The function is:
(9x^2 - 36)
f(x) = ---------------------
3x + 6
You can simplify that function to a linear function for all x for which 3x + 6 ≠ 0
=> x ≠ - 2.
So, for x ≠ - 2, you can do:
(9x^2 - 36)
f(x) = --------------------- =
3x + 6
9(x^2 - 4)
f(x) = ---------------------
3(x + 2)
3(x + 2)(x - 2)
f(x) = --------------------- = 3(x - 2) = 3x - 6
(x + 2)
So, the graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2 as the function is not defined for x = -2. That is the second graph of the second picture.
The trig function sine, often abbreviated as "sin" (pronounced the same way as "sine"), is essentially the ratio or fraction of the opposite side and the hypotenuse. See the attached image for a reference.
The leg opposite angle B is side AC. Note how B is not present in the sequence "AC". Visually, we are as far away as possible from point B. This side is 16 units long. So AC = 16
The hypotenuse is the longest side of the right triangle. Always always always. This longest side is opposite the largest angle (90 degrees). Therefore the hypotenuse is BC = 17.46
In summary so far, we have,
opposite side = AC = 16
hypotenuse BC = 17.46
Let's use those values to compute sin(B)
sin(Angle) = opposite/hypotenuse
sin(B) = AC/BC
sin(B) = 16/17.46
sin(B) = 0.916 (this is approximate)
sin(B) =
0.92 (rounding to nearest hundredth)
This points to the
final answer of choice A) 0.92--------------------------------
Edit: Sorry nearly forgot about the reference image. I attached it just now.
Answer:
m = 4√2
Step-by-step explanation:
This is a right angled isosceles triangle whose sides are in the ratio 1:1:√2.
So = 8 / √2
= 8 *√2 / 2
= 4√2
The answer is going to be A.) -2
Answer:
h(n) = h(n - 1) + 12
Step-by-step explanation:
Generate the first few terms using the explicit formula
h(1) = - 10 + 12 = 2
h(2) = - 10 + 24 = 14
h(3) = - 10 + 36 = 26
h(4) = - 10 + 48 = 38
This is an arithmetic sequence. To find a term in the sequence add 12 to the previous term, thus
h(n) = h(n - 1) + 12 with h(1) = 2