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The table shows the heights in inches of trees after they
have been planted. What is the height of a tree that is 64 in.
tall in its pot?
Height in pot, x Height Without Pot, y
30 18
36 24
42 30
48 36
To find the height of a tree that is 64 inches tall in its pot, we need to use the given information to determine the relationship between the height in the pot (x) and the height without the pot (y).
Looking at the given data, we can observe that the height without the pot (y) is always 12 inches less than the height in the pot (x).
Therefore, to find the height without the pot (y) when the height in the pot (x) is 64 inches, we subtract 12 from 64.
Height without pot = Height in pot - 12
Height without pot = 64 - 12
Height without pot = 52 inches
So, the height of the tree without the pot is 52 inches.
Determine which ordered pair is a solution of y=8x
To determine which ordered pair is a solution of the equation y = 8x, we need to substitute the given values of x and y into the equation and check if the equation holds true.
The given ordered pairs are:
1) (3, 24)
2) (5, 40)
3) (6, 48)
Let's substitute the values from the first ordered pair (3, 24) into the equation:
y = 8x
24 = 8(3)
24 = 24
The equation holds true for the first ordered pair.
Now, let's substitute the values from the second ordered pair (5, 40) into the equation:
y = 8x
40 = 8(5)
40 = 40
The equation holds true for the second ordered pair as well.
Lastly, let's substitute the values from the third ordered pair (6, 48) into the equation:
y = 8x
48 = 8(6)
48 = 48
The equation holds true for the third ordered pair as well.
Thus, all three ordered pairs (3, 24), (5, 40), and (6, 48) are solutions of the equation y = 8x.
To find the height of a tree that is 64 inches tall in its pot, you can use the given data to create a linear equation.
Let's define:
x = Height in pot
y = Height without pot
Using the given data:
30 -> 18
36 -> 24
42 -> 30
48 -> 36
We can form four data points:
(30, 18), (36, 24), (42, 30), (48, 36)
Now, we can find the equation of the line using two points, let's say (30, 18) and (48, 36).
First, find the slope (m):
m = (y2 - y1) / (x2 - x1)
= (36 - 18) / (48 - 30)
= 18 / 18
= 1
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (30, 18):
y - 18 = 1(x - 30)
y - 18 = x - 30
y = x - 30 + 18
y = x - 12
In this equation, x represents the height in the pot, and y represents the height without the pot.
To find the height of a tree that is 64 inches tall in its pot:
64 = x - 12
Rearranging the equation to solve for x:
x = 64 + 12
x = 76
Therefore, the height of the tree without the pot is 76 inches.
To find the height of a tree that is 64 inches tall in its pot, we need to determine the height without the pot. In the given table, we can see that there is a linear relationship between the height in the pot (x) and the height without the pot (y).
To calculate the height without the pot, we can use a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Calculate the slope (m)
To find the slope of the line, we need two points from the table. Let's choose the first two points (30, 18) and (36, 24):
m = (y2 - y1) / (x2 - x1)
m = (24 - 18) / (36 - 30)
m = 6 / 6
m = 1
Step 2: Calculate the y-intercept (b)
To find the y-intercept, we can substitute the values of one of the points (30, 18) and the slope (m) into the equation y = mx + b and solve for b.
18 = 1 * 30 + b
18 = 30 + b
b = 18 - 30
b = -12
Step 3: Use the equation to find the height without the pot (y)
Now that we have the slope (m = 1) and y-intercept (b = -12), we can substitute the given x-value (64) into the equation y = mx + b and solve for y.
y = 1 * 64 + (-12)
y = 64 - 12
y = 52
Therefore, the height of a tree that is 64 inches tall in its pot is 52 inches without the pot.