Let p and q be the propositions p: you drive over 65 miles per hour. q: you get a speeding ticket. identify the expression that represents the proposition "if you do not drive over 65 miles per hour, then you will not get a speeding ticket." using p and q and logical connectives (including negations).

- p ⇒ - q

Step-by-step explanation:

p : Drive over 65 miles

q : You get a speeding ticket.

So then we get the negations.

- p : You do not drive over 65 miles

- q : You don't get a speeding ticket.

So, we need to connect the sentences. For that we use ⇒.

⇒ : then.

So, the sentence, If you do not drive over 65 miles per hour, then you will not get a speeding ticket

Can be written as : -p ⇒ -q

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer:

c) the x-coordinate of the center of the circle increases by 3