What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.

The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:

1) Translation (x, y) → (x + 8, y + 2)

2) Reflection across the x-axis (x, y) → (x, -y)

So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.

The transformation rules are:

The pentagons in the graph have vertices as

For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)

For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)

Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".

Applying the Translation rule for the pentagon ABCDE:

The rule is (x, y) → (x + a, y + b)

So, the variation is

-4 + a = 4

⇒ a = 4 + 4 = 8

5 + b = 7

⇒ b = 7 - 5 = 2

So, the pentagon ABCDE is translated by (x + 8, y + 2).

Applying the Reflection rule for the translated pentagon:

The translated pentagon has vertices (x + 8, y + 2).

When applying the reflection across the x-axis,

(x + 8, y + 2) → {(x + 8), -(y + 2)}

Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}

Verification:

A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"

B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"

C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"

D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"

E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"

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The best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):

A class can be defined as a user-defined blueprint (prototype) or template that is typically used by software programmers to create objects and define the data types, categories, and methods that should be associated with these objects.

In object-oriented programming (OOP) language, a class that is written or created to implement an interface in a software would most likely implement all of that interface's method declarations without any coding error.

In this scenario, the best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):

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Complete Question:

A car dealership needs a program to store information about the cars for sale. For each car, they want to keep track of the following information: number of doors (2 or 4), whether the car has air conditioning, and its average number of miles per gallon. Which of the following is the best design?

(A) Use four unrelated classes: Car, Doors, AirConditioning, and MilesPerGallon.

(B) Use a class Car with three subclasses: Doors, AirConditioning, and MilesPerGallon.

(C) Use a class Car, with fields: numDoors, hasAir, and milesPerGallon.

(D) Use a class Car, with subclasses of Doors, AirConditioning, and MilesPerGallon.

(E) Use classes: Doors, AirConditioning, and MilesPerGallon, each with a subclass Car.

Answer:no but maybe

Step-by-step explanation:if you distribute the 3 and multiply the 3 with box the 2 and 1 you would get 6x+3 which is not equal to 5x+4 but if you take one from the 6 and add it to the 3 it would be even so i dont know but maybe

Option 2) the first set of data has values that are closer to the mean because the standard deviation is lower is correct

If two samples have the same mean, then it means that the two values in the two samples are centered around the same value. However, this does not mean that the data values in the samples vary equally around this center and thus the standard deviations may also differ.

It depends what the standard deviations are. The standard deviation is a measure of how close the results are to the mean, a low standard deviation means that the measurements are accurate, so close to the mean. A high standard deviation means that the measurements are more spread out.

We need to find that if two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets

The first set of data has values that are closer to the mean because the standard deviation is lower because in first set standard deviation is 1.4 and in second set standard deviation is 5.7

The one with smaller standard deviation are least spead from the mean

Hence the first set of data has values that are closer to the mean because the standard deviation is lower.

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Answer:

7/13

Step-by-step explanation:

in all there are 13 balls and the number of balls that aren't white are 7

Answer:

7/13

Step-by-step explanation:

To find the probability that it is not white

P( not white) = number of balls that are not white / total balls

The balls that are not white are red and green = 4+3

                      = (4+3)/ ( 4+6+3)

                       = 7/13

An example of a rational expression is 2x+3/x-2.

The complete question wasn't found. Therefore, a overview will be given. It should be noted that a rational expression simply means quotient of two polynomials.

A rational expression is a fraction whose numerator and denominator are polynomials.

In this case, an example of a rational expression is 2x+3/x-2

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The 95% confidence interval based on the same data is 5.15 < μ < 6.05

Because it has a longer interval, the 95 percent confidence interval offers more details.

The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.

Confidence intervals quantify how certain or uncertain a sampling technique is.

Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.

The 90% confidence interval is given by:

Mean - 1.645(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.645(S.D./[tex]\sqrt{n}[/tex])

2μ = 5.22 + 5.98 = 11.2

μ = 11.2 / 2 = 5.6

Thus,

5.6 - 5.22 = 1.645(S.D./[tex]\sqrt{n}[/tex]) = 0.38

S.D./[tex]\sqrt{n}[/tex] = 0.38 / 1.645 = 0.231

The 95% confidence interval is given by:

Mean - 1.96(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.96(S.D./[tex]\sqrt{n}[/tex])

=5.6 - 1.96(0.231) < μ < 5.6 + 1.96(0.231)

= 5.6 - 0.4528 < μ < 5.6 + 0.4528

= 5.15 < μ < 6.05

The 95% confidence interval provides more information because it has a larger interval.

