pleaseeee help!!!!!!

From Vieta's formulas, we have

[tex]3x^2 - 4x + 1 = 3 (x - \alpha) (x - \beta) \\\\ ~~~~~~~~~~~~~~~~~ = 3x^2 - 3 (\alpha + \beta) + 3\alpha\beta \\\\ \implies \begin{cases} \boxed{\alpha + \beta = \frac43} \\\\ \boxed{\alpha\beta = \frac13} \end{cases}[/tex]

a) Note that

[tex](\alpha + \beta)^2 = \alpha^2 + 2\alpha\beta + \beta^2 \\\\ \implies \alpha^2 - \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta - 2\beta^2[/tex]

We have exact values for [tex]\alpha+\beta[/tex] and [tex]2\alpha\beta[/tex], but sadly not for [tex]-2\beta^2[/tex]. This means we'll need to solve for [tex]\beta[/tex] explicitly.

By factorizing, we have

[tex]3x^2 - 4x + 1 = (3x - 1) (x - 1) = 0 \\\\ \implies x = \dfrac13 \text{ or } x = 1[/tex]

Then the value of [tex]\alpha^2-\beta^2[/tex] depends on which is chosen to be the larger root, and

[tex]\alpha^2 - \beta^2 = \dfrac1{3^2} - 1^2 = \boxed{-\dfrac89} \text{ or } \alpha^2 - \beta^2 = 1^2 - \dfrac1{3^2} = \boxed{\dfrac89}[/tex]

While we're at it, we can also immediately find

[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = \left(\dfrac43\right)^2 - 2\cdot\dfrac13 = \dfrac{10}9[/tex]

b) Combine fractions to get

[tex]\dfrac2{\alpha^2} + \dfrac2{\beta^2} = \dfrac{2\beta^2 + 2\alpha^2}{\alpha^2\beta^2} \\\\ ~~~~~~~~~~~~~ = 2 \cdot \dfrac{\alpha^2 + \beta^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = 2\cdot \dfrac{\frac{10}9}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{20}[/tex]

c) Combine fractions again.

[tex]\dfrac2{\alpha^2} - \dfrac2{\beta^2} = 2 \cdot \dfrac{\beta^2 - \alpha^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = -2\cdot \dfrac{\pm\frac89}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{\pm16}[/tex]

Answer:

From the way the problem is worded:

CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.

EDH is outside CDE and is of measure 6x + 15.

Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.

Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.

The rate of decrease in the revenue reduces each year, resulting in an

approximate quadratic equation model that is concave upwards.

The variables are;

x = Number of years since 2,000

y = Revenue for  physically recorded music in millions of dollars

Find out -

To model the decline using a quadratic equation.

The general form of the quadratic equation is; y = a·x² + b·x + c

When y = 5547, x = 8

We get;

5547 = a·8² + b·8 + c = 64·a + 8·b + c

5547 = 64·a + 8·b + c...(1)

When y = 3113, x = 11

We get;

3113 = a·11² + b·11 + c = 121·a + 11·b + c

3113 = 121·a + 11·b + c...(2)

When y = 2056, x = 14

We get;

2056 = a·14² + b·14 + c = 196·a + 14·b + c

2056 = 196·a + 14·b + c...(3)

Subtracting equation (2) from equation (1) gives;

5547 - 3113 = 64·a + 8·b + c - (121·a + 11·b + c) = -57·a - 3·b

2434 =  -57·a - 3·b...(4)

Subtracting equation (3) from equation (2) gives;

3113 - 2056 = 121·a + 11·b + c - (196·a + 14·b + c) = -75·a - 3·b

1057 = -75·a - 3·b...(5)

Subtracting equation (5) from equation (4) gives;

2434 - 1057 = -57·a - 3·b - (-75·a - 3·b) = 18·a

1377 = 18·a

a = 76.5

From, equation (4), 2434 =  -57·a - 3·b, we have;

2434 =  -57 × 76.5  - 3·b

Therefore;

b = -2264.8

From equation (1), we get;

5547 = 64 × 76.5 + 8×(-2264.8) + c

Therefore;

c = 5547 - (64 × 76.5 + 8×(-2264.8)) = 18769.

c = 18769.

