Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
x 1 3 5 10
y 4 12 20 40
a. direct variation; y=4x
b. direct variation; xy=1/4
c. inverse variation; xy=4
d. inverse variation; xy=1/4
Has anyone found the answer? i cant figure it out :(
It’s a
Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
x 1 3 5 10
y 4 12 20 40
a. direct variation; y=4x
b. direct variation; xy=1/4
c. inverse variation; xy=4
d. inverse variation; xy=1/4
The data represents direct variation.
The equation to model the data would be: y = 4x
Find the LCD of the pair of expressions.
2/7x^10y^4 x 2/14x^8y^7
The prime factorization of each denominator is:
7x^10y^4 = 7 * x^10 * y^4
14x^8y^7 = 2 * 7 * x^8 * y^7
The LCD includes the highest power of each prime factor that appears in either denominator. Thus, the LCD of 2/7x^10y^4 and 2/14x^8y^7 is:
2 * 7 * x^10 * y^7
Therefore, the LCD is 14x^10y^7.
Use the remainder theorem to determine which of the following binomials are factors of 2x^3+6x^2+8. Select all that apply.
(x-4)
(x-1)
(x+1)
(x+2)
(x+8)
We can use the remainder theorem by dividing the polynomial 2x^3 + 6x^2 + 8 by each of the given binomials and checking if the remainder is zero.
When divided by (x-4), we get:
2x^3 + 6x^2 + 8 = (x-4)(2x^2 + 4x + 10) + 48
Since the remainder is not zero, (x-4) is not a factor of 2x^3 + 6x^2 + 8.
When divided by (x-1), we get:
2x^3 + 6x^2 + 8 = (x-1)(2x^2 + 8x + 8) + 0
Since the remainder is zero, (x-1) is a factor of 2x^3 + 6x^2 + 8.
When divided by (x+1), we get:
2x^3 + 6x^2 + 8 = (x+1)(2x^2 + 4x + 4) + 4
Since the remainder is not zero, (x+1) is not a factor of 2x^3 + 6x^2 + 8.
When divided by (x+2), we get:
2x^3 + 6x^2 + 8 = (x+2)(2x^2 + 2x + 2) + 4
Since the remainder is not zero, (x+2) is not a factor of 2x^3 + 6x^2 + 8.
When divided by (x+8), we get:
2x^3 + 6x^2 + 8 = (x+8)(2x^2 - 10x + 82) - 648
Since the remainder is not zero, (x+8) is not a factor of 2x^3 + 6x^2 + 8.
Therefore, the only binomial that is a factor of 2x^3 + 6x^2 + 8 is (x-1).
To determine whether the data in the table represents a direct variation or an inverse variation, we need to analyze the relationship between the variables x and y.
In direct variation, the ratio between x and y remains constant. In other words, y is directly proportional to x, so as x increases, y increases proportionally. This can be represented by the equation y = kx, where k is the constant of proportionality.
In inverse variation, the product of x and y remains constant. In other words, y is inversely proportional to x, so as x increases, y decreases proportionally. This can be represented by the equation xy = k, where k is the constant of proportionality.
Looking at the table, we can see that as x increases, y also increases. The ratio between x and y remains the same for each entry. This means that the data represents a direct variation.
To find the equation that models the data in the table, we can use any of the given options and substitute the values from the table to check if they hold true.
Let's try option a: y = 4x
Using the values from the table:
For x = 1, y = 4(1) = 4
For x = 3, y = 4(3) = 12
For x = 5, y = 4(5) = 20
For x = 10, y = 4(10) = 40
All the calculated values of y match the corresponding values in the table. Therefore, the equation y = 4x accurately models the data in the table.
So, the correct answer is:
a. direct variation; y = 4x