Answer:
Slope: 5/4
Step-by-step explanation:
As given the equation is 5x-4y =24
=5x-24 = 4y (switch over the y, turning the sign from negative to positive)
=5/4x -6 =y (divide everything by 4)
Answer:
Step-by-step explanation:
![3\log_5(x-10)-\dfrac{1}{2}\log_54=5\log_52\\\\\text{Domain:}\ x-10>0\to x>10\\\\\text{use}\\\\\log_ab^n=n\log_ab\\\\\log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\========================\\\\\log_5(x-10)^3-\log_54^\frac{1}{2}=\log_52^5\qquad\text{use}\ a^\frac{1}{2}=\sqrt{a}\\\\\log_5(x-10)^3-\log_5\sqrt4=\log_532\\\\\log_5(x-10)^3-\log_52=\log_532\\\\\log_5\dfrac{(x-10)^3}{2}=\log_532\iff\dfrac{(x-10)^3}{2}=32\qquad\text{multiply both sides by 2}\\\\(x-10)^3=64\to x-10=\sqrt[3]{64}\\\\x-10=4\qquad\text{add 10 to both sides}\\\\x=14\in D](https://tex.z-dn.net/?f=3%5Clog_5%28x-10%29-%5Cdfrac%7B1%7D%7B2%7D%5Clog_54%3D5%5Clog_52%5C%5C%5C%5C%5Ctext%7BDomain%3A%7D%5C%20x-10%3E0%5Cto%20x%3E10%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%5C%5C%5C%5Clog_ab%5En%3Dn%5Clog_ab%5C%5C%5C%5C%5Clog_ab-%5Clog_ac%3D%5Clog_a%5Cleft%28%5Cdfrac%7Bb%7D%7Bc%7D%5Cright%29%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5C%5C%5Clog_5%28x-10%29%5E3-%5Clog_54%5E%5Cfrac%7B1%7D%7B2%7D%3D%5Clog_52%5E5%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%5Cfrac%7B1%7D%7B2%7D%3D%5Csqrt%7Ba%7D%5C%5C%5C%5C%5Clog_5%28x-10%29%5E3-%5Clog_5%5Csqrt4%3D%5Clog_532%5C%5C%5C%5C%5Clog_5%28x-10%29%5E3-%5Clog_52%3D%5Clog_532%5C%5C%5C%5C%5Clog_5%5Cdfrac%7B%28x-10%29%5E3%7D%7B2%7D%3D%5Clog_532%5Ciff%5Cdfrac%7B%28x-10%29%5E3%7D%7B2%7D%3D32%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%202%7D%5C%5C%5C%5C%28x-10%29%5E3%3D64%5Cto%20x-10%3D%5Csqrt%5B3%5D%7B64%7D%5C%5C%5C%5Cx-10%3D4%5Cqquad%5Ctext%7Badd%2010%20to%20both%20sides%7D%5C%5C%5C%5Cx%3D14%5Cin%20D)
Answer:
1.6 hours
Step-by-step explanation:
Their separation speed is 95 +105 = 200 miles per hour. The time required for the given distance is ...
time = distance/speed
time = (320 mi)/(200 mi/h) = 1.6 h
It will take 1.6 hours for the trains to be 320 miles apart.
Answer:
A
Step-by-step explanation:
x+x+1+x+2=33
3x+3=33
3x=30
x=10
so x+1 =11
x+2 =12
