Algebra Answers

1.log₁₁(x²+3x) =log₁₁(3x+16)

2.In(4-3x) -In(7x) =In(11)

3.log(x) +log(x+12)=log(x-10)

4.In(x) =In(15-x) -In(x+1)

5.log₈(4x+1) =-1

6.log₆(3x) -log₆(x+5) =1

Test the consistency of the following system x+6y=9, 3x+18y=6.

A car's value depreciates at a rate of 20%

each year. If you paid $20,000 for this car 6

years ago, what is the current value of your

car?

y = a(1 - r)^t

A formula for calculating the magnitude of an earthquake is M=2

3

log(E

E

)

 that uses the common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude 3.9

 on the MMS. If a second earthquake has 800

 times as much energy as the first, find the magnitude of the second quake.

Round to the nearest hundredth.

The magnitude of the second earthquake was ???

Atmospheric pressure P

 in pounds per square inch is represented by the formula P=14.7e

−0.21x

, where x

 is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.124

 pounds per square inch? (Hint: there are 5,280

 feet in a mile)

If q is a double root of the equation

x² + ax + b=0. Prove that

a=-3q², b= 2q³ and hence

4a³ + 27b²=0

If a, b, c and d are the roots of the equation

2x⁴-4x³+6x²+10x+12=0.

Find the value of a²+b²+c²+d².

For what value(s) of k, if any, will the system have no solution, a unique solution, and infinitely many solutions? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

x − 2y + 8z = 6

x + y + z = k

2x − y + 9z = k²

Show complete solution:

1.f(x)=2 sin (x-​π/​4)

2.f(x)=sin (x+π/​3)

3.f(x)=3 cos (x+π/​6)

4.f(x)=2 cos (x-2π)

5.f(x)=tan x