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3 years ago

The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below.

Mathematics

2 answers:

DochEvi [55]3 years ago

5 0

Answer:

There are two rational roots for f(x)

Step-by-step explanation:

We are given a function

$f(x) = x^6-2x^4-5x^2+6$

To find the number of rational roots for f(x).

Let us use remainder theorem that when

f(a) =0, (x-a) is a factor of f(x) or x=a is one solution.

Substitute 1 for x

f(1) = 1-2-5+6=0

Hence x=1 is one solution.

Let us try x=-1

f(-1) = 1-2-5+6 =0

So x =-1 is also a solution and x+1 is a factor

We can write f(x) by trial and error as

$f(x) = (x-1)(x+1)(x^2-3)$

We find that $f(x) (x^2-3)$ factor gives two irrational solutions as

±√3.

Hence number of rational roots are 2.

Assoli18 [71]3 years ago

4 0

Answer:

B. 2

Step-by-step explanation:

got it right on the quiz

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What is an equation of the line that passes through the points (0, -7) and (-8, 3)?

avanturin [10]

Answer (assuming it can be in slope-intercept form):

$y = -\frac{5}{4} x-7$

Step-by-step explanation:

1) First, find the slope of the line by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(3)-(-7)}{(-8)-(0)}\\m = \frac{3+7}{-8-0} \\m = \frac{10}{-8} \\m = -\frac{5}{4}$

So, the slope is $-\frac{5}{4}$ .

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute real values for the $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{4}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:

$y-(-7) = -\frac{5}{4} (x-(0))\\y + 7 = -\frac{5}{4} x\\y = -\frac{5}{4} x-7$

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2 years ago

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4 years ago

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The table shows the charges for using an internet service. Nicholas use the internet service for 16 hours and 40 Minutes last mo

yanalaym [24]

Answer:

A. Nicholas will have to pay less using plan A

B. He will pay US$ 4 less than plan B

Step-by-step explanation:

Let's compare how much Nicholas will pay on internet service in Plan A and plan B, after using it 16 hours and 40 minutes.

Plan A

Up to 10 hours = US$ 6

Every subsequent 1/2 hour: $1

10 hours + 14 (1/2 hour)

Nicholas will pay 6 + 14 * 1 = US$ 20

Plan B

Up to 12 hours = US$ 4

Every subsequent 1/2 hour: $2

12 hours + 10 (1/2 hour)

Nicholas will pay 4 + 2 * 10 = 24

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3 years ago

At a raffle, 1500 tickets are sold at $2 each. There are four prizes given for $500, $250, $150, and $75. You buy one ticket. Us

wolverine [178]

Answer:

The expected value of every ticket is a loss of $ 1.35

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of tickets sold at the raffle = 1,500

Price of each ticket = $ 2

Total prizes = 1 * $ 500 + 1 * $ 250 + 1 * $ 150 + 1 * $ 75

2. Use a probability distribution table to calculate the expected value of your gain. Your expected value is_____ ?

Let's answer the question using a probability distribution for the gains, this way:

Probability of 1st prize of $ 498 (500 - ticket) = 1/1,500
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Probability of 3rd prize of $ 148 (150 - ticket) = 1/1,500
Probability of 4th prize of $ 73 (75 - ticket) = 1/1,500
Probability of losing $ 2 (ticket) = 1,496/1,500

Now, we calculate the mean for all the tickets (winners and non-winners), this way:

Expected value = [(1,496 * -2) + (1 * 498) + (1 * 248) + ( 1 * 148) + ( 1 * 73)]/1,500

Expected value = [- 2,992 +498 + 248 + 148 + 73)/1,500

Expected value = -2,025/1,500 = - 1,35

The expected value of every ticket is a loss of $ 1.35

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4 years ago

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Answer:

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Step-by-step explanation:

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