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lesantik [10]
3 years ago
13

Triangular numbers can be represented with equilateral triangles formed by dots the first fire triangle numbers are 1 3 6 10 and

15 is there a direct variation between a triangle number and its position in the sequence explain your reasoning
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
3 0

Answer:

There's no direct variation

Step-by-step explanation:

Required

Determine if there's a direct variation between the number and its position

I'll start by giving an illustration of how the triangle is represented using stars (*)

*

**

***

****

*****

Represent the line number with y and it's position with x

On line 1:

y = 1, x = 1

On line 2:

y = 2, x = 3

On line 3:

y = 3, x = 6

On line 4:

y = 4, x = 10

On line 5:

y = 5, x = 15

Note that, x is gotten by calculating the accumulated number of stars while y is the line number.

Direct variation is represented by

y = kx

Or

kx = y

Where k is the constant of variation

For line 1:

Substitute 1 for y and 1 for x

k * 1 = 1

k = 1

For line 2:

Substitute 2 for y and 3 for x

k * 3 = 2

Divide through by 3

k = ⅔

Note that the values of k in both computations differ.

This implies that there's no direct variation and there's no need to check further.

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Given ABC find the values of x and y. In your final answer, include all of your calculations.
kow [346]

So with this, we will be using proportions. To solve for x, our proportion will be \frac{x}{6} =\frac{6}{x-9}


Firstly, cross-multiply: x^2-9x=36


Next, subtract 36 on both sides: x^2-9x-36=0


Next, replace -9x with 3x-12x x^2+3x-12x-36=0


Next, factor x^2+3x and -12x-36 separately: x(x+3)-12(x+3)=0 . After, rewrite it as (x-12)(x+3)=0


Next, solve for x separately in the two parentheses:

x-12=0\\ x=12

x+3=0\\ x=-3


Since we can't have a negative length, x = 12.



To solve for y, our proportion will be \frac{y}{9} =\frac{12}{y}


Firstly, cross-multiply: y^2=108


Next, just square root each side, and your answer will be (rounded to hundredths) y=10.39



In short, x = 12 and y = 10.39.

5 0
3 years ago
Solve 14x-7y= 21 for y<br> A. y = 2x - 21<br> B. y=-14x + 21<br> C. y = 14x +3<br> D. y=2x-3
jonny [76]

Answer:D

Step-by-step explanation::

3 0
1 year ago
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M^2 × n^(-2) ........
5 0
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2.5 x 2.5 X 2.5 - 1.4 x 1.4 x 1.4÷(2.5) + 2.5 X 1.4 + (1.4)​
Nana76 [90]

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Step-by-step explanation:

4 0
3 years ago
The net of a square pyramid is shown
Wewaii [24]

Answer:

Option (D)

Step-by-step explanation:

Surface area of a square pyramid is determined from the formula,

Surface area = Area of the square base + 4(Area of one lateral triangular side)

Area of the base = (Side)²

                            = 8²

                            = 64 cm²

Area of one lateral triangle = \frac{1}{2}(\text{Base})(\text{Height})

                                             = \frac{1}{2}(8)(8)

                                             = 32 cm²

Therefore, surface area of the square pyramid = 64 + 4(32)

                                                                              = 64 + 128

                                                                              = 192 cm²

Therefore, Option (D) will be the correct option.

3 0
3 years ago
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