Answer:
(x-4) (x-3) (x+3)
Step-by-step explanation:
x^3 - 4x^2 - 9x + 36
Make 2 groups
x^3 - 4x^2 - 9x + 36
We can factor out x^2 from the first group and -9 from the second group
x^2 (x-4) - 9(x-4)
Now factor out (x-4)
(x-4) (x^2 -9)
This may be an answer choice but we can still factor
(x^2 -9) is the difference of squares
(x^2-9) = (x-3) (x+3)
Replacing this
(x-4) (x-3) (x+3)
Y=-1/2x-3
You can rewrite the equation “y=mx+b” and fill in what you know. So your equation would look like y=-1/2x+b when filling in what you know. Now you can take the (x,y) coordinates that you were given and plug them into the equation and solve for b. So now it would be -5=-1/2(4)+b
Answer:
15/17
Step-by-step explanation:
in the described scenario AB is the vertical leg of the right-angled triangle, that can be seen as the trigonometric triangle of the angle at C.
this triangle would be inscribed inside a circle with the center at C and the radius being BC.
the sine value of an angle is the length of the vertical leg of the trigonometric triangle inside the normed circle with radius 1.
if inside a larger circle, to get the sine value, these lengths must be scaled back to the norm of radius = 1.
and that is what the sine ratio is : the actual length of the vertical leg scaled to the radius of 1 (by dividing it by the actual radius) :
sin(theta) = AB / BC = 15/17
FYI
sin(theta) = 15/17 = 0.882352941...
and the angle theta is then 61.92751306...°
cos(theta) = CA / BC = 8/17 = 0.470588235...
and of course, this gives us the same angle.
we know that
the perimeter of the rectangle is equal to
![P=2W+2L](https://tex.z-dn.net/?f=%20P%3D2W%2B2L%20)
where
P is the perimeter of the rectangle
W is the width of the rectangle
L s the length of the rectangle
In this problem
![P=146\ units \\ W=2x\\ L=3x+3](https://tex.z-dn.net/?f=%20P%3D146%5C%20units%20%5C%5C%20W%3D2x%5C%5C%20L%3D3x%2B3%20)
Substitute the values in the formula above
![P=2W+2L\\ 146=2*(2x)+2*(3x+3)\\ 73=2x+3x+3\\ 5x=70\\ x=14\ units](https://tex.z-dn.net/?f=%20P%3D2W%2B2L%5C%5C%20146%3D2%2A%282x%29%2B2%2A%283x%2B3%29%5C%5C%2073%3D2x%2B3x%2B3%5C%5C%205x%3D70%5C%5C%20x%3D14%5C%20units%20%20)
![W=2x=2*14=28\ units\\ L=3x+3=3*14+3=45\ units](https://tex.z-dn.net/?f=%20W%3D2x%3D2%2A14%3D28%5C%20units%5C%5C%20L%3D3x%2B3%3D3%2A14%2B3%3D45%5C%20units%20)
therefore
the answer is
the length of the longer side of the rectangle is equal to ![45\ units](https://tex.z-dn.net/?f=%2045%5C%20units%20)