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lesantik [10]
2 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]2 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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Write and equivalent exponential expression for "five to the third power"
Alinara [238K]

Answer:

<h3>5^3</h3>

Step-by-step explanation:

There should be a regular 5 with a little three to the top right corner of the 5.

6 0
3 years ago
Kim purchased a $65.00 dress for 20% off. How much did she save?
Ainat [17]
The best thing to do here is to find ten percent, and then double it.
To do this, you divide the number you have by 10.
65.00/10= 6.50
Therefore, you've now got to multiply this by 2.
6.5*2= 13
Therefore, Kim saved $13 on the price of the dress.
Hope this helps :) 
6 0
3 years ago
12
Sergeu [11.5K]

Answer:

5 pints per hour.

Step-by-step explanation:

Morning:

Given:

Number of strawberries packed in every 4 minutes = 3

∴ Number of strawberries packed in every one minute = \frac{3}{4}

So, number of strawberries packed in every 60 minutes = \frac{3}{4}\times 60=45

1 hour = 60 minutes.

So, strawberries are packed at a rate of 45 pints per hour in the morning.

Afternoon:

Number of strawberries packed in every 3 minutes = 2

∴ Number of strawberries packed in every one minute = \frac{2}{3}

So, number of strawberries packed in every 60 minutes = \frac{2}{3}\times 60=40

1 hour = 60 minutes.

So, strawberries are packed at a rate of 40 pints per hour in the afternoon.

Difference between the packing rates is given as:

Morning rate - Afternoon rate = 45 - 40 = 5 pints per hour.

So, she packed 5 more pints in one hour in the morning than in the afternoon.

3 0
3 years ago
Please help!<br> What's the answer to this?: (-5x^2)^3
timurjin [86]
The answer is -125x^6
You do
(-5)^3 * (x^2)^3
8 0
3 years ago
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The formula for the nth square number is S_n = n^2. Use the formula to find the 11th square number​.
Klio2033 [76]

Answer:

121.

Step-by-step explanation:

S_{11} = 11^{2} = 121. So, the 11th  square number is 121.

4 0
3 years ago
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