1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marissa [1.9K]
3 years ago
14

Prove algebrically that o.o15 can be written as 1/66

Mathematics
1 answer:
Sav [38]3 years ago
4 0
Call x = 0.0151515... (i)

Multiply both sides by 100:

100x = 100 * 0.0151515...

100x = 1.5151515...

That can be expressed as this sum:

100x = 1.5 + 0.0151515... (ii)

Now, subtract (i) from (ii):

100x - x = 1.5 + 0.0151515... - 0.0151515..

99x = 1.5

Multiply both sides by 10, so you get rid of decimals:

10 * 99x = 10 * 1.5

990x = 15

Therefore,

x = 15/990

Now, reduce that fraction by dividing both numerator and denominator by gcd(15, 990) = 15, and you finally get

x = (15 : 15)/(990 : 15)

x = 1/66 <----- there it is.

0.0151515... = 1/66

I hope this helps. =)
You might be interested in
Just a bunch of easy ones
Scilla [17]

Answer:

1. 5lb bag is cheaper

2. 6 mpm (minutes per miles)

3. Brycen

4. 18 mpm faster

5. 32 total shapes

6. 75

7. not enough info

8. 50 miles

9. 2

10. 2

Step-by-step explanation:

3lb=$3.54=1lb=$1.18

5lb=$5.85=1lb=$0.85

12 minutes/2 miles=6 mpm

24 minutes/1 mile=24 mpm

24-6=18 mpm faster

25% of 100= 4

4×8=32

60% of 80= 75

process of elimination:

24.5 is less than 35 so no

50×.7=35, total miles is 50

5 0
3 years ago
Read 2 more answers
Solve by factorizing x² + 8x + 15 + 0
shusha [124]

Download

GET

Algebra

Factor

Factor the polynomial.

(

x

+

3

)

(

x

+

5

)

Tap to view FREE steps...

()|[]√≥

789≤

456/^×>∩∪

123-+÷<π∞

,0.%=

Factor

x

2

+

8

x

+

15

+

0

Regroup terms.

x

2

+

0

+

8

x

+

15

Add

x

2

and

0

.

x

2

+

8

x

+

15

Factor

x

2

+

8

x

+

15

using the AC method.

Tap for fewer steps...

Consider the form

x

2

+

b

x

+

c

. Find a pair of integers whose product is

c

and whose sum is

b

. In this case, whose product is

15

and whose sum is

8

.

3

,

5

Write the factored form using these integers.

(

x

+

3

)

(

x

+

5

)

4 0
3 years ago
Read 2 more answers
Brainly for correct answer -- step by step explination &lt;3
prohojiy [21]

Answer:

694 ft²

Step-by-step explanation:

Calculate the area of all 6 walls, noting that the front and back faces are congruent as are the 2 side faces and top/bottom faces

area = 2(13 × 8.5) + 2(11 × 8.5) + 2(13 × 11)

       = 221 + 187 + 286 = 694 ft²

4 0
4 years ago
The variable overhead rate variance can be defined as which of the​ following? A. Standard rate x​ (Actual hours​ - Standard hou
Katena32 [7]

Answer:

Step-by-step explanation:

In costing analysis, direct materials, labour and direct expenses aggregate to prime cost.  Alternately, the aggregate of indirect materials, labour  and expenses is termed as overhead.  Overheads are classified into fixed and variable.

Variable overhead is one which varies directly as per number of units produced

Variable overhead rate variance = actual costs -(AHxSR)

= Actual costs - (Actual hours x std rate)

= Actual hours x actual rate - actual hours  x std rate

Hence option D is right.

5 0
4 years ago
The smaller triangle is the image of the larger triangle after a dilation. The center of the dilation is (−3,−2). What is the sc
SIZIF [17.4K]

Try this option:

Scale_factor (s_f) is new_size:initial_size:

s_f=8/2=4

answer: 4

7 0
3 years ago
Other questions:
  • The Audubon Society at Enormous State University (ESU) is planning its annual fund raising "Eat-a-thon." The society will charge
    13·1 answer
  • Can someone please help me?
    12·1 answer
  • A sphere and cylinder have the same radius and height. The volume of the cylinder is 30m^3. What is the volume of the sphere?
    8·1 answer
  • the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what
    9·2 answers
  • What is 7- (7r+7)= 6r+7
    10·1 answer
  • Express the confidence interval 0.866 ± 0.037 in open interval form (i.e., (0.155,0.855)).​
    11·1 answer
  • Ashelie is buying fruits at a store. She buys b bananas at $0.99 each and a apples at $0.58 each. What does the expression 0.99b
    5·1 answer
  • El perímetro de un rectángulo es de 30 pulgadas. Si su longitud es 3 veces su ancho, calcula las dimensiones. Please answer in e
    13·1 answer
  • What is the coordinate of the midpoint of WQ?
    11·1 answer
  • Anna paid € 2800 for a dress. Payment was made after the price of the dress was reduced by 30%. What was the starting price?​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!