Describe the zero product property and explain how tu use it to solve (2x + 10) (x - 7) = 0

Mathematics

1 answer:

Korolek [52]2 years ago

8 0

Answer:

See below

Step-by-step explanation:

Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:

$2x+10=0\\2x=-10\\x=-5$

$x-7=0\\x=7$

Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:

$(2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0$

$(2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0$

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Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t

NeTakaya

Answer:

$\mu = 11$

$\sigma = 2.08$

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when $Z = -1.44, X = 8$ . So