The y-value of the vertex is positive 3, as shown by the +3 on the right hand side of the equation, and the x-value is -1, from the (x+1)^2 (remember, when the number is inside the brackets, flip the sign) The vertex would be (-1, 3)
If you are looking for a rigorous answer (calculus), we must find the mininum point of the equation: f(x) = (x+1)^2 + 3 f
f'(x) = 2(x+1) = 2x + 2
2x + 2 = 0
x = -1
f(1) = (-1 + 1)^2 + 3
f(1) = 0 + 3 = 3
(-1, 3)
Add five to each side, then divide each side by 2. you will get 6.5 in the end
Answer:
Dog is 2 years old
Step-by-step explanation:
Let dog's age = d
Let friend's age = f
Your dog is 8 years younger than your friend:
d +8 = f
In 2 years, your friend will be three times as old as your dog:
3(d+2) = (f+2)
3d+6 = f+2
3d = f - 4
(sub in f=d+8 from above)
3d = f - 4
3d = d+8 - 4
2d = 4
d = 2
1.
√(16+20)=√36=6
C
2.
√(21-9)=√(12)=(√4)(√3)=2√3
B
3. 2*√3=2*1.73205=3.464
B
1.C
2.B
3.B
Answer:
1) Place the compass point at the vertex of the angle and open it to any width. Draw an arc that intersects of the sides of the angle.
2) Place the compass point at the one of the intersection points. Place the pencil at the other intersection point. This sets the compass with.
3) Draw an arc inside the angle.
4) Move the compass point to the intersection point on the other side of the angle being sure to keep the compass width the same. Draw a second arc inside the angle.
5) Make a point where the 2 arcs intersect the angle. Use a straight edge to draw a ray from the vertex of the angle through the point.
