Select all the ratios that are equivalent to the ratio 12 : 3. explain how you know.
a. 6: 1
b. 1: 4
c. 4: 1
d. 24 : 6
e. 15: 6
f. 1,200 : 300
g. 112: 13

the answers are c, d, &f

Step-by-step explanation:

the equivalence to 12:3

1200:300. = 12:3 (reduce by 100)

12:3= 4:1 (reduce by 3)

24:6= 12:3 (reduce by 2)

The ratio 12: 3 between two quantities A and B means that 12 times A is 3 times B, or 12*A = 3*B.

Then, if we multiply both sides by the same number k, we got:

k*12*A = k*3*B

If K = 2, then 24*A = 6*B, so the option D; 24:6 is equivalent.

if K = 1/3, then: 4*A = B, so the option C; 4:1 is equivalent.

if k = 100, then : 1200*A = 300*B, so the option F; 1200:300 is equivalent.

You can notice that in all the cases the ratio 12:3 is multiplied in both sides by the same number k, this is the relation you need to search for.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.