Therefore, the quadratic model is;

Verifying, we have in year 2012, x = 12

y = 76.5×12² - 2264.8×12 + 18769. = 2607.74

Thus ,the completed table and comparison of the predicted physical revenue and actual values is presented in the attachment;

To learn more about quadratic equation

Visit - https://brainly.com/question/1214333

#SPJ1

In 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.

So,

Let us first calculate the slope of the linear function:

The required linear function can be written as:

When we simplify this, we get:

To calculate per capita consumption in 1995, enter t=15 into this function.

Therefore, in 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.

Know more about per capita consumption here:

https://brainly.com/question/23801178

#SPJ4

The correct question is given below:

For 1983 through 1989, the per capita consumption of chicken in the u.S. Increased at a rate that was approximately linear. In 1983, the per capita consumption was 39.7 pounds, and in 1989 it was 47 pounds. Write a linear model for per capita consumption of chicken in the u.S. Let t represent time in years, where t = 3 represents 1983. Let y represent chicken consumption in pounds. What would you expect the per capita consumption of chicken to be in 1995? What would you expect the per capita consumption of chicken to be in 1995?

Answer:

x - 5 = 65

Step-by-step explanation:

3 is not a character of that set. answer is False

Hey there!

4a + 1 + a + 3

= 4a + 1 + 1a + 3

COMBINE the LIKE TERMS:

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

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

= 4a + a + 1 + 3

= 5a + 4

Therefore, your answer should be:

5a + 4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The equation to express the relationship will be y = 5.05 + 2.45x.

Worth of the card = $5.06

It should be noted that the card increases by $2.45.

Therefore, the equation to express the relationship will be:

y = 5.06 + (2.45 × x)

where x = number of years.

y = value of the card.

y = 5.05 + 2.45x

In conclusion, the equation to express the relationship will be y = 5.05 + 2.45x.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

Your answer will be 11.04

Step-by-step explanation:

1.38 × 8= 11.04

Answer:

8, 18

Step-by-step explanation:

The absolute value is the distance of the point from 0. In this question, it would be the number itself.

Answer:

The answer would be 8 and 18

Step-by-step explanation:

To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations. Solve | x | + 2 = 5. Isolate the absolute value.

Answer:

Correct answer is D.

Step-by-step explanation:

A. 6 = 3-3 ×

B. 1 = -4-3 ×

C. 2 = 1-3 ×

D. 0 = 3-3 ✓

Answer:

Option C.

Step-by-step explanation:

For a table to be linear, the table must have a constant and even rate of change, meaning as X, the input, increases by 1, Y, the output, increases evenly by a random number we're gonna name "a". Now, a, in this case, is -8. The numbers increase evenly by -8(a), which would classify that function as linear. Thus, option C. is the correct answer.

Answer:

Your answer is C.125,000

Step-by-step explanation:

Answer:

5 feet

Step-by-step explanation:

We are told that the height of the dome can be modelled by the equation:

[tex]\boxed{h = -2d^2 + 100}[/tex]

The question is essentially asking us: for what value of d will the value of h be 50 feet?

To solve this, we have to substitute h in the equation with 50 and then solve for d.

∴ [tex]50 = -2d^2 + 100[/tex]

⇒ [tex]50 + 2d^2 + 100[/tex]

⇒ [tex]2d^2 = 100 - 50[/tex]

⇒ [tex]d^2 = \frac{100 - 50}{2}[/tex]

⇒ [tex]d^2 = 25[/tex]

⇒ [tex]d = \sqrt{25}[/tex]

⇒ [tex]d = \bf 5[/tex]

This means that 5 feet from the center of the dome, the height of the dome is 50 feet.

9/2  I think

I hope that helped!

Answer:

13.125 or 105/8 or 13 1/8

Step-by-step explanation:

The error in the closure is equal to the difference in the actual value of evaluation and the measured value of evaluation of the same point which is equal to 0.02 units.

There is a discrepancy between the existing coordinates and the computed coordinates. The amount by which a quantity obtained by a series of related measurements differs from the true or fixed value of the same quantity sometimes known as a closure mistake. The difference between the real value of a series of angles and its exact value in theory. likewise known as an angular mistake of closure. The degree to which two azimuth readings for a line that were obtained through distinct surveys or along different routes do not perfectly match one another. is also known as an azimuth closure error.

