Answer:
Step-by-step explanation:
Factor the given function:
(x + 2)(x + 5)
f(x) = --------------------
(x + 5)(x + 4)
The factor (x + 5) can be crossed out in numerator and denominator. There is a 'hole' at x = -5 (which comes from setting (x + 5) = 0 and solving for x).
If we do cancel the (x + 5) factors, we are left with
(x + 2)
f(x) = ------------- . We can't just substitute x = -5 because the original
(x + 4) function is not defined for that x value. However, we
can locate the hole by letting x have the value of a litle more than -5, obtaining:
( -5+ + 2)
f(-5+) = -------------, which comes out to approx. -3/-1, or +3 .
(-5+ + 4)
So the hole location is (-5, 3).
f(x) = --------------------
(x + 5)(x + 4)
Answer:
1 + 2
Step-by-step explanation:
When we look at the number line, we can see that the inequality is:
x ≤ 19
This means that all values of "x", must be equal to or less than 19.
To find the correct answer choices, we must keep that equation in mind.
1. at most 19 cups - this answer choice does work, because it shows that 19 is the limit (which is what our inequality represents)
2. 19 cups or less - this answer choice works as well because it shows that 19 is the maximum and all other values of "x" must be below that.
3. more than 19 cups - this goes against our inequality, since "x" can't exceed 19. This means that this answer choice must be incorrect.
4. a minimum of 19 cups - this answer choice also cannot be correct since it shows that "x" can go over 19 (which we know is false).
5. no fewer than 19 cups - this is also wrong because it wants "x" to go over the value of 19, which it can't do.
Answer:
45
Step-by-step explanation:
A number consists of 2 digits whose sum is 9 => x + y = 9
If the order of the numbers is inverted, the result is equal to the given number plus 9 units => (10*y + x) + 9 = (10*x + y)
Thus:
x + y = 9 => multiply by -9 => 9*y + 9*x = 81
10*y + x + 9 = 10*x + y => 9*y - 9*x = -9
We are left then that:
9*y + 9*x = 81 (1)
9*y - 9*x = -9 (2)
we add both equations
18y = 72
y = 72/18 = 4
replacing
x + y = 9
x + 4 = 9
x = 5
Therefore the number is (10y + x) => (10 * 4 + 5) => 45
Answer:
37.55 m
Step-by-step explanation:
To find the perimeter, we have to add the lengths of each part of the figure.
We start from the circle on top. We see that its diameter is 10 m, therefore its radius is
r = 5 m
(because the radius is half the diameter). The perimeter of a circle is given by
However, here we have half a circle, so its perimeter is
Then continuing in a clockwise direction, we have to add the length of the side of 2 m:
Then we have two sides of a square of side 5 m, so:
Then we have a quarter of a circle of radius r = 5 m, so its perimeter is:
Finally, we have one more side of length 2 m:
Therefore, the total perimeter is:
