Jackson is conducting an experiment for his Physics class. He attaches a weight to the bottom of a metal spring. He then pulls t

The accurate statements are 0.75 (x,y) = (0.75x, 0.75y), LM is parallel to L'M', and "the vertices of the image are nearer to the origin relative to the pre-image".

Explanation:

It is stated that the triangle ABC underwent dilation as per the rule DO,0.75 (x,y)

DO, 0.75(x,y) signifies the dilation rule, where both x and y values are scaled by 0.75, indicating that the dilation, centered around the origin, has a scale factor of 0.75. The representation for this dilation would be,

Consequently, the first statement holds true.

Since both x and y coordinates are scaled down by 0.75, the sides of the image are parallel, but shorter, with a scale of 0.75 compared to the pre-image’s sides.

Thus, the second statement "LM is parallel to L'M'" is also accurate, while the third and fifth statements are incorrect.

The scale factor of 0.75, being less than 1, suggests that the vertices of the image are closer to the origin compared to those of the pre-image.

Hence, the fourth statement "The vertices of the image are nearer to the origin compared to the pre-image" is indeed correct.

The diagonal that crosses the interior of the cube is the longest segment. The hypotenuse corresponds to the longest side in a right triangle. In this case, the cube's diagonal serves as the hypotenuse of a right triangle, with the legs being the diagonal of one of its faces and one of its edges. The edges are the shortest sections and function as the legs of a right triangle where the face's diagonal acts as the hypotenuse.

$9.62, Mindy has to reimburse Nora.

To calculate this, a specific formula will be necessary. Years = log (total/principal) / [n * log (1 + rate / n)]. Part A) For Calvin: $400 at 5% monthly results in $658.80; Time =? Monthly compounding, n = 12. Thus, Years = log(658.80/400) / [12 * log(1+ (.05/12))]. Subsequently, Years = log( 1.647) / (12 * log(1.0041666667)). Then, Years = 0.21669359917 / 12 * 0.0018058008777. Thus resulting in Years = 0.21669359917 / 0.0216696105. Ultimately, Years ≈ 9.999884362. Part B) For Makayla: $300 at 6% quarterly yields $613.04; Time=? Quarterly compounding, n = 4. Therefore, Years = log(613.04/300) / [4 * log (1 +.06/4)]. This results in Years = log(2.0434666667) / (4 * log(1.015)). Years thus equals 0.31036755784 / (4 * 0.0064660422492), resulting in Years ≈ 11.9999044949. The approximate difference is about 3 years.