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3 years ago

What is an equation of the line that passes through the points (-3,-1) and

Mathematics

1 answer:

NARA [144]3 years ago

6 0

The equation of line that passes through the points (-3,-1) and

(-6,3) is:

$y=-\frac{4}{3}x-5$

Step-by-step explanation:

Given points are:

(-3,-1) =(x1,y1)

(-6,3)=(x2,y2)

The slope-intercept form of equation of line is:

$y=mx+b$

We have to find the slope first

$m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{3-(-1)}{-6-(-3)}\\=\frac{3+1}{-6+3}\\=\frac{4}{-3}$

Putting the value of slope in the slope intercept form

$y=-\frac{4}{3}x+b$

To find the value of b, putting the point (-3,-1) in the equation

$-1=-\frac{4}{3}(-3)+b\\-1= 4+b\\b=-4-1\\b=-5$

Putting the values of b and m

$y=-\frac{4}{3}x-5$

The equation of line that passes through the points (-3,-1) and

(-6,3) is:

$y=-\frac{4}{3}x-5$

Keywords: Equation of line, slope intercept form

Learn more about equation of line at:

#LearnwithBrainly

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Alexxandr [17]

Answer:

1/16

Step-by-step explanation:

2^-4

We know that a^ -b = 1/ a^b

2^-4 = 1/2^4

2^4 =16

so 1/2^4 = 1/16

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3 years ago

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Find the area of trapezoid JKLM. Round the answer to the nearest tenth.

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from the diagram, we can see that the height or line perpendicular to the parallel sides is 8.5.

likewise we can see that the parallel sides or "bases" are 24.3 and 9.7, so

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2 years ago

Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common differen

pshichka [43]

Problem 1

<h3>Answer: Arithmetic, common difference = -4</h3>

-------------------

Explanation:

Pick any term of the sequence, and subtract off the previous term to find that,

term2 - term1 = -12 - (-8) = -12 + 8 = -4
term3 - term2 = -16 - (-12) = -16 + 12 = -4
term4 - term3 = -20 - (-16) = -20 + 16 = -4

Each time we get the same result, so that means we have an arithmetic sequence with common difference -4

This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.

Eg: term2 = term1 - 4 = -8-4 = -12.

==========================================================

Problem 2

<h3>Answer: Arithmetic, common difference = 5</h3>

-------------------

Explanation:

Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one

-6+5 = -1
-1+5 = 4
4+5 = 9

Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.

==========================================================

Problem 3

<h3>Answer: Not arithmetic</h3>

-------------------

Explanation:

Unlike the previous two problems, this sequence is not arithmetic.

We can see that

term2 - term1 = 12 - 3 = 9
term3 - term2 = 48 - 12 = 36

The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.

This sequence is instead geometric because

term2/term1 = 12/3 = 4
term3/term2 = 48/12 = 4
term4/term3 = 192/48 = 4

Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.

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3 years ago

Maria is installing gutters on her rectangular shed that measures 10 ft by 9 ft she has 23 ft of gutter already and need to purc

Paha777 [63]

Answer:

Maria needs 3 lengths of gutter of finish the shed.

Step-by-step explanation:

We need to calculate the perimeter of the rectangular shed to know how much 5 feet gutter is needed.

The perimeter of the shed is p = 2(l + b) where l = 10ft and b = 9 ft

p = 2(10 + 9) = 2(19) = 38 ft

Now, the perimeter of the shed also equal 23 ft of gutter already installed plus 5x ft gutter where x = number of gutters.

So 23 + 5x = 38

collecting like terms, we have

5x = 38 - 23

5x = 15

dividing through by 5 we have

5x/5 = 15/5

x = 15/5

x = 3

So, Maria needs 3 lengths of gutter of finish the shed.

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3 years ago

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Answer:

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Step-by-step explanation:

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C is the first derivative. It crosses the x-axis at each place where B is a min or max. C itself has a local maximum at approximately x=-3/4 and a local minimum at approximately x=3/4.

Finally, A is the second derivative. It crosses the x-axis at each place where C is a min or max.

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