Putting the equations into standard form helps me identify dependent and inconsistent systems. In standard form, the leading coefficient is positive, and all numbers are mutually prime (have no common factors).
1.) 2x + y = -9 . . . . . . multiply the original equation by -1
... 3x - 4y = -8 . . . . . . the system is independent
These two equations will give rise to a single solution.
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2.) 4x + y = 4 . . . . . . divide the original equation by 3
... 4x + y = 5 . . . . . . . the system is inconsistent
These two equations describe parallel lines, so will not have a point of intersection. There are no values of x and y that can satisfy both equations.
3) is y=x because they are directly proportional.
4) is $20 per uniform (read one unit of the graph)
5) is $160 for 8 uniforms
Log(x²-6)=1+log(x-3)
log(x²-6)=log 10 + log(x-3) (log 10=1)
log(x²-6)=log(10(x-3)) (log a+log b=log (a*b))
Then:
x²-6=10(x-3)
x²-6=10x-30
x²-10x+24=0
x=[10⁺₋√(100-96)]/2
=(10⁺₋2)/2
We have two possible solutions:
x₁=(10-2)/2=4
We can check it out this solution:
log(4²-6)=log(16-6)=log 10=1
1+log(x-3)=1+log(4-3)=1 +log 1=1+0=1
This solution is rigth.
x₂=(10+2)/2=6
We can check it out this possible solution:
log(6²-6)=log (36-6)=log 30≈1.477121255
1+log(x-3)=1+log(6-3)=1+ log 3=1.477121255
This solution is right too.
Answer: we have two solutions; x₁=4 and x₂=6.
Answer:
(-5)^3 = -125
Step-by-step explanation:
(-5)^3
= (-5) × (-5) × (-5) = -125
= (-5)^3 = -125
(-5) to the power of 3 is just (-5) multiplied by itself 3 times so (-5) to the power of 3 is (-5)^3 which is -125