Answer:
(i) 7
(ii) y= (8-2x)/3 or g^-1 (x) = (8-2x)/3
Step-by-step explanation:
b) (i) g(x) = (8-3x)/2
g(-2)= (8-3(-2))/2
g(-2) = (8+6)/2
g(-2)= 14/2
g(-2)=7
(ii) Now, for inverse, we just simply switch x and y and solve for y(g(x)):
Before: y = (8-3x)/2
After: x=(8-3y)/2
(solve)
2x= 8-3y (Multiplying both sides by 2)
2x-8 = -3y (Subtracting 8 both sides)
(2x-8)/-3 =y (Dividing by -3 both sides)
(8-2x)/3 = y (Multiplying the negative in numerator[Not necessary, but preferred by most!])
Hope this helps!
Answer:
there are 12 boys for every 4 girls.
Answer:
![\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}](https://tex.z-dn.net/?f=%5Ccos%20x%3D-%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B5%7D%5C%5C%20%5C%5C%5Ctan%20x%20%3D-%5Cdfrac%7B2%7D%7B%5Csqrt%7B21%7D%7D%5C%5C%20%5C%5C%5Ccot%20x%3D-%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B2%7D)
Step-by-step explanation:
Given
![\sin x=\dfrac{2}{5}\\ \\\cos x](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cdfrac%7B2%7D%7B5%7D%5C%5C%20%5C%5C%5Ccos%20x%3C0)
Use formula:
![\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}](https://tex.z-dn.net/?f=%5Ccos%5E2x%2B%5Csin%20%5E2x%3D1%5C%5C%20%5C%5C%5Ccos%5E2x%2B%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%5Cright%29%5E2%3D1%5C%5C%20%5C%5C%5Ccos%5E2x%3D1-%5Cdfrac%7B4%7D%7B25%7D%5C%5C%20%5C%5Ccos%5E2x%3D%5Cdfrac%7B21%7D%7B25%7D%5C%5C%20%5C%5C%5Ccos%20x%3D%5Cpm%20%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B5%7D)
Since
then
![\cos x=-\dfrac{\sqrt{21}}{5}](https://tex.z-dn.net/?f=%5Ccos%20x%3D-%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B5%7D)
By definition,
![\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}](https://tex.z-dn.net/?f=%5Ctan%20x%20%3D%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D%3D%5Cdfrac%7B%5Cfrac%7B2%7D%7B5%7D%7D%7B-%5Cfrac%7B%5Csqrt%7B21%7D%7D%7B5%7D%7D%3D-%5Cdfrac%7B2%7D%7B%5Csqrt%7B21%7D%7D%5C%5C%20%5C%5C%20%5C%5C%5Ccot%20x%3D%5Cdfrac%7B1%7D%7B%5Ctan%20x%7D%3D%5Cdfrac%7B1%7D%7B-%5Cfrac%7B2%7D%7B%5Csqrt%7B21%7D%7D%7D%3D-%5Cdfrac%7B%5Csqrt%7B21%7D%7D%7B2%7D)
The expression is:
(z^2 - 4)
_______
z - 3
_______________
z + 2
___________
z^2 + z - 12
You can factor the numerator z^2 - 4 = (z + 2) (z - 2)
And the denominatior z^2 + z + 12 = (z + 4)(z - 3)
That permits to write the quotient as:
(z + 2)(z - 2)
___________
z - 3
_______________
z + 2
___________
(z + 4)(z - 3)
Now you can multiplicate the numerator of the numerator times the denominator of the denominator, and multtiplicate the denominator of the numerator times the numerator of the denominator to obtain:
(z + 2)(z - 2)(z + 4)(z - 3)
____________________
(z - 3)((z + 2)
Cancel the factors (z - 3) and (z + 2) because they are in both the numerator and the denominator =>
(z - 2)(z + 4) = z^2 + 2z - 8
The restrictions are that none of the cancelled factors can be 0, so z ≠ 3 and z ≠- 4.
If 2 Lines are crossing together to make 2 pairs of Vertical Angles, the sum of all 4 Angles will always be equal to 360°.