To which graph does the point (−1, −4) belong? y ≤ −x + 4 y ≤ −x − 6 y ≤ 2x − 3 y ≤ 5x − 1

The answer is y ≤ -x + 4 ⇒ the first answer

Step-by-step explanation:

∵ The point is (-1 , -4)

∵ y ≤ -x + 4 ⇒ -1 ≤ -(-1) + 4

∴ -1 ≤ 5 ⇒ right inequality

If we try the others

y ≤ -x - 6 ⇒ -1 ≤ -(-1) - 6 ⇒ -1 ≤ -5 not true

y ≤ 2x - 3 ⇒ -1 ≤ 2(-1) - 3 ⇒ -1 ≤ -5 not true

y ≤ 5x - 1 ⇒ -1 ≤ 5(-1) - 1 ⇒ -1 ≤ -6 not true

∴ The answer is first one

1st Graph is correct.

Step-by-step explanation:

Given: Point ( -1 , -4 )

To find : Graph in which given point belong.

We find by putting given point in each graph.

Graph 1).

y ≤ -x + 4

LHS = y = -4

RHS = -x + 4 = -(-1) + 4 = 1 + 4 = 5

LHS ≤ RHS.

So, Given point belong to this graph.

Graph 2).

y ≤ -x - 6

LHS = y = -4

RHS = -x - 6 = -(-1) - 6 = 1 - 6  = -5

LHS ≥ RHS.

So, Given point does not belong to this graph.

Graph 3).

y ≤ 2x - 3

LHS = y = -4

RHS = 2x - 3 = 2(-1) - 3 = -2 - 3  = -5

LHS ≥ RHS.

So, Given point does not belong to this graph.

Graph 4).

y ≤ 5x - 1

LHS = y = -4

RHS = 5x - 1 = 5(-1) - 1 = -5 - 1  = -6

LHS ≥ RHS.

So, Given point does not belong to this graph.

Therefore, 1st Graph is correct.

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.