Solve for x in the equation x^2+20x+100=36

1 answer:

6 0

Factoring - I always found this to be easy (one of the few things in math that I felt was easy!)

x^2 + 20x + 100 = 36

First step is to get the right side to zero. Do this by subtracting 36.

x^2 + 20x + 64 = 0

Now we have to factor the expression. We could use quadratic formula, completing the square, or use the product/sum rule if possible (which it is).

64's factors are:
1, 64
2, 32
4, 16
8, 8

We need the two factors that sum to 20...

(x + 4)(x + 16) = 0
Set each factor to zero
x + 4 = 0 and x + 16 = 0

Solve each equation
x = -4 and x = -16

You should always check for extraneous solutions. I recommend using desmos.com to check answers!

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An advertising agency that serves a major radio station wants to estimate the mean amount of time the station’s audience members

Flura [38]

Answer:

$n=(\frac{1.645(45)}{5})^2 =219.18 \approx 220$

So the answer for this case would be n=220 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\sigma = 45$ represent the population deviation

$ME = 5$ represent the margin of error

The margin of error for the true mean is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (4) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 90% of confidence interval now can be founded using the normal distribution. The significance level is $\alpha=1-0.9=0.1$ and the critical value would be $z_{\alpha/2}=1.645$ , replacing into formula (b) we got: