What is the 185th digit in the following pattern 12345678910111213141516...?

The proof diagram to complete the question state the missing reason in the proof for the letter given

melisa1 [442]

ANSWER

First proved that line p is parallel to line r

to proof

As given in the question

∠1 ≈∠5

∠1 and ∠5 are corresponding angles

by using the property of the corresponding angles

two lines are cut by a transversal so that the corresponding angles are

congruent, then these lines are parallel.

As shown in diagram q is transversal line.

Thus by using the above property

line p is parallel to line r.

proof of 1(a)

REASON

Vertically opposite angle

The pair of angles formed when two lines intersect each other are called vertically opposite angles.

Thus

∠4 and ∠1 are vertically opposite angle

thus

∠4 ≈∠ 1

proof of 2(b)

REASON

Alternate interior angle

the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles . If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .

as line p is parallel to line r (proof above)

q is transversal

thus

∠4 ≈∠ 5

Hence proved

proof of 3 (c)

As ∠4 ≈∠5 (proof above)

REASON

If two lines are cut by a transversal so that the alternate interior angles

are congruent, then these lines are parallel.

Thus by above property

line p is parallel to line r

Hence proved

4 0

3 years ago

Read 2 more answers

The volume of two spheres are in the ratio 27:125. What is the ratio of their areas?

ExtremeBDS [4]

The volume of two spheres are in the ratio 27:125. The ratio of their areas is 9:25

6 0

2 years ago

How many years will it take an account to double in value, assuming a 5.2% interest rate compounded quarterly? Round your answer

zhuklara [117]

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years.

<h3>How to determine the doubling time of money account</h3>

The compound interest takes into account the change of money deposited in time in contrast with the simple interest, which only takes the initial amount of money into account. Please notice that four quarters equals a year.

The compound interest formula is described below:

C = C' · (1 + r/100)ⁿ (1)

Where:

r - Interest rate
n - Number of periods
C' - Initial money amount
C - Current money amount

If we know that C = 2 · C' and r = 5.2, then the doubling time is:

n = /㏒ C/C'/㏒ (1 + r/100)

n = ㏒ 2/㏒ 1.052

n ≈ 13.674

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years. $\blacksquare$