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3 years ago

Find the sum of the roots of the quadratic x^2 + 7x - 13 = 0

Mathematics

1 answer:

Hoochie [10]3 years ago

6 0

Answer:

-7

Step-by-step explanation:

You use the quadratic formula of $ax^{2} +bx+c = 0$ to get:

a = 1

b = 7

c = -13

then you plug that into x= (-b ± √b²-4ac)/(2a) :

x= ( -7 ± √7²- 4(1)(-13) )/(2(1))

$x=-\frac{7}{2} + \frac{\sqrt{101}}{2} \\\\x=-\frac{7}{2} - \frac{\sqrt{101}}{2}$

The sum of these two x values turns out to be:

$x=-\frac{7}{2} + \frac{\sqrt{101}}{2}+( -\frac{7}{2} - \frac{\sqrt{101}}{2} )= -\frac{14}{2} = 7$

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In exercises 21 through 24 is it possible to construct a triangle if the given side lengths? If not explain why.

sattari [20]

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4 years ago

Jane is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a number

sleet_krkn [62]

Answer:

The expected value of playing the game is $0.75.

Step-by-step explanation:

The expected value of a random variable is the weighted average of the random variable.

The formula to compute the expected value of a random variable X is:

$E(X)=\sum x\cdot P(X=x)$

The random variable X in this case can be defined as the amount won in playing the game.

The probability distribution of X is as follows:

Number on spinner: 1 2 3 4 5 6

Amount earned (X): $1 $4 $7 $10 -$8.75 -$8.75

Probability: 1/6 1/6 1/6 1/6 1/6 1/6

Compute the expected value of X as follows:

$E(X)=\sum x\cdot P(X=x)$

$=(1\times \frac{1}{6})+(4\times \frac{1}{6})+(7\times \frac{1}{6})+(10\times \frac{1}{6})+(-8.75\times \frac{1}{6})+(-8.75\times \frac{1}{6})$

$=\frac{1}{6}+\frac{4}{6}+\frac{7}{6}+\frac{10}{6}-\frac{8.75}{6}-\frac{8.75}{6}$

$=\frac{1+4+7+10-8.75-8.75}{6}$

$=0.75$

Thus, the expected value of playing the game is $0.75.

5 0

3 years ago

HELP!!!!!!!!!!!!!!!!!!!!! Do all real numbers have a decimal expansion? Select each correct answer. Some numbers, such as 1 10

ankoles [38]

Answer:

1. Some numbers, such as $\frac{1}{10}$ , have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as $\frac{1}{18}$ , have a decimal expansion that repeats but does not terminate.

Step-by-step explanation:

According to the options, we have,

1. Some numbers, such as $\frac{1}{10}$ , have a decimal expansion that terminates.

It is correct as the decimal expansion of $\frac{1}{10}$ is 0.1, which terminates.

2. All real numbers have a decimal expansion.

This is also correct as both rational and irrational numbers can be written in decimal form.

3. Some numbers, such as $\sqrt{13}$ do not have a decimal expansion

This is not correct as $\sqrt{13}=3.605551275$ i.e. it has a decimal expansion.

4. Only some real numbers have a decimal expansion.

It is not correct as 2 is correct.

5. Some numbers, such as $\frac{1}{18}$ , have a decimal expansion that repeats but does not terminate.

It is correct as $\frac{1}{18}=0.0555555..$ , which is non-terminating decimal expansion.

So, the correct options are,

1. Some numbers, such as $\frac{1}{10}$ , have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as $\frac{1}{18}$ , have a decimal expansion that repeats but does not terminate.

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4 years ago

2.24 Exit poll: Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walke

iVinArrow [24]

Answer:

0.4929 = 49.29% probability that he voted in favor of Scott Walker

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Having a college degree.

Event B: Voting for Scott Walker.

They found that 57% of the respondents voted in favor of Scott Walker.

This means that $P(B) = 0.57$

Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree

This means that $P(A|B) = 0.33$

Probability of having a college degree.

33% of those who voted for Scott Walker(57%).

45% of those who voted against Scott Walker(100 - 57 = 43%). So

$P(A) = 0.33*0.57 + 0.45*0.43 = 0.3816$

What is the probability that he voted in favor of Scott Walker?

$P(B|A) = \frac{0.57*0.33}{0.3816} = 0.4929$

0.4929 = 49.29% probability that he voted in favor of Scott Walker

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3 years ago

Can someone help me with this problem

kirza4 [7]

Answer: A 18 1/5 - 22 2/5 - 40 1/5

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3 years ago