<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>
Answer:
he makes $12 less.
Step-by-step explanation:
$80X12=960 - Matts income for the year
960-816=144 -How much less James makes than Matt per year
144/12=12 - How much less James makes than Mat per month
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We can tell from the data that there is a midpoint between the lowest and highest point of the clock, which is at a height of 9.5 feet.
Moreover, the lowest point occurs at 6 o clock, and the highest occurs at 12 o clock.
The amplitude of variation from the mid-point is 0.5 feet given by (10 - 9) / 2.
Finally, the time period for the equation is 12 hours. Thus, the answer is:
h = 0.5cos(πt/6) + 9.5, option B
Answer:
N=27 participants
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.
If we assume that we have 
independent variables and we have 
individuals, we can define the following formulas of variation:
And we have this property
The degrees of freedom for the model on this case is given by 
where k =2 represent the number of variables.
The degrees of freedom for the error on this case is given by 
. Sinc we know k we can find N.
And the total degrees of freedom would be 
On this case the correct answer would be N=27 participants
Answer:
x =19.20
Step-by-step explanation:
We can use ratios to solve
14 wings 12 wings
------------- = ---------------
22.40 x
Using cross products
14x = 22.40 * 12
14x =268.8
Divide each side by 14
14x/14 = 268.8/14
x =19.20
