Mathematics, 23.02.2020 02:19 brookemcelhaney

I need assistance please!!

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Answer from: lackin2056

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 7x - 5

Comparing with the slope intercept form, slope = 7

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (2, 1) is 7

To determine the intercept, we would substitute m = 7, x = 2 and

y = 1 into y = mx + c. It becomes

1 = 7 × 2 + c = 14 + c

c = 1 - 14

c = - 13

The equation becomes

y = 7x - 13

If the two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (2, 1) is - 1/7

To determine the intercept, we would substitute m = - 1/7, x = 2 and

y = 1 into y = mx + c. It becomes

1 = - 1/7 × 2 + c = - 2/7 + c

c = 1 + 2/7

c = 9/7

The equation becomes

y = - x/7 + 9/7

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

one set of data has more variation than the other. hope this !

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