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.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

it would open into a square depending on the type of envelope i’m not sure about the second part