Find the perimeter of each figure select the figure that have a perimeter of 20 units
2 answers:
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Answer:
Please check the explanation.
Step-by-step explanation:
- Two lines are parallel if their slopes are equal.
- Two lines are perpendicular if the product of their slope is -1
We also know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept
Given the lines
1)
- y = 6х - 3
Comparing with y=mx+b, the slope of y = 6х - 3:
m₁=6
- y = - 1/6x + 7
Comparing with y=mx+b, the slope of y = - 1/6x + 7:
m₂=-1/6
As
m₁ × m₂ = -1
6 × - 1/6 = -1
-1 = -1
Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.
2)
- y = 3x + 2
Comparing with y=mx+b, the slope of y = 3x + 2:
m₁=3
- 2y = 6x - 6
simplifying to write in slope-intercept form
y=3x-3
Comparing with y=mx+b, the slope of y=3x-3:
m₂=3
As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.
i.e. m₁ = m₂ → 3 = 3
Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.
3)
- 8x - 2y = 3
simplifying to write in slope-intercept form
y = 4x - 3/2
Comparing with y=mx+b, the slope of y = 4x - 3/2:
m₁=4
- x + 4y = - 1
simplifying to write in slope-intercept form
y=-1/4x-1/4
Comparing with y=mx+b, the slope of y=-1/4x-1/4:
m₂=-1/4
As
m₁ × m₂ = -1
4 × - 1/4 = -1
-1 = -1
Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.
4)
- 3x+2y = 5
simplifying to write in slope-intercept form
y = -3/2x + 5/2
Comparing with y=mx+b, the slope of y = -3/2x + 5/2:
m₁=-3/2
- 3y + 2x = - 3
simplifying to write in slope-intercept form
y = -2/3x - 1
Comparing with y=mx+b, the slope of y = -2/3x - 1:
m₂=-2/3
As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.
5)
- y - 5 = 6x
simplifying to write in slope-intercept form
y=6x+5
Comparing with y=mx+b, the slope of y=6x+5:
m₁=6
- y - 6x = - 1
simplifying to write in slope-intercept form
y=6x-1
Comparing with y=mx+b, the slope of y=6x-1:
m₂=6
As the slopes of y - 5 = 6x and y - 6x = -1 are equal.
i.e. m₁ = m₂ → 6 = 6
Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.
6)
- y = 3х + 9
Comparing with y=mx+b, the slope of y = 3х + 9:
m₁=3
- y = -1/3x - 4
Comparing with y=mx+b, the slope of y = 1/3x - 4:
m₂=1/3
As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.
a) The probability that both John and Jane watch the show is 0.12.
b.The probability that Jane watches the show, given that John does is 0.1714.
c)They do watch show independent of each other.
Step-by-step explanation:
Here, as given in the question:
Probability that John watches a certain show = 0.7 ⇒ P(J) = 0.7
Probability that Jane watches a certain show = 0.3 ⇒ P(Je) = 0.3
Probability that John watches a certain show given Jane watches it to
= 0.4 ⇒ P(J/Je) = 0.4
a. ) Here, we need to find the probability of both Jane and John watching a show , P(J∩Je)
Now, by BAYES THEOREM:
Hence the probability that both John and Jane watch the show is 0.12.
b.) The probability that Jane watches the show, given that John does is P(J/Je)
By BAYES Theorem:
Hence, the probability that Jane watches the show, given that John does is 0.1714.
c) As we can see P(Jane ∩ John) = 0.12
So, the probability of both of them seeing the show TOGETHER is 0.12.
Hence, they do watch show independent of each other and the probability of doing that is 1.0.12 = 0.88