Answer:
-8
Step-by-step explanation:
1. x + 23 = 15
2. x + 23 = 15
-23 -23
3. x = -8
First, you have to find the equation of the perpendicular bisector of this given line.
to do that, you need the slope of the perpendicular line and one point.
Step 1: find the slope of the given line segment. We have the two end points (10, 15) and (-20, 5), so the slope is m=(15-5)/(10-(-20))=1/3
the slope of the perpendicular line is the negative reciprocal of the slope of the given line, m=-3/1=-3
step 2: find the middle point: x=(-20+10)/2=-5, y=(15+5)/2=10 (-5, 10)
so the equation of the perpendicular line in point-slope form is (y-10)=-3(x+5)
now plug in all the given coordinates to the equation to see which pair fits:
(-8, 19): 19-10=9, -3(-8+5)=9, so yes, (-8, 19) is on the perpendicular line.
try the other pairs, you will find that (1,-8) and (-5, 10) fit the equation too. (-5,10) happens to be the midpoint.
Answers:
Part 1 (the ovals)
Domain = {-6,-1,1,5,7}
Range = {-4,-1,2,4}
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Part 2 (the table)
Domain = {1,-3,-2}
Range = {-2,5,1}
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Part 3 (the graph)
Domain = {1, 2, 3, 4, 5, 6}
Range = {-1, 0, 1, 2, 3, 6}
===============================================
Explanation:
Part 1 (the ovals)
The domain is the set of input values of a function. The input oval is the one on the left.
All we do is list the numbers in the input oval to get this list: {-6,-1,1,5,7}
The curly braces tell the reader that we're talking about a set of values.
So this is the domain.
The range is the same way but with the output oval on the right side
List those values in the right oval and we have {-4,-1,2,4}
Which is the range. That's all there is to it.
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Part 2 (The tables)
Like with the ovals in part 1, we simply list the input values. The x values are the input values. Notice how this list is on the left side to indicate inputs.
So that's why the domain is {1, -3, -2}. Optionally you can sort from smallest to largest if you want. Doing so leads to {-3, -2, 1}
The range is {-2,5,1} for similar reasons. Simply look at the y column
Side Note: we haven't had to do it so far, but if we get duplicate values then we must toss them.
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Part 3 (the graph)
Using a pencil, draw vertical lines that lead from each point to the x axis. You'll notice that you touch the x axis at the following numbers: 1, 2, 3, 4, 5, 6
So the domain is the list of those x values (similar to part 2) and it is {1, 2, 3, 4, 5, 6}
Erase your pencil marks from earlier. Draw horizontal lines from each point to the y axis. The horizontal lines will arrive at these y values: -1, 0, 1, 2, 3, 6
So that's why the range is {-1, 0, 1, 2, 3, 6}
Answer:
4
Step-by-step explanation:
And let the missing number be x
We can solve using Algebra
11x - 10 = 34
11x = 34 + 10
11x = 44
x = 44/11
x = 4
For verification:
4(11) - 10 = 34
44 - 10 = 34
34 = 34
Hence, Proved
