An equation for the parabola would be y²=-19x.
Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis. This means we will use the standard form
(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.
Beginning with the directrix:
x=h-p=4.75
h-p=4.75
Since the vertex is at (0, 0), this means h=0 and k=0:
0-p=4.75
-p=4.75
p=-4.75
Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x
Answer:
Either x = 3, y = 2
or
(3,2) is your answer.
Step-by-step explanation:
2x +y = 8 (1)
y = - x+ 5 (2)
Put equation (2) into equation (1). Use the y value in (2) to go into the y value in (1).
2x - x+5 = 8 Combine the x values
x + 5 = 8 Subtract 5 from both sides
x + 5-5 = 8-5
x=3
Now go back to (2). Put x in for the value of -x. Watch the sign.
y = -3+ 5
y = 2
So the answer is (3,2)
Set it up in a proportion.
8 (oil)/5 (salad dressing) = x/7
cross multiply to get 11.2
Answer:
∠APC ≅ ∠DPB angles adjacent to the same angle are congruent to each other.
Explanation:
Because they share an angle created by P, they are adjacent.
I hope this helped :)
5)
Equilateral triangle, all sides are equal
So 2x + 5 = 11
2x = 6
x = 3
Answer is the first one
3; Equilateral theorem
6)
Isosceles triangle has at least two congruent sides.
So 6x = 24
x = 4
Answer x = 4
Converse of the Base Angle Theorem
7)
5x + 7 = 52
5x = 45
x = 9
Answer
x = 9
Base angle theorem
8)
5y - 14 = 3y
2y = 14
y = 7
Answer
7; Equiangular theorem
