The sum or difference modeled by the algebra tiles is (-x^2 + 2x + 3) + (-x^2 - 2x - 1) = -2x^2 + 2
<h3>How to determine the sum or difference is modeled by the algebra tiles?</h3>
The tiles that complete the question are added as an attachment
From the attached tiles, we have:
Red tiles = -x^2 + 2x + 3
Blue tiles = -x^2 - 2x - 1
Evaluate the difference
Difference = (-x^2 + 2x + 3) - (-x^2 - 2x - 1)
This gives
(-x^2 + 2x + 3) + (-x^2 - 2x - 1) = -2x^2 + 2
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Answer:
WATER IS not wet
Step-by-step explanation:
Water is NOT wet by itself, however it makes other materials wet when it sticks to the surface of them.
a) The value of
as a function of "x" is ![\theta = tan^{-1}\frac{250}{x}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D)
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = ![\theta](https://tex.z-dn.net/?f=%5Ctheta)
Using the SOH CAH TOA identity
![tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%20%5C%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B250%7D%7Bx%7D%20%5C%5C%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D)
Hence the value of
as a function of "x" is ![\theta = tan^{-1}\frac{250}{x}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D)
b) If x = 450m
![\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D%5C%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B250%7D%7Bx%7D%5C%5C)
Differentiate both sides with respect to "x"
![sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}](https://tex.z-dn.net/?f=sec%5E2%20%5Ctheta%20%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-250%7D%7Bx%5E2%7D%20%20%5C%5C%20%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%20%5Cfrac%7B1%7D%7Bsec%5E2%5Ctheta%7D%20%5Ctimes%20%5Cfrac%7B-250%7D%7Bx%5E2%7D)
Substitute x = 450m and
into the resulting expression to have:
![\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%20%5Cfrac%7B1%7D%7Bsec%5E260%5E0%7D%20%5Ctimes%20%5Cfrac%7B-250%7D%7B450%5E2%7D%5C%5C%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%20%28cos60%29%5E2%5Ctimes%20%5Cfrac%7B-250%7D%7B202%2C500%7D%5C%5C%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%200.5%5E2%5Ctimes%20%5Cfrac%7B-250%7D%7B202%2C500%7D%5C%5C%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D-0.000308)
Hence the rate of change of the angle with respect to x is -0.000308rad/m
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Answer:
C. 1/4 of all teams in the Northeast have not won a single Super Bowl.
Step-by-step explanation:
There are 2 teams that have won 3 Super Bowls out of 32 total teams; this is 2/32 = 1/16. This is not 1/8.
There are 2 teams who have won 5 Super Bowls, and neither of them are from the Northeast.
There are 8 teams in the Northeast. Out of these, 2 have not won a Super Bowl; this is 2/8 = 1/4.
There are 2 teams that have won 3 Super Bowls. Out of them, 1 is from the West; this is 1/2, not 2/3.
The only true answer was C.