What are the roots of the polynomial equation x3 - 6x= 3x2 - 8? Use a graphing calculator and a system of equations

Answer:

hole at x=-3

Step-by-step explanation:

The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)

The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.

So anyways we have (x+3)/(x^2-9)

= (x+3)/((x-3)(x+3))

Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.

Answer:

x= -3

Step-by-step explanation:

(2x/3)-2=-4

Add 2 to both sides

2x/3=-2

multiply both sides by 3

2x=-6

divide both sides by 2

x= -3

Answer:

x = -3

Step-by-step explanation:

2x/3 - 2 = -4

Add 2 to both sides.

2x/3 = -2

Multiply both sides by 3/2.

x = -2 * 3/2

x = -3

Answer:

f(x) = 8x

Explanation:

4 x 2 =8

9514 1404 393

Answer:

  B. (x-2)^2=12

Step-by-step explanation:

The constant that completes the square is the square of half the coefficient of the x-term. That value is (-4/2)^2 = 4.

There is already a constant of 2 on the left side of the equal sign, so we need to add 2 to both sides to bring that constant value up to 4.

  x^2 -4x +2 = 10 . . . . . . . given

  x^2 -4x +2 +2 = 10 +2 . . . . complete the square (add 2 to both sides)

  (x -2)^2 = 12 . . . . . . . . . write as a square

Answer:

(a)[tex]0.15731[/tex]

(b)0.02275

Step-by-step explanation:

We are given that

Mean=0

Standard deviation=0.5 g

True weight of a sample=166 g

Let X denote the normal random variable  with mean =166+0=166

(a)

P(166.5<X<167.5)

=[tex]P(\frac{166.5-166}{0.5}<\frac{X-\mu}{\sigma}<\frac{167.5-166}{0.5})[/tex]

=[tex]P(1<Z<3)[/tex]

=[tex]P(Z<3)-P(Z<1)[/tex]

[tex]=0.99865-0.84134[/tex]

[tex]=0.15731[/tex]

(b)

[tex]P(X>167)=P(Z>\frac{167-166}{0.5})[/tex]

[tex]=P(Z>2)[/tex]

[tex]=1-P(Z<2)[/tex]

[tex]=1-0.97725[/tex]

[tex]=0.02275[/tex]

Answer:

you mean the mean not the meaning right?

The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.

Answer:

10 pounds of potatoes would cost $15.

Step-by-step explanation:

Set up proportion.

4/6=10/x

simplify 4/6 into 2/3,

2/3=10/x

cross product,

2*x=3*10

2x=30

x=30/2

x=15

lemme just add some to the great reply above,

[tex]\begin{array}{ccll} lbs&\$\\ \cline{1-2} 4&6\\ 10&x \end{array}\implies \cfrac{4}{10}=\cfrac{6}{x}\implies 4x = 60\implies x = \cfrac{60}{4}\implies x = 15[/tex]

Answer:

7.5

Step-by-step explanation:

it is feometeic progression

r=0.5

Answer:

Option D is answer.

Step-by-step explanation:

Hey there!

Given;

f(x) = 10/9 X + 11

Let f(X) be "y".

y = (10/9) X + 11

Interchange "X" and "y".

x = (10/9) y + 11

or, 9x = 10y + 99

or, y = (9x-99)/10

Therefore, f'(X) = (9x-99)/10.

Hope it helps!

width = x

length = 3 + x

perimeter = x + x + ( 3 + x ) + (3+x)

18 = x + x + ( 3 + x ) + (3+x)

x + x + ( 3 + x ) + (3+x) = 18

6 + 4x = 18

4x = 12

x = 3

Answer:

A - $214.40

Step-by-step explanation:

Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:

4= b

and

3 = n

into the given equation to solve for C.

Using the order of operations we start inside our parentheses and work from there:

C= $25.60*4 + $14.00*4(3 - 1)

C= $25.60*4 + $14.00*4(2)

C= $102.40 + $112

C= $214.40

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Answer:

2ml

Step-by-step explanation:

50mg of some potent agent has to be given every 12 hours.

there is a solution that has a concentration of that agent of 125mg/5ml

we need to administer some part of this solution, which we cannot (or should not) change in its structure.

that means the ratio of agent to overall solution stays the same, no matter how much of the solution we administer.

all we need to do is to transit the ratio of 125/5 to represent 50/x (maintaining the said ratio).

in other words, we need to find how many ml we need to administer, so that 50mg of the agent enter the body.

so,

125/5 = 50/x

125x/5 = 50

25x = 50

x = 50/25 = 2

2ml of the solution needs to be administered every 12 hours.

Answer:

20

Step-by-step explanation:

4 + 2 + 5 + 4 + 0 + 1 + 1 + 3 = 20

Answer:

y - 1 =  -1/4(x+5)

Step-by-step explanation:

Answer:

300 + 15x = 500

15x = 200

x = 200/15

x=13.333

14 pair of shoes

Step-by-step explanation:

Answer:

L = 0.16 yd, W = 0.22 yd

Step-by-step explanation:

Dimensions of play ground 23/147 yd x 3/14 yd

reducing factor 2/147

Let the original length is L.

[tex]L - \frac{2L}{147} = \frac{23}{147}\\\\L\frac{143}{147} = \frac{23}{147}\\\\L=\frac{23}{143} yd[/tex]

L = 0.16 yd

Let the width is W.

[tex]W - \frac{2W}{147} = \frac{3}{14}\\\\W\frac{143}{147} = \frac{3}{14}\\\\W=0.22 yd[/tex]

Answer:

262.5 miles

Step-by-step explanation:

Correct me if I am wrong

Answer:

C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]

D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]

Step-by-step explanation:

We are given that

n=18

Mean, [tex]\mu=6.75[/tex]

Standard deviation, [tex]\sigma=2.28[/tex]

c.

