4.644*10^12
hope this helps!!
Answer:
![e=\sqrt{f^{2}+d^{2}}](https://tex.z-dn.net/?f=e%3D%5Csqrt%7Bf%5E%7B2%7D%2Bd%5E%7B2%7D%7D)
Step-by-step explanation:
We are given that,
The acute angle of the right angled triangle is 65°.
Length of the side opposite to the acute angle = f
Length of the side adjacent to the acute angle = d
Length of the hypotenuse = e
Using 'Pythagoras Theorem', which states that 'the sum of square of length of the sides of a right triangle is equal to the square of the length of the hypotenuse'.
i.e. ![Hypotenuse^{2}=Opposite^{2}+Adjacent^{2}](https://tex.z-dn.net/?f=Hypotenuse%5E%7B2%7D%3DOpposite%5E%7B2%7D%2BAdjacent%5E%7B2%7D)
i.e. ![e^{2}=f^{2}+d^{2}](https://tex.z-dn.net/?f=e%5E%7B2%7D%3Df%5E%7B2%7D%2Bd%5E%7B2%7D)
i.e. ![e=\pm \sqrt{f^{2}+d^{2}}](https://tex.z-dn.net/?f=e%3D%5Cpm%20%5Csqrt%7Bf%5E%7B2%7D%2Bd%5E%7B2%7D%7D)
As, the length of the hypotenuse cannot be negative.
So, the expression showing the value of e is
.
Answer:
ƒ(x) = 3(4x - 1)(3x + 2)
Step-by-step explanation:
Your function is: ƒ(x) = 36x² + 15x - 6
1. Remove the common factor
36x² + 15x - 6 = 3(12x² + 5x - 2)
2. Factor the quadratic
(a) Multiply the leading coefficient and the constant
12 × (-2) = -24
(b) Find two numbers that multiply to give -24 and add to give 5.
Possible pairs are 1, 24; 2, 12; 3, 8; 4, 6
One of the numbers must be negative. Start with the numbers near the end of the list.
By trial and error, you will find that 8 and -3 work:
-3 × 8 = -24 and -3 + 8 = 5
(b) Rewrite 5x as -3x + 8x
12x² - 3x + 8x - 2
(c) Factor by grouping the first two and the last two terms
(3x)(4x - 1) + 2(4x - 1) = (4x + 1)(3x + 2)
ƒ(x) = 3(4x -1)(3x + 2)
This is the correctly factored form that you can use to find the zeros.
The anser is 11 you can see