Answer:
f⁻¹(x) = (x + 3) / 2
Step-by-step explanation:
y = 2x − 3
To find the inverse, switch x and y, then solve for y.
x = 2y − 3
x + 3 = 2y
y = (x + 3) / 2
4 – 3(x – y) = –8x + 2
Apply distributive property to left side.
4 - 3x + 3y = -8x + 2
Add 8x to both sides.
4 + 5x + 3y = 2
Subtract 4 from both sides.
5x + 3y = -2
<h3><u>The correct answer is C.</u></h3>
Answer:
b=24
Step-by-step explanation:
Option A
The binomial factor is 3x + 4y
<em><u>Solution:</u></em>
We have to find the binomial factor of given equation
<em><u>Given equation is:</u></em>
![9x^2+24xy+16y^2](https://tex.z-dn.net/?f=9x%5E2%2B24xy%2B16y%5E2)
<em><u>Let us factor the given expression</u></em>
![9x^2+24xy+16y^2](https://tex.z-dn.net/?f=9x%5E2%2B24xy%2B16y%5E2)
![\mathrm{Rewrite\:}9\mathrm{\:as\:}3^2\\\\=3^2x^2+24xy+16y^2\\\\\mathrm{Rewrite\:}16\mathrm{\:as\:}4^2\\\\=3^2x^2+24xy+4^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\3^2x^2=\left(3x\right)^2\\\\=\left(3x\right)^2+24xy+4^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\4^2y^2=\left(4y\right)^2](https://tex.z-dn.net/?f=%5Cmathrm%7BRewrite%5C%3A%7D9%5Cmathrm%7B%5C%3Aas%5C%3A%7D3%5E2%5C%5C%5C%5C%3D3%5E2x%5E2%2B24xy%2B16y%5E2%5C%5C%5C%5C%5Cmathrm%7BRewrite%5C%3A%7D16%5Cmathrm%7B%5C%3Aas%5C%3A%7D4%5E2%5C%5C%5C%5C%3D3%5E2x%5E2%2B24xy%2B4%5E2y%5E2%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5C%3Aa%5Emb%5Em%3D%5Cleft%28ab%5Cright%29%5Em%5C%5C%5C%5C3%5E2x%5E2%3D%5Cleft%283x%5Cright%29%5E2%5C%5C%5C%5C%3D%5Cleft%283x%5Cright%29%5E2%2B24xy%2B4%5E2y%5E2%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5C%3Aa%5Emb%5Em%3D%5Cleft%28ab%5Cright%29%5Em%5C%5C%5C%5C4%5E2y%5E2%3D%5Cleft%284y%5Cright%29%5E2)
![=\left(3x\right)^2+24xy+\left(4y\right)^2\\\\\mathrm{Rewrite\:}24xy\mathrm{\:as\:}2\cdot \:3x\cdot \:4y\\\\=\left(3x\right)^2+2\cdot \:3x\cdot \:4y+\left(4y\right)^2\\\\ \mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=3x,\:b=4y\\\\=\left(3x+4y\right)^2\\\\\rightarrow (3x+4y)^2 = (3x+4y)(3x+4y)](https://tex.z-dn.net/?f=%3D%5Cleft%283x%5Cright%29%5E2%2B24xy%2B%5Cleft%284y%5Cright%29%5E2%5C%5C%5C%5C%5Cmathrm%7BRewrite%5C%3A%7D24xy%5Cmathrm%7B%5C%3Aas%5C%3A%7D2%5Ccdot%20%5C%3A3x%5Ccdot%20%5C%3A4y%5C%5C%5C%5C%3D%5Cleft%283x%5Cright%29%5E2%2B2%5Ccdot%20%5C%3A3x%5Ccdot%20%5C%3A4y%2B%5Cleft%284y%5Cright%29%5E2%5C%5C%5C%5C%20%5Cmathrm%7BApply%5C%3APerfect%5C%3ASquare%5C%3AFormula%7D%3A%5Cquad%20%5Cleft%28a%2Bb%5Cright%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5C%5C%5C%5Ca%3D3x%2C%5C%3Ab%3D4y%5C%5C%5C%5C%3D%5Cleft%283x%2B4y%5Cright%29%5E2%5C%5C%5C%5C%5Crightarrow%20%283x%2B4y%29%5E2%20%3D%20%283x%2B4y%29%283x%2B4y%29)
Thus the binomial factor is 3x + 4y
Thus Option A is correct