<span>1) We are given that PA = PB, so PA ≅ PB by the definition of the radius.
</span>When you draw a perpendicular to a segment AB, you take the compass, point it at A and draw an arc of size AB, then you do the same pointing the compass on B. Point P will be one of the intersections of those two arcs. Therefore PA and PB correspond to the radii of the arcs, which were taken both equal to AB, therefore they are congruent.
2) We know that angles PCA and PCB are right angles by the definition of perpendicular.
Perpendicularity is the relation between two lines that meet at a right angle. Since we know that PC is perpendicular to AB by construction, ∠PCA and ∠PCB are right angles.
3) PC ≅ PC by the reflexive property congruence.
The reflexive property congruence states that any shape is congruent to itself.
4) So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by CPCTC (corresponding parts of congruent triangles are congruent).
CPCTC states that if two triangles are congruent, then all of the corresponding sides and angles are congruent. Since ΔACP ≡ ΔBCP, then the corresponding sides AC and BC are congruent.
5) Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of the perpendicular bisector.
<span>The perpendicular bisector of a segment is a line that cuts the segment into two equal parts (bisector) and that forms with the segment a right angle (perpendicular). Any point on the perpendicular bisector has the same distance from the segment's extremities. PC has exactly the characteristics of a perpendicular bisector of AB. </span>
There was 3000 general admission tickets sold and 500 kid ticket sold.
How did I get this?
First, we need to see what information we have.
$2.50 = General admission tickets = (G)
$0.50 = kids tickets = (K)
There were 6x as many general admission tickets sold as kids. G = 6K
We need two equations:
G = 6K
$2.50G + $.50K = $7750
Since, G = 6K we can substitute that into the 2nd equation.
2.50(6K) + .50K = 7750
Distribute 2.50 into the parenthesis
15K + .50K = 7750
combine like terms
15.50K = 7750
Divide both sides by 15.50, the left side will cancel out.
K = 7750/15.50
K = 500 tickets
So, 500 kid tickets were sold.
Plug K into our first equation (G = 6k)
G = 6*500
G = 3000 tickets
So, 3000 general admission tickets were sold,
Let's check this:
$2.50(3000 tickets) = $7500 (cost of general admission tickets)
$.50(500 tickets) = $250 (cost of general admission tickets)
$7500 + $250 = $7750 (total cost of tickets)
Answer:
40m^2
Step-by-step explanation:
Hope it helps!!:)
(0,5.25)(10,13.75)
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (13.75 - 5.25) / (10 - 0) = 8.5/10 = 0.85
y = mx + b
(0,5.25)...x = 0 and y = 5.25
slope(m) = 0.85
now we sub, we r looking for b, the y int
5.25 = 0.85(0) + b
5.25 = b
so ur equation is : y = 0.85x + 5.25 or C(t) = 0.85t + 5.25 <==
cost of a 12 min taxi ride.....sub in 12 for t
C(t) = 0.85t + 5.25
C(12) = 0.85(12) +5.25
C(12) = 10.20 + 5.25 = 15.45
so a 12 min ride would cost u : $ 15.45 <==
