Answer: An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable.
Answer:
Y-intercept: (0,-0.7)
X-intercept: (-1.2,0)
Explanation:
The Y-intercept is the spot where the line crosses the Y axis (the vertical axis). This always occurs where X=0. For this problem the Y value at this point is -0.7. So, for the coordinates (X,Y) X is 0 and Y is -0.7 so it is (0,-0.7)
The X-intercept is the spot where the line crosses the X axis (the horizontal axis). This always occurs where Y=0. For this problem the X value at this point is -1.2. So, for the coordinates (X,Y) X is -1.2 and Y is 0 so it is (0,-0.7)
Answer: Choice B) (24,10)
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Work Shown:
2x - 4y = 8
2( x ) - 4y = 8
2( 3y-6 ) - 4y = 8 ... notice x has been replaced with 3y-6
2(3y)+2(-6) - 4y = 8
6y-12 - 4y = 8
2y-12 = 8
2y-12+12 = 8+12 ... add 12 to both sides
2y = 20
2y/2 = 20/2 ... divide both sides by 2
y = 10
If y = 10, then
x = 3y-6
x = 3*10-6 ... replace y with 10
x = 30-6
x = 24
Put together, the solution is (x,y) = (24,10)
which is why the answer is choice B
As a check, we can plug (x,y) = (24,10) into each equation
x = 3y-6
24 = 3*10 - 6
24 = 30 - 6
24 = 24 ... true equation
and similarly for the second equation as well
2x-4y = 8
2*24 - 4*10 = 8
48 - 40 = 8
8 = 8 ... true equation
Both equations are true when (x,y) = (24,10) so the solution is confirmed
Answer: 6
Step-by-step explanation: The absolute value of -3 is 3 and the opposite of -3 is 3. That means 3 + 3 = 6.
