Note that c is the hypotenuse of the blue triangle, and that the Pyth. Thm. states that (length of one leg)^2 + (length of the other leg)^2 = (hyp)^2.
Therefore, (hyp)^2 = c^2 = [2sqrt(x^2+3x)]^2 + 3^2, or
= 4(x^2+3x) + 9, or
= 4x^2 + 12x + 9 = (2x+3)^2
Taking the sqrt of both sides, c = plus or minus (2x+3). Eliminate -(2x+3) because the middle term of the square of this would be negative, in conflict with the given +12x.
c=2x+3 is the correct answer.
Answer:
Step-by-step explanation:
Since ΔABC ~ ΔEDC, ∠B = ∠D.
Since both triangles appear to be similar, the corresponding angles are the same, and corresponding sides are the same or have the same ratio.
We can write an equation to resemble the problem:
8x + 16 = 120
Solve for x.
8x + 16 = 120
~Subtract 16 to both sides
8x + 16 - 16 = 120 - 16
~Simplify
8x = 104
~Divide 8 to both sides
8x/8 = 104/8
~Simplify
x = 13
Therefore, the answer is 13.
Best of Luck!
Answer:
(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)
Here we have the equation:
We can rewrite this as:
Now we can add and subtract cos^2(x)*sin^2(x) to get:
We can complete squares to get:
and we know that:
cos^2(x) + sin^2(x) = 1
then:
This is the closest expression to what you wrote.
We also know that:
sin(x)*cos(x) = (1/2)*sin(2*x)
If we replace that, we get:
Then the simplification is:
Answer:
AM = 6
Step-by-step explanation:
Using the property of a parallelogram
• The diagonals bisect each other
MO is a diagonal, hence
AM = AO = 6
