Answer:
1. 54ft squared 2. 48 cm squared
Step-by-step explanation:
We are given two binomials: x+4 , x^2-9.
x+4 can't be factored. Therefore, it is a prime.
Let us work on x^2-9.
9 could be written as 3^2.
Therefore, x^2-9 = x^2 - 3^2.
Now, we can apply difference of the squares formula to factor it.
We know a^2 -b^2 = (a-b) (a+b).
Therefore, x^2 - 3^2 can be factored as (x-3) (x+3).
So, x^2-9 is not a prime binomial because it can be factored as (x-3) (x+3).
Answer:
A) The model exists: f(x) = -3x^2 +4x -4
Step-by-step explanation:
A quadratic model will always exist for 3 given points, provided they are not on a line. In that case, a linear model is appropriate.
Here, the slope between -1 and 0 is positive, and the slope between 0 and 3 is negative. Thus, we know these points are not collinear, and a model must exist.
The model is most easily found using a quadratic regression tool. Such is shown in the attachment. It tells us that ...
f(x) = -3x^2 +4x -4
Answer:
.894
Step-by-step explanation:
First thing to do is to solve for the height of the triangle, BD. That's easy. We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8. Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest. For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB. First let's use geometric mean to find AD. The formula for that, now that we know the height, is

Filling that in with numbers we have
and
64 = 16(AD). Solve for AD to get that AD has a length of 4. Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.
and
so
c=√80 which simplifies to 4√5. That means that the sin ratio for x is

which divides out to .894