If 2+sqrt(3) is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root

Answer:

13

Step-by-step explanation:

[tex] \sqrt{ {(8 - 3)}^{2} + {( - 4 - 8)}^{2} } [/tex]

[tex] \sqrt{ {5}^{2} + {( - 12)}^{2} } [/tex]

[tex] \sqrt{25 + 144} = \sqrt{169} = 13[/tex]

Taking into account the definition of a system of linear equations, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values ​​of the unknowns must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know that:

So, the system of equations to be solved is

Equation 1: B + G + BL= 7000

Equation 2: 6B + 4G + 2BL= 26400

Equation 3: B= 1/3BL

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, replacing equation 3 in equation 1 and isolating the variable G, you get:

1/3BL + G + BL= 7000

4/3BL + G= 7000

G= 7000 - 4/3BL

Substituting this expression and equation 3 into equation 2 you get

6×1/3BL + 4×(7000 - 4/3BL) + 2BL= 26400

Solving:

2BL + 4×7000 - 4×4/3BL + 2 BL= 26400

2BL + 28000 - 16/3BL + 2 BL= 26400

2BL - 16/3BL + 2 BL= 26400 - 28000

-4/3BL= -1600

BL= (-1600)÷ (-4/3)

BL= 1200

Remembering that B= 1/3BL and G= 7000 - 4/3BL and replacing the value of BL you get:

B= 1/3BL= 1/3×1200 → B= 400

G= 7000 - 4/3BL= 7000 - 4/3×1200 → G= 5400

In summary, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.

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Answer:

She scored 12

therefor she did pass

Step-by-step explanation:

Answer:

  11,179,000 mi/min

Step-by-step explanation:

You want the given speed of light expressed in miles per minute.

To convert the speed from km/s to mi/min, we need to multiply by factors of s/min and mi/km.

  [tex]\dfrac{299792\text{ km}}{\text{s}}\times\dfrac{60\text{ s}}{\text{min}}\times\dfrac{1\text{ mi}}{1.609\text{ km}}=\dfrac{299792\cdot 60}{1.609}\,\dfrac{\text{mi}}{\text{min}}\\\\\approx\boxed{11,\!179,\!000\text{ mi/min}}[/tex]

Answer:

x = −2, 2

Step-by-step explanation:

[tex]f(x)=\frac{\left(x^{2}+3x+6\right)}{x^{2}-4}[/tex]

Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.

Vertical Asymptotes:

x=−2,2Horizontal Asymptotes:

y=1

No Oblique Asymptotes

Full Explanation

The line x=L is a vertical asymptote of the function [tex] y=\frac{x^{2} + 3 x + 6}{x^{2} - 4}[/tex] if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x=−2, check: [tex] \lim_{x \to -2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=-\infty [/tex]

Since the limit is infinite, then x=−2 is a vertical asymptote.

x=2, check: [tex]\lim_{x \to 2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=\infty[/tex]

Since the limit is infinite, then x=2 is a vertical asymptote.

Vertical asymptotes: x=−2; x=2

Based on the figure, the graph that shows the data on long distance calls on a 10-by-10 grid with appropriate scales is Graph C.

The data is to be shown on a 10-by-10 grid which means that the range of numbers on the x and y axis should be between 0 and 10.

The scales should also be appropriate which means that Time (hours) should represent the x axis and Cost (dollars) should be on the y axis.

Only Graph C has this which makes it the right one.

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The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph

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

Let x represent the speed of the fast plane and y represent the speed of the slow plane.

Their speeds differ by 90mph, hence:

x - y = 90      (1)

The planes meet after 3 hours, hence:

3x + 3y = 2670    (2)

From both equations:

x = 490, y = 400

The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph

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Answer ANSWER (x+3) 12

Step-by-step explanation:

The number of girls is 147 and the number of boys is 245 in the introductory geology course

Students enrolled in the introductory geology course = 392 students

The ratio of boys to girls in the course = 5:3

Let the number of girls in the course be x, then the number of boys will be 392-x

Formulating the equation we get:

Number of boys/Number of girls = Ratio of boys/Ratio of girls

= 392-x/x = 5/3

= (392-x)*3 = 5x

= 1176-3x = 5x

=1176 = 8x

x = 147

Hence, the number of girls is 147 and the number of boys is 245

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Answer:

5x = 8(x - 3)

5x = 8x - 24 → Expand the brackets

-3x = -24 → Collect like terms ,which simply means that you'll transfer 8x to the other side , which will make it -8x

x = 8 → Divide both sides by the coefficient of x (3) : minus cancels minus; then 24 ÷ 3 = 8.

The graph that best describes the equations y = x + 1  y = −x − 1 is: A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 and 0.

A graph is a pictorial representation of data used in several disciplines. Graphs makes it easier to understand how a particular data relates with the other.

There many types of graphs, the type used here is the that of a straight line. The graph would have to cut through based on the signs that it has in the equation. That is if it is negative or positive.

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The similarities between the expressions in all the three problems is that after opening brackets both of the expressions are the same.

Two expressions are similar if their values after solving are equal.

12. -3 and -(3)

Here, when we open the bracket for -(3), we obtain -3 which is the same as the first expression.

13. -1(7) and -(7)

Solving for the first expression, we get -1×7 = -7 and

-(7) = -7.

We can see that both expressions are similar.

14. -2(4) and -(2•4)

Solving -2(4), we get -2×4 = -8

And, -(2·4) = -(8) which is the same as -8

Hence, both expressions are similar.

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Answer:

Natural number are the numbers: 1, 2, 3... (The ... means the pattern continues.  These were the first numbers that you learned about when you were little.

The whole numbers at the number 0 to the list.  0,1,2,3,...