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Answer:

1083 seats

Step-by-step explanation:

i just answered that.

arithmetic sequence

a1 = 10

an = an-1 + 1 = a1 + (n-1)×1 = 10 + (n-1) = 9 + n

a38 = 9 + 38 = 47 seats

the sum of such an arithmetic sequence

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

Answer:

One dollar

Step-by-step explanation:

So you divide 8.70 by 87 to get 0.10. So then you multiply 0.10 by 10 to get a dollar

Sending 87 text messages cost $8.70. Sending 10 text messages would cost $1.00.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that,

Cost to send 87 text messages: $8.70

Number of text messages: 87

To find out how much it would cost to send 10 text messages,

Use a proportion.

If it cost Jose $8.70 to send 87 text messages,

Set up the proportion:

$8.70 / 87 messages = x / 10 messages

To solve for x,

Cross-multiply and divide:

($8.70 x 10) / 87 = $1.00

Therefore, it would cost $1.00 to send 10 text messages.

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ANSWER - The first seems more accurate according to my view it's A

The sequence for the cost of bracelet in dollars = $0, $3, $6, $9 and $12.

Also the sequence for the cost of necklace is = $0, $6, $12, $18, $24.

The column given concerning the products contains the following amounts of products such as 0, 1, 2, 3, and 4 pieces.

Therefore to calculate the amount to be used to buy each product of bracelet and necklace in each column multiplication is carried out.

That is, 0×3, 1 ×3, 2×3, 3×3, and 4×3

which is = $0, $3, $6, $9 and $12 respectively for the bracelet.

0×6, 1 ×6, 2×6, 3×6, and 4×6

Which is = $0, $6, $12, $18, $24. respectively for the necklace.

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Answer:

The sum of all 2 digit multiples of 6 is 810

Step-by-step explanation:

12+18+24+30+36+42+48+54+60+66+72+78+84+90+96 = 810

Answer:

810

Step-by-step explanation:

2 digit multiples of 6 are 12,18,24...90,96

You can just add them on your calculator.

2000 feet can be represented as 20 blue whales in a row of each 100 feet.

What is a blue whale?

I feet = 30.48 centimeters

To explain what the length of 2000 feet looks like:

Take the example of a blue whale of 100 feet.

Now, imagine placing up 20 blue whales one behind the other.

20 × 100 feet = 2000 feet

Therefore, 2000 feet can be represented as 20 blue whales in a row of each 100 feet.

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Answer:

10 m

Step-by-step explanation:

If we draw the diagonal of the rectangle, we form a right triangle where the diagonal is the hypotenuse and the legs are 6 and 8.

This is a well-known Pythagorean triple, which gives the diagonal to be 10 m.

The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]

[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]

[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]

[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]

[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

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Answer:

He has 2 maple boards and 13 oak boards.

Step-by-step explanation:

Assuming all boards are oak : 6*15=90

Maple minus oak = 3

96-90=6 6/3=2 maple boards

Verification : 2*9+6*13 = 96

Answer:

13 oak, 2 maple

Step-by-step explanation:

o = oak

m = maple

o + m = 15

6o + 9m = 96

o + m = 15

o = 15 - m

6o + 9m = 96

6(15 - m) + 9m = 96

90 - 6m + 9m = 96

90 + 3m = 96

3m = 6

m = 2

o + 2 = 15

o = 13

6(13) + 9(2) = 96 (Yes, correct!)

Brainliest, please :)

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a quadratic equation is:

y = ax² + bx + c

The graph of a quadratic equation is a parabola.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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The company earned 68 billion dollars from 2008 to 2018.

According to the statement

we have given that the company's particular sales in expression are represented by (t² + 10t + 68)

And we have to find the constant terms in this expression which represent the sale of the company.

So, The given expression is (t² + 10t + 68)

From above expression it is clear that the it is in the form of Quadratic Equations.

So, The Quadratic equation, is an equation containing a single variable of degree 2. Its general form is ax^2 + bx + c = 0, where x is the variable and a, b,c are the known numbers and C is the Constant.

The general representation of Quadratic equation is

ax^2 + bx + c = 0  -(1)

and the given expression are

(t² + 10t + 68)  -(2)

After comparing both equations

Here C =68 = Constant.

So, 68 is the Constant term of the expression represent in terms of the context.

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Disclaimer: The question was incomplete. Please find the full content below.

Question:

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

The company earned 68 billion dollars from 2008 to 2018.

The company earned 68 billion dollars in 2008.

The company earned 10 billion dollars from 2008 to 2018.

The company earned 10 billion dollars in 2008.

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Answer: D. the y-intercept is (0,1)

Step-by-step explanation:

For all exponential functions without a vertical shift, the y-intercept is (0,1).

The area of the shape is 84.78 square units

The formula for calculating the area of a circle is expressed as:

A = πr²

where

r is the radius of a circle

Given the following

r = 6 units

pi = 3.14

Substitute

A = 3.14 * 6²

A = 113.04 square units

If the figure is 3/4 of a circle, the area of the shape will be:

A = 3/4 * 113.04

A = 84.78 square units

Hence the area of the shape is 84.78 square units

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Third option Base angles theorem is the correct answer as it contains the information that statement 4 is missing.

