question number 10 !
question number 16
question number 19
and this question !
Question 10: Note that since the lines are parallel, their slopes must be the same [and negative since the line is going downward] and they also differ in their y-intercepts [one + and one -] as well based on the graph.
D does have the same slope, but notice that both y-intercepts are positive...the graph has 1 equation that has a negative y-intercept.
C also has one that is x -y which means the x would become positive again once it is moved to the other side...while the other equation still has a negative x...
A has x, 2x, and 2y, so notice that the slopes would dramatically differ...
Only B makes sense since you notice that x + y = # andx + y = -#...the slopes are equal and the #'s are opposite signs.
Question 16: y is definitely greater than 0...but notice that is restricted to a maximum of y = 3. Only choice C makes sense.
Question 19: On the graph, when x = 1 when y = 0.
y = -ln x --> 0 = - ln(1)...Yes!
y = e^-x --> 0 = e^(-1)...No!
y = e^x --> 0 = e^1...No!
y = ln x --> 0 = ln 1...Yes!
Now, notice that if we took ln(0.9) we would get -0.1053605156578263...and this graph is in the positive range when x <1...so, -lnx would make it positive...A.
I'm going to do the last one
$$y=\sqrt{25-x^2}\\
when\; x=4\\
y=\sqrt{25-16}=\sqrt9=3$$
So you have a rectangle with length 2 units and height 3 units.
So the area is 2*3=6u^2
Question 10: Note that since the lines are parallel, their slopes must be the same [and negative since the line is going downward] and they also differ in their y-intercepts [one + and one -] as well based on the graph.
D does have the same slope, but notice that both y-intercepts are positive...the graph has 1 equation that has a negative y-intercept.
C also has one that is x -y which means the x would become positive again once it is moved to the other side...while the other equation still has a negative x...
A has x, 2x, and 2y, so notice that the slopes would dramatically differ...
Only B makes sense since you notice that x + y = # andx + y = -#...the slopes are equal and the #'s are opposite signs.
Question 16: y is definitely greater than 0...but notice that is restricted to a maximum of y = 3. Only choice C makes sense.
Question 19: On the graph, when x = 1 when y = 0.
y = -ln x --> 0 = - ln(1)...Yes!
y = e^-x --> 0 = e^(-1)...No!
y = e^x --> 0 = e^1...No!
y = ln x --> 0 = ln 1...Yes!
Now, notice that if we took ln(0.9) we would get -0.1053605156578263...and this graph is in the positive range when x <1...so, -lnx would make it positive...A.