Integers are the whole numbers and their opposites.  Zero is not positive or negative.  ...,-3, -2 -1 , 0, 1, 2, 3,....  The list does not include numbers like 1/2 or .75

Rational numbers are numbers that can be written as an integer/ integer.  This would include numbers like 1/2 and .75 because you can write .75 as 75/100(an integer over and integer.

Step-by-step explanation:

Do not get frustrated.  They are just asking for definitions of different classes of numbers.

Answer:

x=− 3n/4

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

The value equals 26

9 × 4 = 36

36 - 10 = 26

Distance between EF is 20.09 units.

By considering the given information

E=  (-4,2)

F= (16,4)

Distance between EF =

[tex]\sqrt{(16+4)^{2}+(4-2)^{2} } \\=\sqrt{400+4} \\=\sqrt{404} \\=20.09[/tex]

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In coordinate geometry, the distance between two given points is calculated using the distance formula. The formula for calculating the separation between two points

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The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<2 - <1 = 30 degrees

Add the above equations

So, we have

2<2 = 210

Divide both sides by 2

<2 = 105

Substitute <2 = 105 in <2 - <1 = 30

So, we have

105 - <1 = 30

Evaluate

<1 = 85

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 85

<4 = 105

Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

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The equation that relates the total amount of gasoline in the tank is;

y = x + 4.

For the given question;

The amount of gasoline already present in tank is 4 gallons.

The number of gallons filled above the the previous gasoline is x.

Thus, now the total gasoline present in this tank is x + 4.

If y shows the total gasoline in tank;

Then,

y = x + 4.

Therefore, the total amount of gasoline present in tank is given by equation is; y = x + 4.

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[tex]{\huge\color{black}{\boxed{\fcolorbox{green}{red}{꧁ANSWER꧂}}}}[/tex]

Existence of an Inverse

There are two numbers that f takes to 4, f(2) = 4 and f(-2) = 4. If f had an inverse, then the fact that f(2) = 4 would imply that the inverse of f takes 4 back to 2. On the other hand, since f(-2) = 4, the inverse of f would have to take 4 to -2.

Answer:

2, 3

Step-by-step explanation:

The prime factorization of 6 is 2(3), so one possibility is 2 and 3.

Answer: True

Step-by-step explanation:

Option a: Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price

Given,

Braxton’s average monthly usage of lotion = 8 ounces

The amount of two different brands of lotion are given:

Brand A: 24 ounces for $3.30

Brand B: 40 ounces for $4.60

We have to find the monthly savings of Braxton if he purchases the brand that has the lowest price per ounce versus the highest price:

We have to calculate amount for one ounce for the two brands given:

Brand A:

24 ounces for $3.30

Amount for one ounce = 3.30/24

Amount for one ounce = $0.1375

Brand B:

40 ounces for $4.60

Amount for one ounce = 4.60/40

Amount for one ounce = $0.115

Now, we have to calculate the amount for 8 ounces.

Brand A:

8 x 0.1375 = 1.1

$1.1 for 8 ounces of Brand A lotion.

Brand B:

8 x 0.115 = 0.92

$0.92 for 8 ounces of Brand B lotion.

Now, we have to calculate the savings:

Brand A – Brand B

1.1 – 0.92 = 0.18

That is, Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price.

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Step-by-step explanation:

this is an exercise to take the logical definition of an operation and apply it.

we have first a triangle operation that simply stands for the sum of the 3 included values divided by 3.

in other words, FYI, it creates the mean value of 3 given numbers.

so, we need to calculate

mean value (7, 4, 4) + mean value (8, 2, 11).

(7 + 4 + 4)/3 + (8 + 2 + 11)/3 = 15/3 + 21/3 = 36/3 = 12

the second calculation is based on a table defining a new operation Delta :

2 Delta 2 = 20

2 Delta 5 = 5

2 Delta 3 = 5

5 Delta 2 = 3

5 Delta 5 = 10

5 Delta 3 = 23

3 Delta 2 = 3

3 Delta 5 = 2

3 Delta 3 = 50

so, now we need to use this to calculate

(5 Delta 2) Delta (2 Delta 3)

3 Delta 5

2

the result is 2.

Answer:

Solution

x= 2l  (2) 14+l

Step-by-step explanation:

Divide both sides

2l

2

2l

2

x

​

=

2l

2

14+l

​

The number of weeks whwn the Vasquez family both visit their grandmother and host the neighborhood party is 24 weeks.

The weeks will all three events occur is 48 weeks.

From the information, the Vasquez family visit their grandmother every three weeks and host a neighborhood party every eight weeks.

Therefore, this situation is just to find the least common factor of 3 and 8. This is 24

Therefore, the number of weeks whwn the Vasquez family both visit their grandmother and host the neighborhood party is 24 weeks.

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2304 times 3 goes into 6912 and gives the remainder as 0.

The numerator number in the given division number 6912 by 3 is known as a dividend, and the denominator number is known as a divisor. As a result, 6912 is the dividend number and 3 is the divisor number.

Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. Division is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.

Division is a basic arithmetic operation in which a larger number is divided into smaller groups with the same number of items. For example, how many total groups will be formed if 30 students must be divided into groups of 5 students for a sporting event? Such problems are easily solved by using the division operation. Here, we must divide 30 by 5. 30 5 = 6 will be the result. As a result, there will be six groups of five students each.

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The solution to the given equation round to the nearest tenth as required in the task content is; 0.7.

According to the task content, the solution to the equation given is to be determined round to the nearest tenth.

On this note, the equation can be solved as follows;

53/2 = 18/x

By cross-multiplication; we have;

53 × x = 2 × 18

53x = 36

x = 36/53

x = 0.679

However, when round to the nearest tenth, x = 0.7.

Ultimately, The solution to the given equation round to the nearest tenth as required in the task content is; 0.7.

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