[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]

[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]

[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]

Using the formula

[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]

[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]

[tex]P(7.0039<x<7.8026)=0.1334[/tex]

D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]

Answer:

B. 7

Step-by-step explanation:

Recall: according to thee Mid-segment Theorem of a triangle, the Mid-segment of a triangle is half the length of the base of the triangle

Base length of the traingle, RQ = 14 (given)

Mid-segment = TS

Therefore,

TS = ½(RQ)

Plug in the value

TS = ½(14)

TS = 7

Answer:

51 ?

Step-by-step explanation:

90-39= 51. I hope its correct

Answer:

51 degrees

Step-by-step explanation:

Well if you look at the picture angle b and the 39 degrees angle together must make a 90 degree angle

90-39 is  51 so therefor angle b must be 51 degrees

Answer:

17

Step-by-step explanation:

Given the regression model :

Y=ax+b

x = Hours of TV watched per day

y= number of sit-ups a person can do

A=-1.341

B=32.234

Y = - 1.341x + 32.234

Predict Y, when x = 11

Y = - 1.341(11) + 32.234

Y = −14.751 + 32.234

Y = 17.483

Hence, the person Cann do approximately 17 sit-ups

Answer:

The sum is 2275

Step-by-step explanation:

Given

[tex]75,76,77....99,100[/tex]

Required

The sum

Using arithmetic progression, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where:

[tex]T_1 = 75[/tex] --- first term

[tex]T_n = 100[/tex] --- last term

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 100 - 75 + 1 = 26[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]

[tex]S_n = 13*175[/tex]

[tex]S_n = 2275[/tex]

Answer:

25 ; 35

Step-by-step explanation:

Given :

____________For __ Against __ No Opinion

21-40 years _________20 _______5

41-60 years ___20 ______________20

Over 60 years _55____ 15________ 5

Given that :

40% of 21-40 are against

Then :

40% = 20

To a obtain 100% of 21 - 40

40% = 20

100% = x

Cross multiply

0.4x = 20

x = 20/0.4

x = 50

100% of 21 - 40 = 50 people

For = 50 - (20 + 5)

= 50 - 25

= 25

2.)

Total who have no opinion :

(5 + 20 + 5) = 30

30 = 15%

Total number surveyed will be , x :

30 = 15%

x = 100%

Cross multiply :

0.15x = 30

x = 30/0.15

x = 200

Number of 41 - 60 against an increase, y:

(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200

165 + y = 200

y = 200 - 165

y = 35

Answer:

x = -2; y = 1

Step-by-step explanation:

See picture below.

We are told matrices B is the inverse of matrix A.

The product of a matrix and its inverse is the identity matrix.

Answer:

The expected value is of 5 green balls.

Step-by-step explanation:

For each experiment, there are only two possible outcomes. Either it is a green ball, or it is not. Since there is replacement, the probability of a green ball being taken in an experiment is independent of any other experiments, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

20 experiments

This means that [tex]n = 20[/tex]

There is equal probability of selecting the red, black, green, or blue ball.

This means that 1 in 4 are green, so [tex]p = \frac{1}{4} = 0.25[/tex]

What is the expected value of getting a green ball out of 20 experiments with replacement?

[tex]E(X) = np = 20*0.25 = 5[/tex]

The expected value is of 5 green balls.

The expected value of getting a green ball out of 20 experiments with replacement is 5.

The binomial probability distribution of the number of successes in a sequence of n independent experiments is the binomial distribution with parameters n and p.

As it is given that the probability of all the balls coming out of the bag is equal. Therefore, the probability of a green ball coming can be written as,

[tex]\text{Probability of Green Ball} = 0.25[/tex]

Also, we can write the probability of not getting a green ball can also be written as,

[tex]\rm Probability(\text{Not coming Green Ball}) = P(Red\ ball)+P(Black\ ball)+P(Blue\ ball)[/tex]

                                                         [tex]=0.25+0.25+0.25\\\\=0.75[/tex]

Now, as there are only two outcomes possible, therefore, the distribution of the probability is a binomial distribution. And we know that the expected value of a binomial distribution is given as,

[tex]\rm Expected\ Value, E(x) = np[/tex]

where n is the number of trials while p represents the probability.

Now, substituting the values, we will get the expected value,

[tex]\rm Expected\ Value, E(Green\ ball) = 20 \times 0.25 = 5[/tex]

Hence, the expected value of getting a green ball out of 20 experiments with replacement is 5.

Learn more about Binomial Distribution:

https://brainly.com/question/12734585

Step-by-step explanation:

f(x) = 3 - 4x

f(1+a)= 3-4(1+a)

=3-4+4a

=4a-1

Answer:

Discount amount = $328.73

Step-by-step explanation:

Below is the calculation for the discount amount:

The marked price of bicycle = 2000

Purchase price = Rs 1921

VAT = 13%

First find the purchase price excluding VAT = 1921  - (13% of 1921) = 1671.27

Discount amount = 2000 - 1671.27

Discount amount = $328.73

Step-by-step explanation:

ok for a. the both are 126

and for b. the both are 30

for c. i believe its true

Answer: 9

Step-by-step explanation:

[tex]\frac{1}{4} (c^{3}+d^{2})[/tex]

Substitute in the values into the expression:

[tex]\frac{1}{4} ((-4)^{3}+10^{2})\\\\=\frac{1}{4}(-64+100)\\\\=\frac{1}{4}(36)\\\\=\frac{36}{4} =9[/tex]