A student writes the equation for a line that has a slope of -6 and passes through the point (2, –8). y -(-8) = -6(x - 2) y -(-8

Response:

Congruent:  (x, y)→(x+3, y-4); (x, y)→(-x, -y)

Not Congruent:  (x, y)→(3x, 3y); (x, y)→(0.4x, 0.4y); (x, y)→(x/3, y/3)

Explanation in steps:

Transformations that yield congruent figures include translations, reflections, and rotations. In contrast, dilations result in figures that are not congruent.

The first transformation, (x, y)→(x+3, y-4), represents a translation 3 units right and 4 units down, leading to congruent figures since it merely shifts the figure.

The second transformation, (x, y)→(3x, 3y), indicates a dilation by a factor of 3, which enlarges the figure and therefore makes it non-congruent.

The third transformation, (x, y)→(0.4x, 0.4y), involves a dilation by a factor of 0.4, which shrinks the figure, leading to non-congruence.

The fourth transformation, (x, y)→(x/3, y/3), results in a dilation by a factor of 1/3, also shrinking the figure and rendering it non-congruent.

The fifth transformation, (x, y)→(-x, -y), reflects the figure, maintaining its size while modifying its orientation, thus ensuring congruence.

Answer:

Yes, Bill surpassed his target by £2,200.

Step-by-step explanation:

The cost for the laptops totals = 50 x 400

= 20,000

He sold 40 laptops with a profit margin of 30%

Calculating that gives (40 x 400) x 1.30

= 20,800

He sold 10 laptops with a profit of 15%

Calculating that gives (15 x 400) x 1.15

= 6900

Thus, the overall sales revenue totals

= 20800 + 6900 = 27,700

To address this question effectively, it's essential to clarify the characteristics of the given geometric terms.

A quadrilateral is defined as a four-sided figure.

Parallelograms are a subset of quadrilaterals characterized by having two pairs of parallel sides, with congruent opposite sides and angles. Instances of parallelograms include squares, rectangles, and rhombuses.

Trapezoids are also categorized under quadrilaterals but are distinguished by having only one pair of parallel sides.

In our investigation, we seek to determine whether there exists a four-sided shape without parallel sides. The included image presents an example of a quadrilateral that does not qualify as either a parallelogram or a trapezoid. Therefore, in accordance with the definitions of these polygons, the correct choice is B.

Answer:

d) Both blocks experienced equivalent energy loss due to friction

Explanation:

As stated in the question, two tractors are pulling two identical stone blocks the same distance across similar surfacesAdditionally, block A moves at double the speed of block B when completing the race

This implies both blocks suffer from comparable friction loss

Moreover, we understand that

Energy loss from friction is

Thus, the friction loss should be identical for both blocks

therefore, option d is the accurate choice