To learn more about error of closure, Visit:

https://brainly.com/question/20561582

#SPJ4

Answer:17.67

Step-by-step explanation:

Answer:

infinite solution

Step-by-step explanation:

because thats the right answers

The ratio of cell A's length to cell B's length is  [tex]2\times10^{15} :1[/tex]

It is given that length of cell A is [tex]2\times10^7m[/tex] which is in scientific notation and length of cell B is 0.00000001 m which is in standard form.

On converting length of B in scientific notation , we get

[tex]0.00000001 =1.0\times10^{-8}m[/tex]

The ratio of length A to length B is given by

[tex]\frac{2\times10^7}{1.0\times10^{-8}} =\frac{2\times10^{15}}{1}[/tex]

which can be written as [tex]2\times10^{15} :1[/tex]

Yes, finding ratios is easier when numbers are represented in scientific notation. This is because scientific notation is a mathematical methodology used to describe very large or very small numbers in a compact and simple form, raised to powers of ten.

Hence , it is easier to calculate or solve mathematical operations using numbers in scientific notation.

Learn more about scientific notation here :

https://brainly.com/question/2786224

#SPJ9

As the sample size increases, the margin of error a. decreases

In a random survey sample, the margin of error is a statistical measure that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The number of distinct samples that are measured or observations that are used in a survey or experiment is known as the sample size. For instance, your sample size is 100 if you examine 100 samples of soil for signs of acid rain. If 30,500 completed questionnaires from an online survey were returned, your sample size is 30,500.

Hence, as the sample size increases, the margin of error decreases.

Learn more about sample on:

https://brainly.com/question/25574075

#SPJ4

the price of the Shredmaster 5000 will be $ 959.2 and the function is g (x) = 0.8 x for x > 1000.

If the purchase is made for $ 1000 and above. the discount = 20 %

Now the cost of Shredmaster 5000 = $ 1199

Now, the price after the discount will be

Price = 1199 - 20 % of 1199

Price = 1199 - 20 / 100 × 1199

Price = 1199 - 0.20 × 1199
Price = 1199 - 239.8

Price = $ 959.2

The function will be:

g (x) = x - 0.2 x

g (x) = 0.8 x for x > 1000.

Therefore, the price of the Shredmaster 5000 will be $ 959.2 and the function is g (x) = 0.8 x for x > 1000.

Learn more about function here:

https://brainly.com/question/25638609

#SPJ9

The most specific name for the figure in the image is a  Rectangle. Option B

This is further explained below.

Generally, According to the principles of Euclidean geometry, a Rectangle is considered to be a regular quadrilateral since it has four sides of equal length amongst opp two sides

Another way to describe it is as a rectangle with two neighboring sides that have the same length.

The term coordinate is pronounced exactly the same as o-ordinate. When used as an adjective, these phrases might signify to have the same status or rank, to have something to do with coordination, or to have something to do with an intersection of indices.

In conclusion, A Rectangle is the most accurate description of the shape that can be seen in the picture. Alternative B

Read more about square

https://brainly.com/question/14198272

#SPJ1

The temperature required on Thursday at 5:00 a.m. was observed as -7°F

given,

The temperature on Wednesday at 5:00 p.m. = 15°F

the temperature dropped 22°F in the following 12hours

The temperature on Thursday at 5:00 p.m. was 27°F.

the temperature on Thursday at 5:00 a.m. is calculated with a vertical number line.

number line - A number line is defined as the number marked on the line calibrated into an equal number of units.

For example -1, 0, 1, and so on.

Thus, the temperature on Thursday at 5:00 a.m. is

=15° - 22°

= -7°

The temperature required on Thursday at 5:00 a.m. was observed as -7°F

To know more about temperature

https://brainly.com/question/13459685

#SPJ1

If M is the midpoint of AB , B(-7,16) and M(-2,8)  then coordinates of the missing endpoint A are (3,0).

