Determine the image of A(1,-3) after the following composition of transformations:

Rotation 90 degrees about the origin
Translation: f(x,y)=(x+2,y)f(x,y)=(x+2,y)

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]

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.

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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.

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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

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.

12 lies between 9 and 16 so √12 lies between 3 and 4.

Perfect square-: Those whole numbers in which we can pair the factors are known as perfect square.

We can write the number 40 as 2 × 2 × 2 × 5. This is not a perfect square because we cannot pair the factors.

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.

We write 40−−√ to be the square root of 40, and can investigate between which two whole numbers it lies.

Consider the table of perfect squares below:

Whole number 1 2 3 4 5 6 7 8 9 10 11 12

Whole number squared 1 4 9 16 25 36 49 64 81 100 121 144

The number 40 lies between 36 and 49 hence 40−−√ lies between 6 and 7.

Similarly, 12 lies between 9 and 16 so √12 lies between 3 and 4.

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The simplification of the given algebraic expression is;

yz = (z + 1)/z(z - 1)

We are given y left parenthesis z right parenthesis which is expressed as; yz

Now, we are given the algebraic expression that yz equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction

z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction is expressed as; (z² - 1)/z(z - 1)²

Thus, our main expression is;

yz = (z² - 1)/z(z - 1)²

Factorizing the numerator and denominator gives;

yz = (z + 1)(z - 1)/z(z - 1)(z - 1)

(z - 1) is common to both numerator and denominator and as such, we now have;

yz = (z + 1)/z(z - 1)

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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;

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Answer:

Your answer will be 11.04

Step-by-step explanation:

1.38 × 8= 11.04

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.

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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 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.

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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

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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.

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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.

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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:

Correct answer is D.

Step-by-step explanation:

A. 6 = 3-3 ×

B. 1 = -4-3 ×

C. 2 = 1-3 ×

D. 0 = 3-3 ✓

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:)

Answer:

x - 5 = 65

Step-by-step explanation:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:

y = -0.4908x² + 5.8845x + 1.3572

For the number of students that are absent 10 days after the outbreak, we have:

y = -0.4908(10)² + 5.8845(10) + 1.3572

y = -0.4908(100) + 58.845 + 1.3572

y = -49.08 + 58.845 + 1.3572

Number of students, y = 11.12 ≈ 11 students.

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To empty the tank in the shape of prism completely, Colin has to wait 150 minutes for the water of the pond to at zero level.

What is the prism volume formula?

Given :

A pond in the shape of a prism.

Colin uses a pump to empty the pond. The level goes down by 20 cm in the first 30 minutes.

Solution :

We know that the volume of the prism is given by,

Volume = ( Base area ) × height

Base area = 1/2 ( 1.4 + 0.6 ) × 2    ⇒2 m²

Volume  = 2 × 1 = 2m³

Given that the level of pond goes down by 20 cm in the first 30 minutes. Therefore, the volume becomes,

Volume = 2 × 0.8 = 1.6m³

Now, the rate of emptying the tank is,

[tex]= \frac{2 - 16}{30} = \frac{1}{75}[/tex]  m³/min

time = volume / rate

        = [tex]\frac{2}{\frac{1}{75} }[/tex]  = 150

Therefore, Colin has to wait 150 minutes for the pond to completely empty

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Answer:

x = -1

Step-by-step explanation:

x² + 6x = -5

x² + 6x -( -5) = 0

x = (-x + 4)/2

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x = (-6 + 4)/2

x = (-6 - 4)/2

x = -1

Answer:17.67

Step-by-step explanation:

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).

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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.

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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.

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

Answer: Even functions

Symmetric about the yy-axis

When you plug -x−x into the function, it will simplify to be the same as the original function. This means that it doesn’t matter whether you plug in xx or -x−x, your output will be the same. So

f(-x)=f(x)f(−x)=f(x)

Below are graphs that are even and symmetric about the yy-axis.

even functions are symmetric about the y-axis

Odd functions

Symmetric about the origin

When you plug -x−x into the function, it will simplify to be negative of the original function, or the original function multiplied by -1−1. This means that when you plug -x−x into the function, you’ll get the same output as you do when you plug in xx, except it will be negative (or have the opposite sign as the original output). So

f(-x)=-f(x)f(−x)=−f(x)

Below are graphs that are odd and symmetric about the origin. Be sure to visually compare quadrants that are diagonal from each other (quadrants 1 and 3, and quadrants 2 and 4).

odd functions are symmetric about the origin

Neither even nor odd

Not symmetric about the yy-axis, and not symmetric about the origin

The function has no symmetry. It’s possible that a graph could be symmetric to the xx-axis, but then it wouldn’t pass the Vertical Line Test and therefore wouldn’t be a function.

functions that are neither even nor odd

hope this helps!!

Answer:

infinite solution

Step-by-step explanation:

because thats the right answers

Answer:

Your answer is C.125,000

Step-by-step explanation:

9/2  I think

I hope that helped!

Answer:

13.125 or 105/8 or 13 1/8

Step-by-step explanation: