I'm assuming the function is f(x) = 100(0.7)^x. This is the same as y = 100(0.7)^x because y = f(x).
Plug in x = 0 to get
y = 100(0.7)^x
y = 100(0.7)^0
y = 100(1)
y = 100
So (x,y) = (0,100) is one point on this function curve
Plug in x = 2 to get
y = 100(0.7)^x
y = 100(0.7)^2
y = 100(0.49)
y = 49
So (x,y) = (2,49) is another point on this curve
In summary, the two points on this function curve are (0,100) and (2,49)
I think its D but im not 100% sure let me know if its right
Do you know how to graph the equation 2x-1?
If you do then graph it.
After, check the inequality - it is Y is less than the equation so you will be filling in everything below the line you graphed
IF you don't know how to graph:
You will have a line that goes up 2 then right 1
The equation is really 2/1 x as in 2 right 1 right
The line will start from y=-1 or 1 right below 0,0 because of the -1 at the end of the equation and the line will travel in both direction for infinity (Or as big as the graph is)
So start at y=-1 then go up 2, right 1 and place a point. Keep doing that (down 2 left 1 when going in the opposite direction) Finally just make a line through all those points you made
NOT MY WORDS TAKEN FROM A SOURCE!
(x^2) <64 => (x^2) -64 < 64-64 => (x^2) - 64 < 0 64= 8^2 so (x^2) - (8^2) < 0 To solve the inequality we first find the roots (values of x that make (x^2) - (8^2) = 0 ) Note that if we can express (x^2) - (y^2) as (x-y)* (x+y) You can work backwards and verify this is true. so let's set (x^2) - (8^2) equal to zero to find the roots: (x^2) - (8^2) = 0 => (x-8)*(x+8) = 0 if x-8 = 0 => x=8 and if x+8 = 0 => x=-8 So x= +/-8 are the roots of x^2) - (8^2)Now you need to pick any x values less than -8 (the smaller root) , one x value between -8 and +8 (the two roots), and one x value greater than 8 (the greater root) and see if the sign is positive or negative. 1) Let's pick -10 (which is smaller than -8). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive
2) Let's pick 0 (which is greater than -8, larger than 8). If x=0, then (x^2) - (8^2) = 0-64 = -64 <0 so it is negative3) Let's pick +10 (which is greater than 10). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive Since we are interested in (x^2) - 64 < 0, then x should be between -8 and positive 8. So -8<x<8 Note: If you choose any number outside this range for x, and square it it will be greater than 64 and so it is not valid.
Hope this helped!
:)
