Which theorem or postulate proves the two triangles are similar?
1 answer:
Answer:
The corresponding pair of sides are in the same ratio.
Step-by-step explanation:
For two triangles to be similar, the theorem that is required is the corresponding sides of the two triangles are in the same ratio.
Now, see the diagram of two triangles given with the question.
The ratios of the corresponding sides are
If two pairs corresponding sides are in 5 : 4 ratio, then the third pair of corresponding sides will also be in 5 : 4 ratio.
Therefore, the two triangles are similar. (Answer)
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This is a growth exponential equation.
It can be solved 2 ways, but one of them is long and cumbersome and not worth the effort. You could take 2% of the base number and keep doing it 8 times.
The other way is to realize that 100$ + 2% of 100 dollars can be written as 2% = 2/100 = 0.02 and that can be written as
100( 1 + 0.02 ) = 100(1.02) Now if you want this to be raised 8 times, it will look like this
y = 100(1.02)^(n - 1) for any number of weeks
y(8) = 100(1.02)^7 = 114.87
So at week 1 she has 100 dollars and at week 8 she has 114.87 dollars.
Comment
Realize that if her boss does not want to give her compounded interest that she could still make
Ln = L
= 100 + (n - 1)*0.02*100
L
= 100 + 7*0.02*100 = 100 + 14. = 114
By compounding she makes a whole 0.87$ more.
It can be solved 2 ways, but one of them is long and cumbersome and not worth the effort. You could take 2% of the base number and keep doing it 8 times.
The other way is to realize that 100$ + 2% of 100 dollars can be written as 2% = 2/100 = 0.02 and that can be written as
100( 1 + 0.02 ) = 100(1.02) Now if you want this to be raised 8 times, it will look like this
y = 100(1.02)^(n - 1) for any number of weeks
y(8) = 100(1.02)^7 = 114.87
So at week 1 she has 100 dollars and at week 8 she has 114.87 dollars.
Comment
Realize that if her boss does not want to give her compounded interest that she could still make
Ln = L
L
By compounding she makes a whole 0.87$ more.
Answer:
The number of free throws, two-point throw, and three-point throw are 135, 173, and 111 respectively.
Step-by-step explanation:
Let x,y, and z are the numbers of two-point field goals, numbers of three-point field goals, and the number of free-throws (one-point goal) respectively.
The total points= 814
As the number of two-point goals was 49 less than double the number of three-point field goals she made.
Again, the number of free goals was 38 less than the number of two-point field goals she made.
From equations (i) and (iii)
2x+3y+x-38=814
[using equation (ii)]
From equation (ii),
From equation (iii),
.
Hence,
The number of free throws, z= 135
The number of two-point throw, x=173
The number of three-point throw, y=111.