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 father and his son decide to sum their age. The sum is equal to sixty years. Six years ago, the age of the father was five tim
arlik [135]

Answer:

20

Step-by-step explanation:

To solve this you have to make a system of equations.

Since the father and son's age sum up to 60, the first equation will be:

f + s = 60

Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:

6 - (5s) = f

Now, you have to solve the first equation to let it equal to s

f + s = 60

f = 60 - s

Plug in

6 - 5s = 60 - s

     +s          +s

6 - 4s = 60

-6         -6

---------------------

-4s = 54

-----   -----

 -4     -4

   s ≅ 14

14 + 6 = 20

5 0
1 year ago
Read 2 more answers
When two numbers are not equal, an ___ is a sentence that uses the symbols >, <, ≥, ≤, or ≠ to show a relationship.
alukav5142 [94]

Answer:

Inequality

Step-by-step explanation:

Inequality is show a comparison between the two quantities which are unequal.

It can be represented:

≤  ⇒  less than or equal to

< ⇒ less than

≠ ⇒ not equal to

> ⇒ greater than

≥ greater than or equal to

<u><em>Kavinsky</em></u>

5 0
2 years ago
Please help me out. I need help ASAP
katrin [286]
B and D and C in that order
4 0
3 years ago
Read 2 more answers
Use the law of wines to find the value of y. Round to the nearest Tenth
Eva8 [605]

Answer:

y ≈ 2.5

Step-by-step explanation:

Using the Sine rule in Δ XYZ

\frac{sinZ}{XY} = \frac{sinY}{XZ} , substitute values

\frac{sin50}{2} = \frac{sin75}{y} ( cross- multiply )

y sin50° = 2 sin75° ( divide both sides by sin50° )

y = \frac{2sin75}{sin50} ≈ 2.5 ( to the nearest tenth )

4 0
3 years ago
Which statement is always true? A.) The absolute value of an integer is equal to the opposite of the integer B.) a positive inte
Ahat [919]

Answer:

the absolute value of an integer is equation to the opposite of the integer

3 0
3 years ago
Read 2 more answers
Other questions:
  • Express the height of the following rectangular prism in meters. (Note: 1 m = 100 cm)
    13·1 answer
  • Which choice is equivalent to the expression below? √-121
    10·2 answers
  • a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii
    12·1 answer
  • What is the value of x-3
    13·1 answer
  • How many even positive integers less than 300 can be written using the number 2 4 5 and 8?
    12·1 answer
  • Prove that the diagonals of a rhombus are perpendicular using coordinate geometry
    13·1 answer
  • If 5x−4y=22 and 3x+6y=30, what is the value of x−5y
    15·1 answer
  • The total surface area of a cube is 1350sqcm find volume?​
    8·1 answer
  • Зх – 8 = 163 whats the response
    14·2 answers
  • Use synthetic division to find the result when 3x^3 + 13x^2 + x – 12 is divided by<br> X + 4.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!