Determine whether the lines passing through the pairs of points are parallel, perpendicular or neither. Line a: (−4,4) and (8,−1
1 answer:
Answer:
Perpendicular.
Step-by-step explanation:
Find the slopes of each line through
Line a:
m = (-10-4) / (8--4)
= -14/12
= -7/6
Line b:
m = (20-8) / (18 -4)
= 12/14
= 6/7
When lines are parallel, they have the same slope. Since -7/2≠6/7, they are not parallel.
When lines are perpendicular, the product of the slopes equals -1.
-7/6 x 6/7 = -1
The product is -1, hence they are perpendicular lines.
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Hey there :)
We know the volume formula of a triangular prism
Volume = base area × height of prism
We are given:
Base of triangle = 5 ft
Height of triangle = 3 ft
Height of prism = 7.5 ft
Apply the formula
V =
( 5 )( 3 ) × 7.5
= 7.5 × 7.5
= 56.24 ft³
We know the volume formula of a triangular prism
Volume = base area × height of prism
We are given:
Base of triangle = 5 ft
Height of triangle = 3 ft
Height of prism = 7.5 ft
Apply the formula
V =
= 7.5 × 7.5
= 56.24 ft³
Answer:
= 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, since the order in which the students are chosen is important, the permutations formula is used to solve it.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
Desired outcomes:
Drake then Todd, so only one outcome, which means that
Total outcomes:
Two students from a set of 16, so:
What is the probability that the first 2 presentations will be by Drake and Todd, in that order?
= 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.