Answer:
The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.
Step-by-step explanation:
Answer:
5x - y = - 2
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and the line passes through (0, 2) ⇒ c = 2
y = 5x + 2 ← in slope- intercept form
Subtract y from both sides
0 = 5x - y + 2 ( subtract 2 from both sides )
5x - y = - 2 ← in standard form
Answer:
Step-by-step explanation:
All the absolute value functions given in the option are of the form:
, where (h,k) is the vertex
From your description the absolute value graph has vertex at (-4,-2)
Hence h=-4 and k=-2.
We substitute to get:
We simplify to get:
Answer:
a) d(x)=
b)d'(x)=
c)The critical point is x=
d)Closest point is (,
Step-by-step explanation:
We are given the line
Let a point Q() lie on the line.
Point P is given as P(2,0)
By distance formula, we have the distance D between any two points
A() and B() as
D=
Thus,
d(x)=
But we have,
So,
d(x)=
Expanding,
d(x)= - - - (a)
Now,
d'(x)=
i.e.
d'(x)= - - - (b)
Now, the critical point is where d'(x)=0
⇒ =0
⇒ - - - (c)
Now,
The closest point on the given line to point P is the one for which d(x) is minimum i.e. d'(x)=0
⇒
as
⇒y=
So, closest point is () - - -(d)
Step-by-step explanation:
Option C