Answer: Yes, ASA, Triangle ABC is congruent to Triangle AHG.
Step-by-step explanation:
AH is congruent to AB ( given)
Angle AHG is congruent to Angle ABC (given)
Angle HAG is congruent to Angle BAC (vertical angles).
Therefore, Triangle ABC is congruent to Triangle AHG by ASA.
If there are 4 marbles left over each time, then we can forget about them for now.
So the question is, what is the smallest number than can be divided into 6,7 and 8?
the numbers have only one non-1 divisor in common: both 6 and 8 are divisible by 3.
so for our purposes we can "delete" one 2 and ask:
what is the smallest number than can be divided into 3,7 and 8 ?
There are no more divisors in common, so we just have to multiply them: 3*7*8=21*8=168
and the 4 marbles "extra"? We add them to this sum.
the the smallest possible number in the box is 168+4=172.
Answer:
1,414
Step-by-step explanation:
2,525 * ( 1 - 30% ) * ( 1 - 20%) = 2,525 *0.7*0.8 = 1,767.5 * 0.8 = 1,414
Answer:
It will cost $700 to play the entire schedule.
Step-by-step explanation:
Given : 
To Find : A softball league has 5 teams, each of which play the others twice. If the league pays $35 per game, how much will it cost to play the entire schedule?
Solution:
Equation for total no. of games when all the teams play each other twice is 
Now we are given that A softball league has 5 teams, each of which play the others twice.
So, Substitute x = 5 in the given equation


So, The total no. of games = 20
Cost for 1 game = $35
So, cost for 20 games = 
Hence it will cost $700 to play the entire schedule.
Answer:
Options (A) and (D)
Step-by-step explanation:
We can write the given division as,

Option (A)
When (2x² + 6x - 8) is divided (x + 5), the remainder is 12.
True.
Option (B)
When (2x² + 6x - 8) is divided (x - 5), the remainder is 12.
False.
Option (C)
When x = 5,
2x² + 6x - 8 = 12
2(5)² + 6(5) - 8 = 50 + 30 - 8
= 72
False.
Option (D)
When x = -5,
2(-5)² + 6(-5) - 8 = 50 - 30 - 8
= 12
True.
Option (E)
(x - 5) is a factor of 2x² + 6x - 8
If (x - 5) is a factor value of 2x² + 6x - 8 should be zero.
False.
Option (F)
(x + 5) is a factor of 2x² + 6x - 8
If (x + 5) is a factor then by substituting x = -5 in the expression value should be zero.
But the value is 12.
False.