As is the case for any polynomial, the domain of this one is (-infinity, +infinity).
To find the range, we need to determine the minimum value that f(x) can have. The coefficients here are a=2, b=6 and c = 2,
The x-coordinate of the vertex is x = -b/(2a), which here is x = -6/4 = -3/2.
Evaluate the function at x = 3/2 to find the y-coordinate of the vertex, which is also the smallest value the function can take on. That happens to be y = -5/2, so the range is [-5/2, infinity).
Answer: 9 fewer
Step-by-step explanation:
Add 13 and 11 which gives you 24. Then add 8 and 7 which gives you 15. Then subtract 24 - 15 which gives you a difference of 9.
Squares : Triangles
3 : 12
Divide both sides by 3.
The simplest ratio is
1 : 4
The equivalent 90° CCW rotation maps (x, y) to (-y, x).
(4, -2) becomes (2, 4) after rotation.
Answer:
(-5,5)
Step-by-step explanation:
Multiply the first equation by -2,and multiply the second equation by 1.
−2(x+5y=20)
1(2x−7y=−45)
Becomes:
−2x−10y=−40
2x−7y=−45
Add these equations to eliminate x:
−17y=−85
Then solve−17y=−85for y:
(Divide both sides by -17)
y=5
x+5y=20
Substitute 5 for y in x+5y=20:
x+(5)(5)=20
x+25=20(Simplify both sides of the equation)
x+25+−25=20+−25(Add -25 to both sides)
x=-5
