Are the these expressions equivalent 6a + 12 and 3(3a + 4)

No

Step-by-step explanation:

6a + 12  =? 3(3a + 4)

Distribute

6a+12 =? 3*3a + 3*4

6a+12 =? 9a +12

No

The expressions are not equivalent

No, these expressions aren't equivalent.

Step-by-step explanation:

They aren't equivalent because you can't simplify the expression 6a+12 so 3(3a+4) isn't equivalent. Hope this helps! :)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).