Answer:
450
Step-by-step explanation:
There are 900 3-digit numbers in the range 100–999. Of those, exactly half are even numbers.
There are 450 even three-digit numbers.
Answer:
It has amplitude of 
.
It is a horizontal shift of the parent function 
units left.
Step-by-step explanation:
We have the function, 
.
It is clear that the parent function is 
.
So, we see that,
The amplitude of the function f(x) is , which gives, 
.
Also, g(x) is translated units to the left, which gives, 
.
Further, the function is translated 1 unit downward, resulting in .
So, the correct options are,
It has amplitude of .
It is a horizontal shift of the parent function units left.
3.84/16 = 0.24 per tangerine
Answer:
6. E
7. D
8. 5,-8,34
Step-by-step explanation:
A. Parallel to the y-axis and passes through the point (3,5)
For it to be parallel to the y-axis, what this means is that it has an x-intercept and no y intercept.
So what this means is that x = 3 is our line so E is correct
B. Perpendicular to the y-axis means it is parallel to the x-axis
It means is has no x intercept and thus its x value at any point in time is zero
So the equation is y = -5
or simply y + 5 = 0 which means D is correct
C. It is parallel to the line 5x -8y + 12 = 0
Thus: 8y = 5x + 12
dividing both sides by 8
y = 5x/8 + 12/8
y = 5x/8 + 3/2
y = 5x/8 + 1.5
Comparing this with the general equation of a straight line ;
y = mx + c
where m is that slope, this means that 5/8 is the slope of the line
Mathematically if two lines are parallel, they have equal slopes.
So we can say the slope of the other line too is 5/8
Now to find the equation of the other line, we can use the point-slope method
y-y1 = m(x-x1)
where (x1,y1) in this case is (-2,3)
So we have;
y-3 = m(x-(-2))
y-3 = 5/8 (x + 2)
8(y-3) = 5(x + 2)
8y -24 = 5x + 10
5x + 10 + 24 -8y = 0
5x -8y + 34 = 0
So A, B, C = 5, -8, 34
