Answer:
First 3 are functions . Last one is not a function
Step-by-step explanation:
They are all functions except the last one.
The last one is not a function because it has duplicate x- values in the ordered pairs (1, -1) and (1, -6). There are 2 outputs for one input so its a relation but not a function
7 1/12 - 2 3/4
First we have to change mixed numbers to improper fractions
7 1/12 = 7 x 12 + 1 = 85 85/12
2 3/4 = 2 x 4 + 3 = 11 11/4
85/12 - 11/4
Now we need to find the LCD (least common denominator) for 4 and 12
4, 8, 12
12
12 is our LCD, so it becomes our new denominator
85/12 would stay the same because the denominator wasn't changed but for 11/4 our new denominator is 12, so our fraction will change.
11/4 = 33/12
4 goes into 12, 3 times. What you do to the bottom, you do to the top.
3 x 11 = 33
3 x 4 = 12
So, our new fraction is 33/12. Now we subtract
85/12 - 33/12 = 52/12
Now we convert back to a mixed number
52 ÷ 12 = 4 4/12 reduce
4 1/3
Hope this helps.
Answer:
y = -5/3 * x - 40/3
Step-by-step explanation:
A perpendicular line has an opposite and a reciprocal of the slope.
Your equation should be:
-5y = -3x +6
Divide all parts by -5.
y = 3/5x - 6/5
Since the perpendicular line has an opposite and a reciprocal of the slope, the slope will be -5/3.
Now you must make an equation in point-slope form. This is an example of that form. You will need at least one point to make this equation work. In this case we have (-8,0).
In put the y and x coordinates like this:
y - 0 = -5/3(x - (-8)
Start solving the equation.
y - 0 = -5/3(x + 8)
y - 0 = -5/3 * x - 40/3
y = -5/3 * x - 40/3
This is your equation.
y = -5/3 * x - 40/3
(You can make it -5/3x in your answer but it looks weird online. You may think that it is -5 divided by 3 times x, but it actually is 5/3 times x. That's why I wrote it as y = -5/3 * x - 40/3)
You can solve this one by adding their rates, but you have to invert the numbers they give you to find the rate. Rate is measured in something per unit of time, and "per" indicates division. So the rates are: 1/3 of an hour (Sally) and 1/6 of an hour (Steve). So add the rates: 1/3 + 1/6 = 1/2. (1/3 is 2/6, and 2/6 + 1/6 = 3/6). Since their combined rate is 1/2 of a room in one hour, it takes them two hours to paint the room.
This answer makes sense: It takes Sally three hours by herself; with Steve's help, she's faster, but not THAT much faster, because he's pretty slow. You can often spot-check word problem answers like this by giving it a common sense once-over. If we came up with four hours, that would clearly be wrong: it should take her LONGER if she's getting help.
Answer:
n = -45
Step-by-step explanation:
(n-5) /10 = -5
Multiply each side by 10
(n-5) /10 *10= -5*10
n-5 = -50
Add 5 to each side
n-5+5 = -50+5
n = -45
