Which expression is equivalent to (9m^2 + 5mn - 4n^2) - (7m^2 + 3mn + 6n^2)?
Option A.
16m^4 +8m^2n² + 2n²
Option B.
16m² + 8mn + 2n²
Option C.
2m² +8mn + 2n²
Option D.
2m² + 2mn - 10n²
To simplify the expression (9m^2 + 5mn - 4n^2) - (7m^2 + 3mn + 6n^2), we distribute the negative sign:
(9m^2 + 5mn - 4n^2) - (7m^2 + 3mn + 6n^2) = 9m^2 + 5mn - 4n^2 - 7m^2 - 3mn - 6n^2
Now, we can combine like terms:
= (9m^2 - 7m^2) + (5mn - 3mn) + (-4n^2 - 6n^2)
= 2m^2 + 2mn - 10n^2
Therefore, the expression is equivalent to 2m² + 2mn - 10n², which is option D.
The value of y varies directly with x. When x= 14, y= 35.
What is the value of y when x= 16
Option A.
37
Option Be.
6.4
Option C.
40
Option D.
37.5
In a direct variation, if the value of one variable (y) is proportional to the value of another variable (x), then we can write the equation as y = kx, where k is the constant of variation.
To find the value of y when x=16, we need to determine the value of k. We can use the given information when x=14 and y=35 to solve for k.
35 = k * 14
k = 35/14
k = 2.5
Now, we can substitute the value of k and x into the direct variation equation:
y = 2.5 * 16
y = 40
Therefore, the value of y when x=16 is 40, which is option C.