Answer:
You must be no older than 13 to play a game.
Step-by-step explanation:
≤ this sign means equal to or less than in this case it is 13
Given:
To find:
The highest and lowest scores Sam could have made in the tournament.
Solution:
We have,
It can be written as
Add 288 on both sides.
and 
and 
Therefore, the highest and lowest scores Sam could have made in the tournament are 290 and 286 respectively.
<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>
Okay. So, to find the percent change, we have to do change/original. In this case, it would be 12/15, because 15 and 27 are apart by 12. 12/15 is 0.8. Multiply that by 100 and you get 80. There was an 80% markup of the chair sold to the antique dealer.
ANSWER
3) b
EXPLANATION
Given that:
and
Recall that the sine and cosine functions are equal for complementary angles.
This implies that,
