You set up the problem correctly, just keep going.
Expand out your expression:
2x(3x-9) + 4x(x+13)
= 6x^2 -18x + 4x^2 + 52x
= 10x^2 +34x
Remember that the above expression is the area, so it is equal to 24.
10x^2 + 34x = 24
10x^2 + 34x - 24 = 0 (divide by 2)
5x^2 + 17x - 12 = 0
Done.
The answer is [-1,26]. The range between 4 and 9 is 5, and the range between 8 and -10 is 18, so you'd apply this to [4, 8] in order to find the other endpoint.
Answer:
Step-by-step explanation:
log3(x^2)-log3(x+4)=4
Log 3(x^2/x+4)=4 -Combine the logs
x^2/x+4 = 3^4 - Use the relationship Logb(y)=x =>b^x=y
x^2/x+4 = 81
x^2= 81^(x+4)
x^2=81x+324
x^2-81x-324=0
Solving for x using the property x=-b-/+[tex]\sqrt{x} b^2-4ac]/ 2a
=(81 ±√(81)^2-4^11^324)/2
= (81±√6561-1296)/2
=(81±88.63)/2
= (81+88.63)/2
=84.81
