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scZoUnD [109]
3 years ago
9

Which of the following line passes through point (-4,5) and is parallel to the line segment whose endpoints are at (-2,-3) and (

2,5)?
Mathematics
1 answer:
NNADVOKAT [17]3 years ago
8 0

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal.

Then, the requested line will have a slope equal to:

m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5 - (- 3)} {2 - (- 2)} = \frac {5 +3} {2 + 2} = \frac {8} {4} = 2

Thus, the line is of the form:

y = 2x + b

We substitute point (-4,5)and find "b":

5 = 2 (-4) + b\\5 = -8 + b\\5 + 8 = b\\b = 13

Finally, the equation is:

y = 2x + 13

Answer:

y = 2x + 13

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The length of a rectangular garden is three times its width, w. The area of the garden is 300 m². Explain why the expression 3w
kogti [31]

If the length is three times the width and the area of the rectangle is

300 m^{2} then the length of rectangle is 30m and width be 10m.

Given that the length is three times the width and the area of the rectangle is 300 m^{2}.

We are required to find the length and breadth of the rectangle.

Area of the rectangle is basically the product of length and breadth.

let the breadth of rectangle be w.

The length of rectangle will be 3w.

Area=Length*Breadth

300=3w*w

300=3w^{2}

100=w^{2}

w=+10,-10 but ignore -10 because width cannot be negative.

Length=3w=3*10=30m

Width=w=10m

The area can be written as 3w^{2} because the area of rectangle is product of length and breadth.

Hence if the length is three times the width and the area of the rectangle is  300 m^{2} then the length of rectangle is 30m and width be 10m.

Learn more about area at brainly.com/question/25292087

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3 0
2 years ago
In laymens terms how do I find the term of a sequence?
Mazyrski [523]

Answer:

To find the "nth" term of an arithmetic sequence, start with the first term, a(1). Add to that the product of "n-1" and "d" (the difference between any two consecutive terms). For example, take the arithmetic sequence 3, 9, 15, 21, 27.... a(1) = 3. d = 6 (because the difference between consecutive terms is always 6.

Step-by-step explanation:

5 0
3 years ago
What is the equation of the line that passes through (-5, 0) and (4, 3)?
kotegsom [21]

Answer:

y = 1/3x + 5/3

Step-by-step explanation:

An equation contains a slope and y-intercept, in the form y = mx + b. To find the slope or m, you need to plug the coordinates into the slope formula.

y2 - y1/ x2 - 1

3 - 0/ 4 - (-5)

= 3 / 9

= 1/3

Now that we know the slope, we need to plug the values of x and y to find the y-intercept.

y = 1/3x + b

3 = 1/3(4) + b

3 = 4/3 + b

5/3 = b

The equation is y = 1/3x + 5/3

3 0
3 years ago
Use matrices to write the equation of the function in the form y = mx + b that contains the points
Fofino [41]

The line has a slope of -6 and a y intercept of 7.

The linear equation is given by:

y = mx + b;

where m is the slope of the line, b is the y intercept, y, x are variables.

The equation of the line passing through the points (6.-29) and (-4,31) is:

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-29)=\frac{31-(-29)}{-4-6}(x-6)\\\\y+29=-6(x-6)\\\\y=-6x+7

Hence the line has a slope of -6 and a y intercept of 7.

Find out more at: brainly.com/question/13911928

3 0
3 years ago
A library checked out 52 books. 24 are fiction books what is the ratio for fiction to non fiction books. Please show how it is d
GenaCL600 [577]
24:28

52 (total books) minus 24 (fiction books) equals 28 (non fiction books)
8 0
3 years ago
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