Answer:
gf(5) = 289.
fg(x) = 3x^2 + 2.
Step-by-step explanation:
f(5) = 3(5) + 2 = 17
So gf(5) = 17^2 = 289.
fg(x) = 3(x^2) + 2 (we replace the x in f(x) by g(x)).
= 3x^2 + 2.
Our system of equations is:
y = -3x + 9
y = -x - 5
To solve this system of equations, we are going to use substitution. This means that we are going to substitute the second equation into the first equation since both are already solved for y in terms of x.
y = -3x + 9
-x - 5 = -3x + 9
Now, we must simplify by moving all of the constant terms to one side of the equation and all of the variable terms to the other side.
-x - 5 = -3x + 9
2x - 5 = 9
2x = 14
Finally, to undo the multiplication between the coefficient 2 and the variable x, we must divide both sides by 2 to get the variable x alone.
x = 7
Next, we must substitute in this value we have solved for x into one of the original equations to solve for the other variable, y.
y = -3x + 9
y = -3(7) + 9
To simplify, we must multiply through the parentheses and combine like terms by addition.
y = -21 + 9
y = -12
Therefore, your final answer is x = 7 and y = -12, or as an ordered pair (7, -12).
Hope this helps!
The point slope formula is y - y1 = m(x - x1)
the value x1 is the x coordinate of a point
the value y1 is the y coordinate of a point
the value m is the slope, which is 3
therefore, x1 = -2 & y1 = 1
Then, all you do is plug in the points:
y - 1 = 3(x + 2)
NOTE: It is 3(x + 2) instead of 3(x - 2) because the formula is (x - x1). If you plug x1 in, it is (x - (-2)). 2 negatives cancel out to be a positive, so it is (x + 2)
3 5/8 + 2 7/8 = 6 1/8 + 10 1/8 = 16 2/8 so the answer would be 16 2/8