As given in the question,

M is the midpoint of AB

Let coordinates of A(x₁ ,y₁) , B(x₂ ,y₂) and M(x ,y)

So,

x = (x₁ + x₂)/2

⇒-2 = (x₁ + (-7))/2

⇒ x₁ = 7-4

⇒x₁ =3

y = (y₁+ y₂)/2

⇒8 = (y₁ +16)/2

⇒ y₁ = 16-16

⇒ y₁ =0

Therefore, if M is the midpoint of AB , B(-7,16) and M(-2,8)  then coordinates of the missing endpoint A are (3,0).

Learn more about midpoint here

brainly.com/question/28224145

#SPJ1

Answer:

586 students can attend the school dance if we have $1,672 to spend on the dance.

Step-by-step explanation:

1672  = 2p + 500  Subtract 500 from both sides of the equation

1172  = 2p  Divide both sides of the equation by 2

586 = p

The correct option is C. One-third n²(n − 1) units³ = ⅓ n²(n-1) units³; volume of the pyramid.

A right pyramid is one that has the upper end straight just above centroid of a base. A regular pyramid is thus a subset of a right pyramid.

As, per the given question;

Edge Length = n units

Height of the pyramid = n - 1 units

The  formula for volume of a solid right pyramid is;

Volume = ⅓Ah

Where, A is the area of the base.

h is the height of the pyramid

Since, pyramid has the square base;

Calculate the area;

Area, A = edge × edge

A = n × n

A = n²

Put the value of area in volume;

Volume = ⅓Ah

Substitute n² at A and n - 1 at h.

Solve the expression;

Volume = ⅓ × n² × (n - 1)

Volume = ⅓n²(n-1).

Therefore, the volume of the solid right pyramid is calculated as V =  ⅓n²(n-1) units³.

To know more about the solid right pyramid, here

https://brainly.com/question/4151950

#SPJ9

The complete question is -

A solid right pyramid has a square base with an edge length of n units. The height of the pyramid is n minus 1 units.

Which expression represents the volume of the pyramid?

A. One-third n(n − 1) units³

B. One-third n²(n − 1)² units³

C. One-third n²(n − 1) units³

D. One-third n³(n − 1) units³

The amount of potassium you should consume daily is 510 miligrams if 15 percent of potassium you daily need.

Let the total amount of sources of nutrient you consumed daily be x miligrams.

According to the given question.

One-half cup of black beans provides 15 percent of the potassium.

Also, you get remaning nutrients from 2890 miligrams of other sources.

⇒ you get 85 percent of remaining nutrients from other sources.

So, we can say that

85 percent of x = 2890 miligrams

⇒ 85/100 × x = 2890 miligrams

⇒ x = (2890 × 100)/85

⇒ x = 3400

So, the total amount of source of nutrients is 3400.

Therefore,

The amount of potassium you should consume daily

= 15 percent of 3400

= (15/100) × 3400

= 15 × 34

= 510 miligrams

The amount of potassium you should consume daily is 510 miligrams if 15 percent of potassium you daily need.

Find out more information about percent here:

https://brainly.com/question/14699403

#SPJ4

The sumerian mathematical system was based on units of sixty, ten, and six and survives in what modern system time measurement.

Sumer (a region of Mesopotamia, present-day Iraq) is sometimes referred to as the Cradle of Civilization because it was the origin of writing, the wheel, agriculture, the arch, the plow, irrigation, and many other accomplishments.

We really know more about ancient Sumerian and Babylonian mathematics than we do about early Egyptian mathematics because the Sumerians invented the first known writing system, the pictographic cuneiform script, which uses wedge-shaped symbols engraved on baked clay tablets. In fact, we even have math and geometry problems that seem like school exercises.

The base number 60 was created by adding a "celestial" 6 and a "common" 10 in the Sumerian "sexagesimal" system.

To learn more about sumerian mathematical system from given link

https://brainly.com/question/5659298

#SPJ4

Answer:

3√5

Step-by-step explanation:

You use the Distance Formula to solve this.

d=√(x2-x1)^2 + (y2-y1)^2

Plug in your points.

d=√(3-0)^2 + (-2- -8)^2

Subtract and square.

d=√9 + 36

Add

d=√45

The square root of 45 is 6.70, so you would look for radicals.

3√5 is 45. <3