GEOMETRY!!!! HELP PLS THANK U

What are the potential solutions to the equation 2ln(x+3)=0

skad [1K]

$2\ln(x+3)=0\implies \ln(x+3)^2=0\implies e^{\ln(x+3)^2}=e^0\implies (x+3)^2=1$

Expanding the left side gives

$x^2+6x+9=1\implies x^2+6x+8=0\implies (x+4)(x+2)=0$

which gives two solutions, $x=-4$ and $x=-2$ . But if $x=-4$ , then $\ln(x+3)=\ln(-1)$ , but this number isn't real, so $x=-4$ is an extraneous solution. Meanwhile if $x=-2$ , you get $\ln(-2+3)=\ln1=0$ , so this solution is correct.

"Potential solutions" might refer to both possibilities, but there is only one actual (real) solution.

4 0

3 years ago

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A Ferrari drove 300 kilometers in one and a half hours. How fast was the car going?

irga5000 [103]

I'm assuming you mean how many mph when you refer to how fast the car was going.

So 300 km = 1.5 hrs

1.) Find the number of km per hour
Since we have the equation 300km = 1.5hr, we can just divide 1.5 (to isolate the number of hours) on both sides.

You should get 200 km = 1 hour

2.) Convert km to miles
To do this, you must know the conversion 1 km = 0.621371192 miles

So to convert 200 km to miles, just multiply 200 x 0.621371192.

You should get 124.274238.

That means the Ferrari drove at a pace of roughly 124 mph :)

8 0

3 years ago

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A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.