About The Base Angle Theorem

The two base angles in an isosceles triangle that are opposite the congruent sides must be identical in measure or congruent, according to the base angle theorem.

As a result, JKL and MLK are the base angles of the recognized isosceles triangle. Thus, the two angles, ∠JKL and ∠MLK are congruent or equal to each other by the means of the base angles theorem, and third option -   base angles theorem - the missing justification for statement 4.

About the other options

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Answer: option c

Step-by-step explanation:

Answer: this is the solutions

Answer:

I think it's (B) and (D)

Step-by-step explanation:

As to what I have studied

The correct property of the quadratic parent function is given by:

B. Its vertex is at the origin.

The quadratic parent function is modeled by:

y = x².

It has the vertex at the origin and increases to the left and to the right, into quadrants I and II, forming a function that is graphed by a parabola.

Hence the correct option regarding a property of the quadratic parent function is given by:

B. Its vertex is at the origin.

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Richard Travel 40 feet on the zip line in 1 sec

The diagram is missing and hence the diagram.is shown below

Distance is the total movement of an object without any regard to direction.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis

According to given Diagram

120 - 80 = 40 feet

On the Zip line

80-40=40

So the richard travels 40 feet on the zip line in 1 sec

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Answer:

a=5

b=6

c=3

d=4

surface area: 105.24

Answer:

Area of the right triangular prism = 84 cm²

Step-by-step explanation:

A  is the width of the right side rectangle = 4 cm

B is the length of the rectangle =  6 cm

C is the base of the triangle = 3 cm

D is width of the middle rectangle =  5 cm

b) Area of rectangle = length *width

 [tex]\sf Area \ of \ triangle = \dfrac{1}{2}*base *height\\\\Area of 2 triangles = 2 *\dfrac{1}{2}*base * height = base * height[/tex]

Surface area of the right triangular prism =   area of 2 triangle + area of left rectangle + area of middle rectangle + area of right rectangle

              =  3 * 4  + 3*6 + 5 * 6 + 4 *6

              = 12 + 18 + 30 + 24

              = 84 cm²

The correct option is C. find the real range, find the interval width, and construct the frequency distribution.

To make the information easier to understand, frequency distributions are textured look which organise and present frequency counts. Absolute frequencies as well as frequency distributions, such as percentages or ratios, can be displayed in frequency distributions.

The real range is find by the following method-

The interval width is find by the following method-

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The correct question is-

The three steps for constructing a simple frequency distribution are -

Group of answer choices

A. find the observed range, find the interval width, and construct the frequency distribution

B. find the real range, count the scores, and construct the frequency distribution

C. find the real range, find the interval width, and construct the frequency distribution

D. all of the above

Answer:

2 hours

Step-by-step explanation:

4 square yards to feet: 4*3 = 12ft

3 cows grazing grass at 2 ft per hour: 2*2 = 6 square ft per hour

Time taken: 12ft/6ft per hour = 2 hours

Generally, the equation of a circle is organized like this: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.

We're given the endpoints of the diameter: [tex](-6,-3)[/tex] and [tex](-6,-8)[/tex].

First, we can find the centre of the circle by finding the midpoint of these two endpoints.

[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

Plug in the points:

[tex]midpoint=(\dfrac{-6+-6}{2},\dfrac{-3+-8}{2})\\\\midpoint=(-6,\dfrac{-11}{2})[/tex]

Therefore, the centre of the circle is [tex](-6,\dfrac{-11}{2})[/tex]. Plug this into the general equation:

[tex](x-h)^2+(y-k)^2=r^2\\\\(x-(-6))^2+(y-(-\dfrac{11}{2}))^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=r^2[/tex]

To find the radius of the circle, we can calculate the distance between the centre and one of the given endpoints:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Plug in the centre and one of the endpoints:

[tex]d=\sqrt{(-6-x_1)^2+(\dfrac{-11}{2}-y_1)^2}\\d=\sqrt{(-6-(-6))^2+(\dfrac{-11}{2}-(-3))^2}\\d=\sqrt{(-6+6)^2+(\dfrac{-11}{2}+3)^2}\\\\d=\sqrt{(0)^2+(-5.5+3)^2}\\\\d=\sqrt{(0)^2+(-2.5)^2}\\\\d=\sqrt{(0)^2+(-\dfrac{5}{2})^2}\\\\d=\sqrt{0+\dfrac{25}{4}}\\d=\sqrt{\dfrac{25}{4}}\\\\d=\dfrac{5}{2}[/tex]

Therefore, the radius of the circle is [tex]\dfrac{5}{2}[/tex]. Plug this into the general equation:

[tex](x+6)^2+(y+\dfrac{11}{2})^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=(\dfrac{5}{2})^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

[tex](x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

Answer:

False

Step-by-step explanation:

Prisms can have more than one base.