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3 years ago

Factor 2x2 − 4x − 30 completely.

Mathematics

2 answers:

vova2212 [387]3 years ago

7 0

Answer:

$x^{2} -2x-15=(x-5)(x+3)$

Step-by-step explanation:

The given expression is

$2x^{2} -4x-30$

This is a quadratic expression, which can be equal to zero

$2x^{2} -4x-30=0$

Now, we extract the greatest common factor to obtain an easier expression to factor

$2(x^{2} -2x-15)=0\\x^{2} -2x-15=0$

To factor, first we write two binomials, the sign of the first one must be the same of the linear term and the sign of the second binomila must the product of the sign of the linear term and the constant term

$x^{2} -2x-15=(x-a)(x+b)$

Now, we have to find to number which product is 15 and which difference is 2, those numbers are 5 and 3, because 5 times 3 is 15, and 5 minus 3 is 2.

Therefore, the solution is

$x^{2} -2x-15=(x-5)(x+3)$

Luda [366]3 years ago

3 0

I hope this helps you

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Ricky walked away from a mall at a constant velocity for the first 30 seconds. He stopped at an ice cream parlor for 40 seconds.

Vlada [557]

Answer : option C

We analyze the attached graph

First, Ricky walked away from mall at the constant speed for 30 seconds

Second, he stopped walking for 40 seconds

Third, he walked towards mall at a constant speed for 10 seconds

Fourth , both walked away for next 20 seconds

So total walk time = 30 + 40 + 10 + 20= 100 seconds

Total time is 100 seconds. so we cannot choose option B and d because the graph ends before 100 seconds.

In option A, Ricky walked away from the mall after 70 seconds. so we cannot choose option A.

Option C is the graph best represents Ricky's motion.

4 0

4 years ago

Read 2 more answers

A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount

-Dominant- [34]

Answer:

The company should use a mean of 12.37 ounces.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.17 ounce.

This means that $\sigma = 0.17$

The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)?

This is $\mu$ , considering that when $X = 12$ , Z has a p-value of $1 - 0.985 = 0.015$ , so when $X = 12, Z = -2.17$ .