Determine if the lines are parallel, perpendicular, or neither. x - y = 4 and x + y = 9
2 answers:
Answer:
Perpendicular
Step-by-step explanation:
What I would do first is to rearrange these equations into the equation of a line formula:
To do so, we isolate y:
x - y = 4 -> -y = -x+4 -> (multiply both sides by -1) y=x-4
x+y=9 -> y=-x+9
We know that in the formula y=mx + c, m stands for gradient of a line (The degree of steepness of the line), and we know that if there is no number before x it means that it is 1 or -1 (depending on the sign before x).
so that on y=x-4 the gradient is 1 and on y=-x+9 the gradient is -1.
We now can check if its parallel, perpendicular or neither with these equations:
m1 · m2 = -1 for perpendicular, m1 = m2 for parallel,(where m = gradient)
we plug the values of the two gradients into the first equation
(m1 · m2 = -1) and it fits: 1 x -1 = -1
If we plug the same values into the second equation (m1 = m2), we can check that 1 ≠ -1
In conclusion, we can check that these lines are perpendicular to each other.
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<h3>What are quadrilaterals?</h3>Quadrilaterals are shapes that have four sides and four angles.
The four sides may or may not be congruent, and at the same time the four angles may or may not be congruent
<h3>How to determine the value of x?</h3>The image that completes the question is added at the end of this solution as an attachment
From the attached figure, we have the following highlights
- Opposite angles of the quadrilateral are congruent
- Adjacent sides of the quadrilateral are congruent
This means that:
AD = DC
AB = BC
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ADB = CDB
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Divide both sides by 2
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The first thing you need to do is get the median of the whole set.
The median is the center so since there are 17 numbers the center is 69 and 69 is Q2
Next we need to find Q1 Q3 and Q4 Also, are whiskers are below.
Whisker minimum = 55
Whisker maximum = 91
Now to find Q1 we have to get the median of the first half of the data.
We need to get the median of the following data set.
55, 56, 57, 58, 58, 64, 65, 66
(58+58) / 2 = 58
Q1 = 58
Now we need to find Q3. To do that we get the median of the second half of the data.
75, 77, 78, 81, 81, 85, 86, 91.
(81 + 81) / 2 = 81
Q3 = 81
Now we have all our quartiles and whiskers, which are below, it is time to create our box and whisker plot. Note, create a horizontal or vertical number line with appropriate data. Also the box part is from Q1 to Q3 and your whiskers goes from your minimum to your box and from your maximum to your box.
Whisker Minimum = 55
Q1 = 58
Q2 = 69
Q3 = 81
Whisker Maximum = 91
The median is the center so since there are 17 numbers the center is 69 and 69 is Q2
Next we need to find Q1 Q3 and Q4 Also, are whiskers are below.
Whisker minimum = 55
Whisker maximum = 91
Now to find Q1 we have to get the median of the first half of the data.
We need to get the median of the following data set.
55, 56, 57, 58, 58, 64, 65, 66
(58+58) / 2 = 58
Q1 = 58
Now we need to find Q3. To do that we get the median of the second half of the data.
75, 77, 78, 81, 81, 85, 86, 91.
(81 + 81) / 2 = 81
Q3 = 81
Now we have all our quartiles and whiskers, which are below, it is time to create our box and whisker plot. Note, create a horizontal or vertical number line with appropriate data. Also the box part is from Q1 to Q3 and your whiskers goes from your minimum to your box and from your maximum to your box.
Whisker Minimum = 55
Q1 = 58
Q2 = 69
Q3 = 81
Whisker Maximum = 91