Here’s my working out the green numbers are the answers
Answer:
Area = 30 square units
Step-by-step explanation:
First, let's try to visualize the problem:
(-2, 4) • | • (3, 4)
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|
___________|___________
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(-2, -2) • | • (3, -2)
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|
Let's find the side lengths;
(-2) - 3 = |-5|, the Base of the rectangle is 5 units.
4 - (-2) = 6, the Height of the rectangle is 6 units.
The formula for area of a rectangle is B × H.
5 × 6 = 30, so the area of the rectangle is 30 units.
Answer: -26=18x-b
Step-by-step explanation:
Step-by-step explanation:
8) Consider,
![\frac{1}{1 + \sin(x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B1%20%2B%20%20%5Csin%28x%29%20%7D%20)
Multiplying And Dividing By 1-sinx
![\frac{1}{1 + \sin(x) } \times \frac{1 - \sin(x) }{1 - \sin(x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B1%20%2B%20%20%5Csin%28x%29%20%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%20-%20%20%5Csin%28x%29%20%7D%7B1%20%20-%20%20%5Csin%28x%29%20%7D%20)
![\frac{1 - \sin(x) }{(1 + \sin(x) )(1 - \sin(x)) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%20-%20%20%5Csin%28x%29%20%7D%7B%281%20%20%2B%20%20%5Csin%28x%29%20%29%281%20-%20%20%5Csin%28x%29%29%20%7D%20)
We know (a+b)(a-b)=a²-b²
![\frac{1 - \sin(x) }{1 - \sin ^{2} (x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%20-%20%20%5Csin%28x%29%20%7D%7B1%20-%20%20%5Csin%20%5E%7B2%7D%20%28x%29%20%7D%20)
We know that sin²x+cos²x=1
cos²x=1-sin²x,
uisng this we get,
![\frac{1 - \sin(x) }{ \cos ^{2} (x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%20-%20%5Csin%28x%29%20%20%7D%7B%20%5Ccos%20%5E%7B2%7D%20%28x%29%20%7D%20)
![\frac{1}{ \cos ^{2} (x) } - \frac{ \sin(x) }{cos ^{2} (x)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Ccos%20%5E%7B2%7D%20%28x%29%20%7D%20%20-%20%20%5Cfrac%7B%20%5Csin%28x%29%20%7D%7Bcos%20%5E%7B2%7D%20%28x%29%7D%20)
We know that 1/cosx=secx and sinx/cosx=tanx
Using this we get,
![\sec {}^{2} (x) - \frac{ \tan(x) }{ \cos(x) }](https://tex.z-dn.net/?f=%20%5Csec%20%7B%7D%5E%7B2%7D%20%28x%29%20%20-%20%20%5Cfrac%7B%20%5Ctan%28x%29%20%7D%7B%20%5Ccos%28x%29%20%7D%20)
Hence Proved
Answer:
The factored form of the polynomial is 11*(x+2)*(x-5/11). The root found was r = -2
Step-by-step explanation:
If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.
Therefore, we prove with negative values.
- x = -1: 11*(-1)²+17*(-1) - 10 = -16
- x = -2: 11*(-2)² + 17*(-2) - 10 = 44-34-10 = 0
Therefore, -2 is a root. We can find the other knowing that
p(x) = 11*(x-r₁)*(x-r₂) = 11*(x-(-2)) * (x-r₂) = 11*(x+2)*(x-r₂)
The independent term is 11*2*(-r₂) = -22r₂ = -10
thus, r₂ = -10/-22 = 5/11.
Therefore, p(x) = 11*(x+2)*(x-5/11)