Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
Answer:
60 degrees
Step-by-step explanation:
Since the angle 120° is in the second quadrant, the reference angle formula is Ar=180°−Ac A r = 180 ° - A c . The reference angle is Ar=60° A r = 60 ° .
Step ![1](https://tex.z-dn.net/?f=%201%20)
<u>Find the length of the side MN</u>
we know that
Applying the Pythagorean Theorem
![ML^{2} =NL^{2} +MN^{2}](https://tex.z-dn.net/?f=%20ML%5E%7B2%7D%20%3DNL%5E%7B2%7D%20%2BMN%5E%7B2%7D%20%20)
Solve for MN
![MN^{2}=ML^{2} -NL^{2}](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3DML%5E%7B2%7D%20-NL%5E%7B2%7D%20%20)
in this problem
![ML=25\ units\\ NL=15\ units](https://tex.z-dn.net/?f=%20ML%3D25%5C%20units%5C%5C%20NL%3D15%5C%20units%20)
Substitute in the formula above
![MN^{2}=25^{2} -15^{2}](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3D25%5E%7B2%7D%20-15%5E%7B2%7D%20%20)
![MN^{2}=400](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3D400%20%20)
![MN=20\ units](https://tex.z-dn.net/?f=%20MN%3D20%5C%20units%20%20)
Step ![2](https://tex.z-dn.net/?f=%202%20)
<u>Find the value of cos (M)</u>
we know that
in the right triangle MNL
![cos (M)=\frac{adjacent\ side\ angle\ M}{hypotenuse}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7Badjacent%5C%20side%5C%20angle%5C%20M%7D%7Bhypotenuse%7D%20%20%20)
![adjacent\ side\ angle\ M=MN=20\ units\\ hypotenuse=ML=25\ units](https://tex.z-dn.net/?f=%20adjacent%5C%20side%5C%20angle%5C%20M%3DMN%3D20%5C%20units%5C%5C%20hypotenuse%3DML%3D25%5C%20units%20)
Substitute
![cos (M)=\frac{20}{25}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7B20%7D%7B25%7D%20%20%20)
![cos (M)=\frac{4}{5}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7B4%7D%7B5%7D%20%20%20)
![cos (M)=0.8](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D0.8%20%20%20)
therefore
The answer is
The value of cos(M) is equal to ![0.8](https://tex.z-dn.net/?f=%200.8%20)