Determine whether each pair of lines are parallel, perpendicular, or neither. line n: y = -2x-4 line m: y = -2x+8

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Likurg_2 [28]

Answer:

54 square feet

Step-by-step explanation:

We need to find the area of the surface touching the floor and deduct it from the total surface area of the block.

The surface area of the entire block is given as:

A = 2(lw + lh + wh)

where l = length

w = width

h = height

The dimensions of the block are 2 feet by 3 feet by 6 feet. This means that:

l = 2 feet, h = 3 feet, w = 6 feet

Therefore, the total surface area is:

A = 2[(2 * 3) + (2 * 6) + (3 * 6)]

A = 2(6 + 12 + 18)

A = 2(36)

A = 72 square feet

The area of the surface that does not need covering is:

A = 3 * 6 = 18 square feet

The surface area of the part of the block that needs covering is therefore:

A = 72 - 18 = 54 square feet

8 0

3 years ago

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

Gnoma [55]

Triangle RST was transformed by using the rule (x,y) → (-x,-y) and the transformation is described by the transformation of 180° rotation about the origin.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Here we have transformed the triangle using the rotation method.

Rotation is the geometric transformation that revolves each point in a shape a predetermined number of degrees around that point. When the number of degrees is positive, the shape spins counterclockwise; when the number of degrees is negative, it rotates clockwise. The following is a broad description of how rotation about the origin can be transformed.

(X,Y) to rotate 90° (-y, x)

180° rotation (x, y) (-x,-y)

To rotate (x,y) 270° (y, -x)

Here the points change to R'(-1,-1) , S'(-3,-1) and T'(-1,-6).

A 180° rotation about the origin will be the transformation.

The triangles RST and R'S'T' are first plotted on a graph. The graph is provided for your reference below.

The original triangle RST, which was in quadrant 1, has changed to triangle R'S'T', which is in quadrant 3, as shown in the graph. The rotation around the origin is 180° from quadrant 1 to quadrant 3.

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Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

R (1, 1)

S (3, 1)

T (1, 6) R' (–1, –1)

S' (–3, –1)

T' (–1, –6)

Which describes the transformation?

The transformation was a 90° rotation about origin.

The transformation was a 180° rotation about origin.

The transformation was a 270° rotation about origin.

The transformation was a 360° rotation about origin.