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In-s [12.5K]
3 years ago
12

Write the equation in slope-intercept form with the point (2,7.5) with an x intercept of −1.

Mathematics
1 answer:
goblinko [34]3 years ago
7 0

Answer:  y=2.5x+2.5

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Since we know that the line passes through the point (2,7.5) and (-1,0), we can find the slope with this formula:

m=\frac{y_2-y_1}{x_2-x_1}

Substituting values, we get:

m=\frac{0-7.5}{-1-2}\\\\m=2.5

In order to find the y-intercept, we can substitute the slope and the point (-1,0) into y=mx+b and then solve fo "b":

0=(2.5)(-1)+b\\\\0=-2.5+b\\\\b=2.5

Then, the equation of this line in Slope-Intercept form is:

 y=2.5x+2.5

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Anyone please help and explain !! thanks
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8 0
3 years ago
Write the series using summation notation.<br><br> 4 + 8 + 12 + 16 + 20+ . . . + 80
zhannawk [14.2K]

Answer:

\sum ^{20} _{n \to \11} 4n

Step-by-step explanation:

In order to write the series using the summation notation, first we need to find the nth term of the sequence formed. The sequence generated by the series is an arithmetic sequence as shown;

4, 8, 12, 16, 20...80

The nth term of an arithmetic sequence is expressed as Tn = a +(n-1)d

a is the first term = 4

d is the common difference = 21-8 = 8-4 = 4

n is the number of terms

On substituting, Tn = 4+(n-1)4

Tn = 4+4n-4

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The nth term of the series is 4n.

Since the last term is 80, L = 4n

80 = 4n

n = 80/4

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According to the series given 4 + 8 + 12 + 16 + 20+ . . . + 80 , we are to take the sum of the first 20terms of the sequence. Using summation notation;

4 + 8 + 12 + 16 + 20+ . . . + 80  = \sum ^{20} _{n \to \11} 4n

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3 years ago
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kogti [31]

Answer:

r = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

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