x
∴ = 36 + (7) x
∴ = 36 + 7 x
Type B:
∵ The initial height = 5 feet
∴ The initial height = 5 × 12 = 60 inches
∵ The rate of grows = 1 inches per year
∵ The number of year = x
∴ = 60 + (1) x
∴ = 60 + x
Equate and
∴ 36 + 7 x = 60 + x
- Subtract x from both sides
∴ 36 + 6 x = 60
- Subtract 36 from both sides
∴ 6 x = 24
- Divide both sides by 6
∴ x = 4
∴ The two trees will be in the same height in 4 years
It will take exactly 4 years for these trees to be the same height
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