Answer:
Final answer is approx x=-0.66.
Step-by-step explanation:
Given equation is
.
Now we need to solve equation
and round to the nearest hundredth.
![5^{-2x-1}=4^{4x+3}](https://tex.z-dn.net/?f=5%5E%7B-2x-1%7D%3D4%5E%7B4x%2B3%7D%20)
![\log(5^{-2x-1})=\log(4^{4x+3})](https://tex.z-dn.net/?f=%5Clog%285%5E%7B-2x-1%7D%29%3D%5Clog%284%5E%7B4x%2B3%7D%29%20)
![(-2x-1)\log(5)=(4x+3)\log(4)](https://tex.z-dn.net/?f=%28-2x-1%29%5Clog%285%29%3D%284x%2B3%29%5Clog%284%29%20)
![-2x \log(5)- \log(5)=4x \log(4)+3 \log(4)](https://tex.z-dn.net/?f=-2x%20%5Clog%285%29-%20%5Clog%285%29%3D4x%20%5Clog%284%29%2B3%20%5Clog%284%29%20)
![-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)](https://tex.z-dn.net/?f=-2x%20%5Clog%285%29%20-4x%20%5Clog%284%29%3D3%20%5Clog%284%29%20%2B%5Clog%285%29)
![x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cleft%283%5Clog%284%29%2B%5Clog%285%29%5Cright%29%7D%7B%5Cleft%28-2%5Clog%285%29-4%5Clog%284%29%5Cright%29%7D)
Now use calculator to calculate log values, we get:
![x=-0.65817959094](https://tex.z-dn.net/?f=x%3D-0.65817959094)
Round to the nearest hundredth.
Hence final answer is approx x=-0.66.
Answer:
Step-by-step explanation:
![\frac{QT}{Q'T'}=\frac{1}{2}\\](https://tex.z-dn.net/?f=%5Cfrac%7BQT%7D%7BQ%27T%27%7D%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C)
Scale factor:
1:2
To solve this problem we can make the following rule of three
6 ---> 3/4
x ----> 1
Clearing x we have:
x = (1/3/4) * (6)
x = (4/3) * (6)
x = 24/3
x = 8
Answer:
Carlos climbs 8 miles for every mile Lara climbs.
Answer:
(x,y)→(y,-x)
Step-by-step explanation:
Parallelogram ABCD:
A(2,5)
B(5,4)
C(5,2)
D(2,3)
Parallelogram A'B'C'D':
A'(5,-4)
B'(4,-5)
C'(2,-5)
D'(3,-2)
Rule:
A(2,5)→A'(5,-2)
B(5,4)→B'(4,-5)
C(5,2)→C'(2,-5)
D(2,3)→D'(3,-2)
so the rule is
(x,y)→(y,-x)