The sum of three consecutive even integers is –78. What are the integers? Describe how you would use the strategy of writing an equation to solve the given problem.

hiya! i've been swamped on this question for a good bit now. i know what the answer is, but i'm not sure how to get there. Why are my integers n, n+2, and n+4? how do you find out those are the ones that you need to use? what's n? how does it work out the way it does? why and how do i get this answer? i just don't understand the process or the mind behind it and i need it to be broken down for me. Thank you!!

Step-by-step explanation:

(Hope this explanation can ease your mind a little if possible! Alright let's go! :D)

Let n be the middle of the 3 consecutive even integers. Therefore, (n - 2) and (n + 2) are the smallest and largest of the 3 numbers respectively.

We know that (n - 2) + n + (n + 2) = 78,

so 3n = 78, and n = 78/3 = 26.

Since the middle number is 26, the smallest number is 26 - 2 = 24 and the largest number is 26 + 2 = 28.

Feel free to comment below if you have any queries!

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).