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3 years ago

11

A line passes through the point (-1, -9) and has a slope of -7.

1 answer:

tia_tia [17]3 years ago

7 0

Answer:

y = -7x - 16

Step-by-step explanation:

The formula for the equation of a line is y=mx+b, where m is the slope and b is the y-intercept. Since we already know the slope, all that is left is the value of b, which can be found by substituting the values of the point (-1, -9) into the equation and solving:

$-9=-7(-1)+b$

$-9=7+b$

$b=-9-7=-16$

With this, we get the value -16, making the equation y = -7x - 16

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Rearrange this to make a the subject

lyudmila [28]

Answer:

w = 3(2a + b) - 4

w = 6a + 3b - 4

a = (w - 3b + 4) / 6

7 0

4 years ago

Read 2 more answers

Find the indicated nth partial sum of the arithmetic sequence.<br> −7, −3, 1, 5, . . ., n = 30

TiliK225 [7]

Step-by-step explanation:

Given the Arithmetic sequence

$-7, -3, 1, 5, . . .$

An arithmetic sequence has a constant difference d and is defined by

$a_n=a_1+\left(n-1\right)d$

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$-3-\left(-7\right)=4,\:\quad \:1-\left(-3\right)=4$

$\mathrm{The\:difference\:between\:all\:of\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$d=4$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=-7$

as

$a_n=a_1+\left(n-1\right)d$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=4\left(n-1\right)-7$ ∵ $d=4$

$\mathrm{Arithmetic\:sequence\:sum\:formula:}$

$n\left(a_1+\frac{d\left(n-1\right)}{2}\right)$

$\mathrm{Plug\:in\:the\:values:}$

$n=30,\:\space a_1=-7,\:\spaced=4$

$=30\left(-7+\frac{4\left(30-1\right)}{2}\right)$

$=30\left(58-7\right)$ ∵ $\frac{4\left(30-1\right)}{2}=58$

$=30\cdot \:51$

$=1530$ ∵ $\mathrm{Multiply\:the\:numbers:}\:30\cdot \:51=1530$

Therefore, the indicated nth partial sum of the arithmetic sequence is 1530.

ANOTHER METHOD

as

$a_n=4\left(n-1\right)-7$

n = 30

$\sum _{n=1}^{30}\:4\left(n-1\right)-7$

$=\sum _{n=1}^{30}4n-11$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \sum a_n+b_n=\sum a_n+\sum b_n$

$=\sum _{n=1}^{30}4n-\sum _{n=1}^{30}11$

as

$\sum _{n=1}^{30}4n=1860$

and

$\sum _{n=1}^{30}11=330$

so

$=1860-330$

$=1530$

7 0

4 years ago

9:45 on Tuesday Questions

Sergio039 [100]

Answer:

95°
85°

Step-by-step explanation:

<u>Given angles are consecutive interior angles which sum up to 180°</u>

9x + 14 + 8x + 13 = 180
17x = 180 - 27
17x = 153
x = 153/17
x = 9

<u>Angles</u>

9x + 14 = 9*9 + 14 = 81 + 14 = 95°
8x + 13 = 85°

8 0

3 years ago

Which options are correct representations of slope?

kakasveta [241]

Answer: Option 2

Step-by-step explanation:

7 0

3 years ago

Graph the line with slope 1/2<br> passing through the point (-4,1).

dem82 [27]

Answer:

from (-4,1) the line will go up to (-2,2) then (0,3)

Step-by-step explanation:

the slope 1/<em>2</em> dictates that the line will go up by 1 unit for every <em>2</em> units, then we just plot said line from the point given (<em>-4</em>,1) where we go up y by 1 and we go left on <em>x</em> by <em>2</em>

image could not be provided at this time, tho the line will have a slope that is between horizontal and increasing (to the left) at roughly 30 degrees ish

5 0

3 years ago