If x varies y and x =20 when y=8 fine the formular connecting x and y x when y=7 y when x=10
"x varies y" is gibberish. I assume you meant that "x varies directly as y"
x = ky
20 = 8k, so k = 5/2
x = 5/2 y
Now use that to answer the other questions
Or, if you meant that "x varies inversely as y"
then xy = k and k = 160
To find the formula connecting x and y, we can use the concept of direct variation. Direct variation is expressed as y = kx, where k is a constant.
Given that x = 20 when y = 8, we can substitute these values into the direct variation equation to solve for the constant k.
8 = k * 20
Divide both sides by 20:
k = 8/20
k = 0.4
Now that we have the constant k, we can use it to write the formula connecting x and y:
y = 0.4x
To find x when y = 7, we can substitute y = 7 into the formula and solve for x:
7 = 0.4x
Divide both sides by 0.4:
x = 7 / 0.4
x = 17.5
To find y when x = 10, we can substitute x = 10 into the formula and solve for y:
y = 0.4 * 10
y = 4
To find the formula connecting x and y, we need to determine the relationship between x and y given the provided information.
Given:
When y = 8, x = 20
To determine the relationship between x and y, we can consider the change in x for every unit change in y. This is also known as the slope of the line.
Change in x = x₁ - x₀ = 20 - x₀
Change in y = y₁ - y₀ = 8 - y₀
Since the given values of x and y are not sequential (x₀ = 20, y₀ = 8), we can't directly determine the slope. So, we need another data point to calculate the slope.
Given:
When y = 7, x = ?
When x = 10, y = ?
We will use these two additional data points to find the relationship between x and y.
Let's start with the first data point (y = 7, x = ?):
Change in x = 20 - x₀ = x - x₀
Change in y = 7 - y₀ = 7 - 8 = -1
Next, let's consider the second data point (x = 10, y = ?):
Change in x = 10 - x₀ = 10 - 20 = -10
Change in y = y - y₀
Now, we can set up a proportion to find the relationship between the changes in x and y:
(change in x₁)/(change in y₁) = (change in x₂)/(change in y₂)
(x - x₀)/(-1) = (-10)/(change in y₂)
Now, we can substitute one of the data points (y = 7, x = ?) to solve for x:
(x - 20)/(-1) = -10/(y - 8)
Simplifying the equation further:
x - 20 = 10 - 10(y - 8)
x - 20 = 10 - 10y + 80
x = 90 - 10y
Therefore, the formula connecting x and y is: x = 90 - 10y.