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o-na [289]
3 years ago
7

{1,2,3,...75,76,77,78}

Mathematics
1 answer:
Vinvika [58]3 years ago
7 0

Answer:

32

Step-by-step explanation:

even numbers are 2,4,6,...,78

it is an A.P.

first term a=2

c.d. d=4-2=2

an=a+(n-1)d

78=2+(n-1)2

76=(n-1)2

n-1=76/2=38

n=38+1=39

now we take multiples of 10

10,20,30,...,70

70=10+(n-1)10

60=(n-1)10

n-1=60/10=6

n=6+1=7

so reqd. number of numbers=39-7=32

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Step-by-step explanation:

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If you didn't notice the pattern, every +5 (<u><em>POSITIVE</em></u> +5), the number in sequence either ends in a 3 or an 8. The equation of the line would be <em>y</em>=5x+5 because the slope (\frac{rise}{run}) is \frac{5}{1}, or 5. Applying Δ<em>y</em>/Δ<em>x</em> ("change in <em>y </em>over change in <em>x</em>": the <em>y</em>-intercept is 5 because the change in <em>y</em> is ±5 (in this explicit case: +5), and the change in <em>x</em> is ±1 (in this explicit case: +1).

The simplest way to find the equation of the line here is utilizing \frac{y2-y1}{x2-x1}. You can use any two points (±) to find the slope, such as (1, 3) and (2,8) ₋ looking at the table I inserted below, you can pick any two points - for instance, 1 & 3 would be (1, 3), 2 & 8 would be (2, 8), 3 & 13 would be (3, 13), and 4 & 18 would be (4, 18). You would find the<em> y</em>-intercept by identifying the change in <em>y</em>, which I did in the paragraph above.

To find slope:

Formula to find the distance between two points: \frac{y2-y1}{x2-x2}

Chosen two points: Point 1 <em>(x1,y1)</em>: (1,3) and Point 2 <em>(x2, y2)</em>: (2,8)

<em>Y2-Y1 </em>will provide the change in<em> y</em> and the rise of the slope. <em>X2-X1 </em>will provide the change in <em>x</em> and the run in slope. \frac{8-3}{2-1}=\frac{5}{1} (8-3=5 and 2-1=1). Therefore, the change in <em>y</em> and rise of the slope is 5, and the change in <em>x </em>and the run in slope is 1. \frac{5}{1} simplifies to 5, so <em>the slope is 5.</em>

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