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zavuch27 [327]
3 years ago
6

Tell whether the lines with the given slopes are parallel, perpendicular, or neither. Line 1: m = 2 2)

Mathematics
1 answer:
stich3 [128]3 years ago
3 0

Answer and Step-by-step explanation: Two lines can be parallel, perpendicular or none of them. The difference is in the slope of a line.

<u>Slope</u> is the change in y over the change in x, or, in other words, it is the steepness of the line.

Two lines are parallel if they don't intersect. So, they have the same slope and different y-intercept. For example:

f(x) = m₁x + b₁

g(x) = m₂x + b₂

Functions f(x) and g(x) are parallel if

m₁ = m₂ and b₁ ≠ b₂

Two lines are perpendicular when they intersect at a 90° angle. For that to happen, the multiplication of the slope of each function must result in -1. For example:

h(x) = m₃x + b₃

j(x) = m₄x + b₄

The functions will be perpendicular if:

m_{3}m_{4}=-1

If the slopes are not the same or reciprocal, the lines are neither.

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g Given the following premises: (1) a∧(b∨a) (2) ~c→~a (3) ~g→~a (4) g→e (5)~(d∨h) Prove the Conclusion: c∧~h?
KIM [24]

Answer:

See the argument below

Step-by-step explanation:

I will give the argument in symbolic form, using rules of inference.

First, let's conclude c.

(1)⇒a  by simplification of conjunction

a⇒¬(¬a) by double negation

¬(¬a)∧(2)⇒¬(¬c) by Modus tollens

¬(¬c)⇒c by double negation

Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.

An alternative approach to De Morgan's law is the following:

By contradiction proof, assume h is true.

h⇒d∨h by addition

(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.    

8 0
3 years ago
Solve for x: x-14=39
Jobisdone [24]
Answer is x=53
hope this helps
8 0
3 years ago
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I need help fasst plz help will give brainliest!!!
guapka [62]

Answer:

B

Step-by-step explanation:

3 0
3 years ago
Use &lt;, &gt;, or = to compare these numbers. 3.08m and 3.8m
dolphi86 [110]
This will be
3.08<3.8 or
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4 0
3 years ago
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Hey, try this one out guys.
MrRissso [65]

Answer:

879cm

Step-by-step explanation:

Radius is 35cm.

Diameter is 70cm.

Pie/Pi is 3.14 and so on.

Perimeter of circle:70×3.14=219.8

219.8×4=879.2

Round Off:879.2cm

6 0
3 years ago
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