Answer:
<h2>Option A = 1*3 = 3 unit² </h2>
![area \: of \: rectangle \: = length \: \times breath](https://tex.z-dn.net/?f=area%20%5C%3A%20of%20%5C%3A%20rectangle%20%5C%3A%20%20%3D%20length%20%5C%3A%20%20%5Ctimes%20breath)
![length \: = distance \: between \: f \: and \: g \: or \: between \: e \: and \: h \:](https://tex.z-dn.net/?f=length%20%5C%3A%20%20%3D%20distance%20%5C%3A%20between%20%5C%3A%20f%20%5C%3A%20and%20%5C%3A%20g%20%5C%3A%20or%20%5C%3A%20between%20%5C%3A%20e%20%5C%3A%20and%20%5C%3A%20h%20%5C%3A%20)
<h3>Distance between f and G = distance between E and H </h3>
F = (3,7)
G = (6,4)
H = (5,3)
E= (2,6)
= (3 units)
<h3>
Distance between FE = GH </h3>
= 1 units
Area = 3* 1
= 3 units²
Answer:
B
Step-by-step explanation:
3 + f = 14
← change to improper fraction
3 + f =
( multiply through by 7 to clear the fraction )
21 + 7f = 100 ( subtract 21 from both sides )
7f = 79 ( divide both sides by 7 )
f =
= 11
→ B
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:
The factors of the polynomial: (b⁴ - 2)(b² - 3)
Step-by-step explanation:
The given polynomial is: ![$ \textbf{b}^{\textbf{6}} \textbf{-3b}^{\textbf{4}} \textbf{-2b}^{\textbf{2}} \textbf{+ 6} $](https://tex.z-dn.net/?f=%24%20%5Ctextbf%7Bb%7D%5E%7B%5Ctextbf%7B6%7D%7D%20%5Ctextbf%7B-3b%7D%5E%7B%5Ctextbf%7B4%7D%7D%20%5Ctextbf%7B-2b%7D%5E%7B%5Ctextbf%7B2%7D%7D%20%5Ctextbf%7B%2B%206%7D%20%24)
We can factor the given polynomial by grouping.
We get: ![$ \{ b^6 - 3b^4\} + \{2b^2 + 6\} $](https://tex.z-dn.net/?f=%24%20%5C%7B%20b%5E6%20-%203b%5E4%5C%7D%20%2B%20%5C%7B2b%5E2%20%2B%206%5C%7D%20%24)
![$ = b^4 (b^2 - 3) -2(b^2 - 3) $](https://tex.z-dn.net/?f=%24%20%3D%20b%5E4%20%28b%5E2%20-%203%29%20-2%28b%5E2%20-%203%29%20%24)
Taking (b² - 3) common outside, we get:
![$ = \{b^2 - 3\} \{b^4 - 2\} $](https://tex.z-dn.net/?f=%24%20%3D%20%5C%7Bb%5E2%20-%203%5C%7D%20%5C%7Bb%5E4%20-%202%5C%7D%20%24)
Hence the polynomial
can be factored as
.
Hence, the answer.
180 degrees counterclockwise because 360 degrees is a full circle and 180 is half a circle because 6x2=12