Answer: 110 -10x
Step-by-step explanation:
You do pemdas
So 11•10 = 110
Then -10•x = -10x
And then you get
110-10x
6+2=8, right? Okay. Next, all you have to do is take away the equation "6+2". Now what you have is... 8x5. That's easy! 40. This is a very easy problem if you think about it.
After solving an equation in Point Slope Form, you're directly given the slope intercept form which is y=mx +b
Answer:
1) The correct option is C. (2) The correct option is D. (3) The correct option is B. (4) The correct option is D. (5) The correct option is D.
Step-by-step explanation:
The slope formula is
(1)
Two points are (-2,5) and (1,4).
![m=\frac{4-5}{1-(-2)}=\frac{-1}{3}tex]Therefore option C is correct.(2)Use the above mentioned formula for each pair of coordinates.[tex]m=\frac{10-13}{17-12}=\frac{-3}{5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-5%7D%7B1-%28-2%29%7D%3D%5Cfrac%7B-1%7D%7B3%7Dtex%5D%3C%2Fp%3E%3Cp%3ETherefore%20option%20C%20is%20correct.%3C%2Fp%3E%3Cp%3E%282%29%3C%2Fp%3E%3Cp%3EUse%20the%20above%20mentioned%20formula%20for%20each%20pair%20of%20coordinates.%3C%2Fp%3E%3Cp%3E%5Btex%5Dm%3D%5Cfrac%7B10-13%7D%7B17-12%7D%3D%5Cfrac%7B-3%7D%7B5%7D)
Therefore option D is correct.
(3)
The pair of points (6, y) and (10, -1). The slope is 
.
Therefore option B is correct.
(4)
For vertical line the x coordinates always remains the same. Therefore when we subtract the same number we get zero in the denominator, therefore the value of slope is undefined for a vertical line.
Therefore option D is correct.
(5)
Two points from the table are (2,110) and (3,165).
Therefore option D is correct.
Answer:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Step-by-step explanation:
The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.
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<h3>top triangle</h3>
The law of sines applied to the top triangle is ...
BC/sin(A) = AC/sin(θ)
Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...
∠A = 180° -θ -θ = 180° -2θ
A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...
sin(A) = sin(180° -2θ) = sin(2θ)
and our above Law of Sines equation tells us ...
BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)
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<h3>bottom triangle</h3>
The law of sines applied to the bottom triangle is ...
DC/sin(B) = BC/sin(D)
d/sin(α) = BC/sin(β)
Multiplying by sin(α) we have ...
d = BC·sin(α)/sin(β)
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Using our expression for BC gives the desired relation:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
