Answer:
Step-by-step explanation:
1a) angle x and angle y are corresponding angles. Both angles lie on the same side of the transversal. Since the lines are parallel, the angles are equal.
1b) angle x and angle y are interior angles on the same side of the transversal. Since the lines are parallel, the angles are equal supplementary.
1c) angle x and angle y are corresponding angles. Both angles lie on the same side of the transversal. Since the lines are parallel, the angles are equal.
1d) angle x and angle y are alternate interior angles. They are between the parallel lines and alternate sides of the transversal. Since the lines are parallel, the angles are equal.
Answer:
The greatest number of 15 inches pieces that can be cut from 5 rolls of length 9 feet is: 35
Step-by-step explanation:
Given
Total length of one roll of ribbon = 9 feet
As the pieces have to be cut into inches, we will convert the measurement in feet to inches
As there are 12 inches in one feet, 9 feet will be equal to:
9*12 = 108 inches
Now first of all, we have to see how many 15 inches pieces can be cut from one role
So,

So the seamstress can cut 7 15-inch long pieces from a roll.
Now given that he has to cut from 5 rolls, the total number of 15-inch pieces will be:

Hence,
The greatest number of 15 inches pieces that can be cut from 5 rolls of length 9 feet is: 35
ANSWER:
6_34/99
STEP:
So yes. When a decimal is repeating, you can take the repeating number (most likely a decimal) and put 99 under it. Since 99 cannot be solved, you put 99. So, 34/99. Though we are not finished. There is still the whole 6 number left. So, you do 6_34/99.
Proof:
10x=6.6...
-x=-0.6...
9x=6
x=6/9=1/3.
<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:

where n is a positive integer.
then we have:

Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.

- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:

( Since, the result was true for n=k )
Hence, we have:

Also, we know that:

(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,

Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
Reciprocals are technically flipped fractions. So it would be 10/9. 9 goes into ten one time, so it's 1 1/9.