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
asambeis [7]
3 years ago
13

Determine whether or not 630 is a triangular number. start with the formula t n = n ( n + 1 ) 2 and then use the quadratic formu

la to make your decision. (a) true or false: 630 is a triangular number:
Mathematics
1 answer:
ziro4ka [17]3 years ago
7 0
Triangular sequence = n(n + 1)/2

If 630 is a triangular number, then:

n(n + 1)/2  = 630

Then n should be a positive whole number if 630 is a triangular number.

n(n + 1)/2  = 630

n(n + 1)  = 2*630

n(n + 1)  = 1260

n² + n = 1260

n² + n - 1260 = 0

By trial an error note that 1260 = 35 * 36

n² + n - 1260 = 0

Replace n with 36n - 35n

n² + 36n - 35n - 1260 = 0

n(n + 36) - 35(n + 36) = 0

(n + 36)(n - 35) = 0

n + 36 = 0   or   n - 35 = 0

n = 0 - 36,   or  n = 0 + 35

n = -36, or 35

n can not be negative. 

n = 35 is valid.

Since n is a positive whole number, that means 630 is a triangular number.

So the answer is True.
You might be interested in
A’s DJ service charges a $200 setup fee and $75 an hour after that.
Bogdan [553]

The total cost includes the setup cost + per hour cost.

Let, x represents the time and y represents the total cost.

y=200+75x .... (1)

Let Y represent the cost for B's DJ service.

y=125x .... (2)

a. Graphing both the equations give the intersection point (solution) as (4,500)

It means for 4 hours, the total cost of both the DJ's is same at $500.

b. Substitution Method.

Plug y = 125x in equation (1)

125x= 200+75x

125x-75x=200

50x=200

x=4

y=125\times 4 =500

Hence, the total cost for 4 hours in both the service is $500.

c. Addition method.

Multiply equation (2) by -1

-y = -125x.... Equation (3).

Add euation (1) and equation (3)

y+(-y) = 200+75x-125x

0=200-50x

50x=200, x=4

y=500

Solution: For x = 4, y = 500 ( same as the previous two methods)

For x = 2, equation (1)

y=200+(75\times 2) = 350

For x = 2, equation (2)

y= 125\times 2 =250

Hence, for 2 hours, DJ B would be a better choice since it would charge $250.

For x = 6 hours, equation (1)

y=200+(75\times 6) =650

For x= 6, equation (2)

y=125\times 6=750

For 6 hours, DJ A would be  better option since it charges $650 for 6 hours.



8 0
3 years ago
A mole of 1 gallon cans of paint could cover every square inch of the surface of how many planets the size of the earth?
Nady [450]

Answer:

The answer is 4.4*10^1^0 planets

Step-by-step explanation:

We ll have to find more information first to solve this question.

1. One mole = 6.022 x 10^23

Assuming one gallon of paint covers the 400 sq ft of area.

Thus total area which can be covered by 1 mole of gallon is

=6.022*10^2^3 * 400\\=2.40*10^2^6

2. Now we will find the surface area of earth

Area = 4\pi R^2

The radius of earth is 2.1 x 10^7 Feet

substituting values

Area = 4*3.14*(2.1*10^7)^2\\Area = 5.5*10^1^5ft^2

3. Now we will find out the number of planets of earth size which can be covered by mole of gallon of paint

= Total area one mole of gallon can cover / area of earth

= 2.40 * 10^2^6/5.5*10^1^5\\=4.4*10^1^0 planets

6 0
3 years ago
WILL MARK BRAINLST plzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me
Andreas93 [3]
B=H+j that is an answer
8 0
2 years ago
Read 2 more answers
Work out the sum of 8.2 and 949.65.
olga2289 [7]

Answer:

957.85

Step-by-step explanation:

  949.65

+     8.2

_________

   957.85

7 0
3 years ago
Read 2 more answers
4.131313.... as a fraction and a mixed number
Musya8 [376]
  • <em>Answer:</em>

<em>  409/99</em>

<em>  4  13/99</em>

  • <em>Step-by-step explanation:</em>

<em>Hi there !</em>

<em>4.131313.. = 4.(13) = 4  13/99 = (4*99+13)/99 = 409/99</em>

<em>Good luck !</em>

6 0
3 years ago
Other questions:
  • Write the decimal expansion for seven ninths
    15·2 answers
  • Find the midpoint of the line segement from (5,-1) to (-2,-4)
    5·1 answer
  • 2/4 plus 1/2. Please help
    14·2 answers
  • What happens to the value of the function as the number of iterations increases?
    15·2 answers
  • 6x over 11 =12over 11
    8·1 answer
  • on a function map, the values for the domain of the function appear on the ______ and the values for the range appear on the ___
    8·1 answer
  • 1 minus what equals 1/4 plus 3/8
    6·1 answer
  • What is the value of x?<br><br><br><br> Enter your answer in the box.
    5·1 answer
  • If TS is a midsegment of PQR find TS
    7·1 answer
  • Which set of tokens represents 0?<br> Positive<br> Negative<br><br><br> Pls helpp!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!