Hello from MrBillDoesMath!
Answer:
x + 9 and (x + ( i - 7)) are factors
Discussion:
If f(x) has roots -9 and 7-i then
f(x) = g(x)(x - (-9)) (x - (7-i)) ( g(x) is a polynomial of degree less than f(x))
That is, x + 9 and (x + ( i - 7)) are factors of f(x)
BTW: if the coefficients of f(x) are real (not stated in the Question) then the conjugate of 7-i, i.e. 7 + i, is also be a root.
Thank you,
MrB
Answer:
x=3
Step-by-step explanation:
Since both triangles are similiar, this means they can have different sized sides, but they are just scaled versions of each other. This also means that no matter what sides they have, their angles are going to be the exact same
Knowing this, it helps to draw them out side by side so you can match them up easier. Both of them have a 90 degree angle, and more specifically they are 45-45-90 triangles (45-45-90 is a special right triangle). You can point this out since they give us a 90 degree angle and two angles that are congruent in the same triangle. In order for that to work, they HAVE to be 45-45-90
With this, we can find out what x equals. Since the two angles markings line up with the two side angles in the other triangle, we know that they are equal to each other.
we can use the equation 15x = 45, since 45 is what the side angle should equal.
now, we just divide 45 by 15, and we should get 3
so x = 3!
I hope this helps :)
You can answer this by using Pythagoras theorem. Okay, let me draw this first.
2 miles
V
________________________
| |
| |
| | << 1.5 miles
|_______________________|
^ Assume this is the rectangle. The long side is 2 miles while the shorter side is 1.5 miles.
So, to get the shortest distance, let's cut out a triangle from the rectangle.
/|
/ |
/ |
What we want to find is this one > / | << 2 miles
/ |
/______|
^ 1.5 miles (I know the size is not logical,but imagine it please)
So to get the diagonal length =

=

= 2.5 miles
To calculate how much shorter = ( 2 miles + 1.5 miles) - 2.5 miles
= 3.5 miles - 2.5 miles
= 1.0 miles
Hope this help !