How many times in a 12 hour period does the sum of the digits on a digital clock equal 6? try to think of a way to solve this without giving through every single time. describe what you did. plz answer this i will give you 100 points

Let the time be wx:yz (so at 11:51, w=1, x=1, y=5, z=1). We can describe the possible values for each variable:  

w: 0, 1  

x: 1, 2, 3, 4, 5, 6, 7, 8, 9 -- except, if w=1, then we know that x = 0, 1, 2  

y: 0, 1, 2, 3, 4, 5  

z: 0, 1, 2, 3, 4, 5, 6, 7, 8 , 9  

We're looking for all the possible w,x,y,z combinations that add up to 6.  

First, assume w=0, so it's between 1:00 and 9:59. Here we need x+y+z to be 6. We can immediately discard any numbers bigger than 6.  

So, write out all the combinations of 3 numbers that add up to 6:  

(6, 0, 0)  

(5, 1, 0 )  

(5, 0, 1)  

(4, 2, 0)  

(4, 0, 2)  

(4, 1, 1)  

(3, 3, 0)  

(3, 0, 3)  

(3, 2, 1)  

(3, 1, 2)  

(2, 4, 0)  

(2, 0, 4)  

(2, 3, 1)  

(2, 1, 3)  

(2, 2, 2)  

(1, 5, 0)  

(1, 0, 5)  

(1, 4, 1)  

(1, 1, 4)  

(1, 3, 2)  

(1, 2, 3)  

You might notice that for each value of x, there are 7-x times. That's because for each x, we need y+z to be 6-x, and there are n+1 ways to write n as the sum of two positive integers.  

Now, we need to think about the times when w=1. That means we need x+y+z to be 5, but remember that x can only be 0, 1, or 2.  

If x = 0, y+z=5, so there are 5+1 ways to do it (see if you can write them out.)  

if x=1, y+z = 4 so there are 4+1 ways to do it  

if x=2, y+z = 3 so there are 3+1 ways to do it.  

So, add up all those ways and we get 21 + 15 = 36 times.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is