Answer:
5
Step-by-step explanation:
4 7/12 + 5/12 = 4 12/12 which equals 5
Answer:
The first one/$9 an hour job.
Step-by-step explanation:
For every 32 hours he works at the $9 per hour job he makes $288.
On the other hand, for every 32 hours he works at the $7 per hour job he only makes $224.
So the only one that'll work where he gets at least $251 is the $9 an hour job.
<u>Hope this helps and have a nice day!</u>
Answer:
See below.
Step-by-step explanation:
So we started off with the equation:

And we subtracted x from both sides to acquire:

Now, this is essentially slope-intercept form. Recall that the slope-intercept form is:

Where m is the slope and b is the y-intercept.
If we rearrange our equation:

And put some parentheses:

We can see that this is indeed slope-intercept form.
And we can see that m is -1 and b is 2.
In other words, the slope is -1 and the y-intercept is 2.
Answer:
78
Step-by-step explanation:
The tricky part of this is figuring out how to assign the unknowns. We are told that we are working with two consecutive even integers. Consecutive means "next to" or "in order" and sum means to add. If we use 2 and 4 as examples of our 2 consecutive even integers and assign x to 2, then in order to get from 2 to 4 we have to add 2. So the lesser of the 2 integers is x, and the next one in order will be x + 2. (2 and 4 are just used as examples; they mean nothing to the solving of this particular problem. You could pick any 2 even consecutive integers and find the same rule applies. All we are doing here with the example numbers is finding a rule for our integers.) Now we have the 2 expressions for the integers, we will add them together and set the sum equal to 158:
x + (x + 2) = 158
The parenthesis are unnecessary since we are adding, so when we combine like terms we get
2x + 2 = 158 and
2x = 156 and
x = 78
That means that the lesser of the 2 integers in 78, and the next one in order would be 80, and 78 + 80 = 158
So you know that this triangle must be a 45-45-90 degree triangle (you can tell this from the picture!)
The side that is length 4 is opposite from the 45 degree angle, and remember that congruent angles also give you congruent sides. This means that the length of a must be equal to the length of 4, because both are located opposite a 45 degree angle.
To find b, you must know that the hypotenuse of a 45-45-90 triangle is just equal to a

. Thus, the length of b= 4 rt. 2