The volumes of two similar solids are 53 cm^3 and 1113 cm^3, which is the ratio of the corresponding sides?
a) 21
b) 3√21
c) √21
d) 7

The ratio of its corresponding sides is

Step-by-step explanation:

we know that

If two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor. And the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z ----> the scale factor

x ----> the volume of the larger solid

y ----> the volume of the smaller solid

so

we have

substitute

therefore

The ratio of its corresponding sides is

correct answer:

b.(19,-2)

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: