- AC is congruent to itself
- AC bisects angle BAD, so that angles BAC and DAC are congruent
- Both angles B and D are right angles, so they are congruent
This means triangles BAC and DAC are a pair of angle-angle-side triangles, so they are congruent to one another. Corresponding parts of congruent triangles are congruent, so the line segments BC and DC are congruent and have the same length.
Then
Since they are different people with different thoughts and knowledge giving them to choose different numbers all though two of them might choose the same number
Answer: 48 tickets
Step-by-step explanation:
Since the expression that gives the number of tickets a player wins if he shoots the ball in the hoop t times is expressed as 3t.
Therefore, the number of tickets that a player wins if he shoots the ball in the hoop 16 times will be:
= 3t
where,
t = 16
Therefore, 3t = 3 × 16 = 48
The player wins 48 tickets.
Answer:
Step-by-step explanation:
When using the substitution method we use the fact that if two expressions y and x are of equal value x=y, then x may replace y or vice versa in another expression without changing the value of the expression.
Solve the systems of equations using the substitution method
{y=2x+4
{y=3x+2
We substitute the y in the top equation with the expression for the second equation:
2x+4 = 3x+2
4−2 = 3x−2
2=== = x
To determine the y-value, we may proceed by inserting our x-value in any of the equations. We select the first equation:
y= 2x + 4
We plug in x=2 and get
y= 2⋅2+4 = 8
The elimination method requires us to add or subtract the equations in order to eliminate either x or y, often one may not proceed with the addition directly without first multiplying either the first or second equation by some value.
Example:
2x−2y = 8
x+y = 1
We now wish to add the two equations but it will not result in either x or y being eliminated. Therefore we must multiply the second equation by 2 on both sides and get:
2x−2y = 8
2x+2y = 2
Now we attempt to add our system of equations. We commence with the x-terms on the left, and the y-terms thereafter and finally with the numbers on the right side:
(2x+2x) + (−2y+2y) = 8+2
The y-terms have now been eliminated and we now have an equation with only one variable:
4x = 10
x= 10/4 =2.5
Thereafter, in order to determine the y-value we insert x=2.5 in one of the equations. We select the first:
2⋅2.5−2y = 8
5−8 = 2y
−3 =2y
−3/2 =y
y =-1.5
Nothing can be further done with the linear equation
