I think that first you need to understand what CPCTC is used for.
Let's start with the definition of congruent triangles.
Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.
A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.
Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.
Problem 1.
Statements Reasons
1. Seg. AD perp. seg. BC 1. Given
2. <ADB & <ADC are right angles 2. Def. of perp. lines
3. <ADB is congr. <ADC 3. All right angles are congruent
4. Seg. BD is congr. seg CD 4. Given
5. Seg. AD is congr. seg. AD 5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD 6. SAS
7. Seg. AB is congr. seg. AC 7. CPCTC
Let the price of a ticket be originally T dollars, and the number of clients be N.
let the price decrease by x 3-dollars.
"there is an average increase of 4 people for every $3 decrease on the price of the ticket."
means:
if the price is decreased by 1-3$:
then N become N+4, and T becomes T-3
if the price is decreased by 2-3$:
then N become N+4+4=N+2*4, and T becomes T-3-3=T-2*3
So if the price is decrease by x-3 dollars:
N becomes N+4x, and T becomes T-3x
"A circus owner sells an average of 340 tickets when the price of a ticket is $75."
In this case N=340, and T=75$
If the owner does not change the price ticket, x=0, the revenue is 340*75,
If the owner decreases the price of the tickets by x-3$, then the revenue will be
(N+4x)(T-3x)=(340+4x)(75-3x) dollars,
If R is the function of the revenue depending on x, then
R(x)=(340+4x)(75-3x) dollars
Answer: R(x)=(340+4x)(75-3x) dollars
Answer:
Choice A.
Step-by-step explanation:
Let x = price of a helmet, y = price of a bat, z = price of a ball.
Company A can provide 9 helmets, 6 bats, and 12 balls for $525.
9x + 6y + 12z = 525
Company B can provide 10 helmets, 8 bats, and 10 balls for $600.
10x + 8y + 10z = 600
Company C can provide 8 helmets, 5 bats, and 15 balls for $500.
8x + 5y + 15z = 500
Answer: Choice A.
Answer:
y=x+20
Step-by-step explanation:
The y-intercept is 20, as the line is on the y-axis while x is 0. The slope would be 0, because the y and x values both increase by 10, so 10/10 which simplifies to 1. The result would be y=10/10x + 20 simplifying to y=1x+20, which is y=x+20.
Hope this helps!
Answer:
Shapes 1 and 3 are congruent
Step-by-step explanation:
The only thing different between them is that the first one is tilted to look different.