Answer:
The solution is (1,2)
Step-by-step explanation:
- 2x - y = - 4
x + 2y = 5
Multiply the second equation by 2 so we can eliminate x
2( x + 2y) = 5*2
2x +4y = 10
Add this to the first equation
- 2x - y = - 4
2x +4y = 10
----------------------
3y = 6
Divide each side by 3
3y/3 = 6/3
y = 2
- 2x - y = - 4
x + 2y = 5
Multiply the first equation by 2 to eliminate y
2(- 2x - y) = - 4*2
-4x -2y = -8
Add this to the second equation
-4x -2y = -8
x + 2y = 5
------------------
-3x = -3
Divide by -3
-3x/-3 = -3/-3
x = 1
The solution is (1,2)
Answer:
The measure of angle x is 25 degrees.
Step-by-step explanation:
Since triangle ABC is an isosceles triangle, the measure of angle BAC is equal to the measure of angle ACB. Angle ABC = 80 degrees, leaving 100 degrees to be divided equally for the measures of the other two angles. Now that you know that angle ACB = 50 degrees, you can calculate the value of angle ACD and determine that angle ACD = 130 degrees. Triangle ACD is also an isosceles triangle, and the two equal legs are AC and CD. Since angle ACD = 130 degrees, the other two angles have a total of 50 degrees. Splitting the 50 degrees equally between the two angles gives you 25 degrees as the value of angle CAD, which is labeled "x."
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.
------------------------------
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:
"The product of a rational number and an irrational number is SOMETIMES irrational." If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational
A better statement would be:
"The product of a non-zero rational number and an irrational number is irrational
Volume of rectangular prism = 1 1/3 x 5/6 x 2/3 = 4/3 x 5/6 x 2/3 = 20/27
Volume of cube = 1/6 x 1/6 x 1/6 = 1/216
Number of cubes that will pack the rectangular prism = 20/27 / 1/216 = 160
