Answer:
a)
The point that is equidistant to all sides of a triangle is called the <u>incenter</u>.
The incenter is located at the intersection of bisectors of the interior angles of a triangle.
b)
The point that is equidistant to all vertices of a triangle is called the <u>circumcenter</u>.
The circumcenter is located at the intersection of perpendicular bisectors of the sides of a triangle.
c)
<em>See the attachment</em>
The blue lines and their intersection shows the incenter.
The red lines and their intersection shows the circumcenter.
As we see the red point- the <u>circumcenter </u>is closer to vertex B.
Answer:
-3(-3x + 4) = 9x - 12
Step-by-step explanation:
-3( Ax + 4) = 9x - 12
-3Ax -12 = 9x - 12
Equating coefficients of x terms on both sides :
-3A = 9
A = -3
Therefore, -3(-3x + 4) = 9x - 12
The number of presale tickets sold is 271
<em><u>Solution:</u></em>
Let "p" be the number of presale tickets sold
Let "g" be the number of tickets sold at gate
<em><u>Given that, total of 800 Pre-sale tickets and tickets at the gate were sold</u></em>
Therefore,
Presale tickets + tickets sold at gate = 800
p + g = 800 ------ eqn 1
<em><u>Given that, number of tickets sold at the gate was thirteen less than twice the number of pre-sale tickets</u></em>
Therefore,
Number of tickets sold at gate = twice the number of pre-sale tickets - 13
g = 2p - 13 ------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
Substitute eqn 2 in eqn 1
p + 2p - 13 = 800
3p -13 = 800
3p = 800 + 13
3p = 813
p = 271
Thus 271 presale tickets were sold
Answer:
Direction parabola opens upward.
Vertex of parabola is (27,-9).
Axis of symmetry is
.
Step-by-step explanation:
Note: Option sets are not correct.
The vertex form of a parabola is
...(1)
where, (h,k) is vertex and x=h is the axis of symmetry.
If a<0, then parabola opens downward and if a>0, then parabola opens upward.
The given function is
...(2)
On comparing (1) and (2), we get
, so direction parabola opens upward.
, so vertex of parabola is (27,-9).
So, axis of symmetry is
.