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2 years ago

The table represents the start of the division of 3x^4+22x^3+37x^2-7x+10by the indicated divisor

Mathematics

1 answer:

andreyandreev [35.5K]2 years ago

8 0

The quotient is x^3 + 4x^2 -x + 1.

Solution:
By polynomial grid division, we start by the divisor 3x + 10 placed on the column headings.
   3x 10
x^3   3x^4

We know that 3x^4 must be in the top left which means that the first row entry must be x^3. So the row and column multiply to 3x^4. We use this to fill in all of the first row, multiplying x^3 by the terms of the column entries.
   3x    10
x^3 3x^4 10x^3
4x^2

We now got 10x^3 though we want 22x^3. The next cubic entry must then be 12x^3 so that the overall sum is 22x^3.
    3x    10
x^3 3x^4    10x^3
4x^2    12x^3

Now we have 40x^2, so the next quadratic entry must be -3x^2 so that the overall sum is 37x^2.
   3x    10
x^3    3x^4    10x^3
4x^2 12x^3 40x^2
-x -3x^2   -10x

This time we have -10x, so the next linear entry must be 3x so that the overall sum is 7x.
   3x 10
x^3 3x^4 10x^3
4x^2 12x^3 40x^2
-x -3x^2 -10x
1    3x 10

The bottom and final term is 10, which is our desired answer. Therefore, we can now read the quotient off the first column:
3x^4+22x^3+37x^2-7x+10 / 3x + 10 = x^3 + 4x^2 -x + 1

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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. One of the x-interc

Marina CMI [18]

3x^2 + 6x - 10 = 0
3(x^2 + 2x) - 10 = 0
3[ (x + 1)^2 - 1 ] - 10 = 0
3(x+1)^2 - 13 = 0

so the vertex is at (-1,-13)
the roots will be same distance from x = -1
that is a distance 1.08 --1 = 2.08

so other root is approximately -1 -2.08 = -3.08

the other intercept is at (-3.08,0)

5 0

3 years ago

Read 2 more answers

Dana is planning to drive 400 miles from

GaryK [48]

Answer:

A. 8 gallons

B. Drive by car is $59.4 cheaper than travel by train

Step-by-step explanation:

According to the scenario, given data are as follows,

Total drive = 400 miles

Total drive per gallon = 50 miles

Fuel cost per gallon = $4.45

A. So, Total fuel required to drive 400 miles can be calculated as follows,

Total fuel required = Total drive ÷ Total drive per gallon

By putting value, we get,

Total fuel required = 400 ÷ 50

= 8 gallons

B. Total cost if drive by car = 8 gallons × $4.45 = $35.6

Cost if travel by train = $95

Hence it is clearly shows that drive by car is much cheaper than travel by train.

Cost saved by travel by car = $95 - $35.6 = $59.4

So, drive by car is $59.4 cheaper than travel by train.

5 0

3 years ago

A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) usi

lbvjy [14]

Using the distributions, it is found that there is a:

a) 0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

b) 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

c) 0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item a:

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

20 tosses, hence $n = 20$ .
Fair coin, hence $p = 0.5$ .

The probability is P(X = 10), thus:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.5)^{10}.(0.5)^{10} = 0.1762$

0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item b:

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.
The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

The probability of an exact value is 0, hence 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item c:

For the approximation, the mean and the standard deviation are:

$\mu = np = 20(0.5) = 10$

$\sigma = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.5)} = \sqrt{5}$

Using continuity correction, this probability is $P(10 - 0.5 \leq X \leq 10 + 0.5) = P(9.5 \leq X \leq 10.5)$ , which is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 9.5.