several people are sitting evenly spaced around a circular table and the positions are labelled 1, 2 ,3 and so on .The people at positions 3 and 15 are directly opposite each other how many people are sitting at the table

Answer:

A. 4 root 3

Step-by-step explanation:

Answer:

a=-2π

b=-17/3

c=-sqrt18

Step-by-step explanation:

eyeball it.

-2π≈-6.28

-17/3 is less than -5 but more than -6, so it's between those 2

-sqrt 18 is between -sqrt 16 and -sqrt 25, so it's a little less than -4

All potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational rots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.

The rational root theorem suggests that for a polynomial function

f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.

In the question, we are asked to find the potential rational roots of

f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3.

Comparing the given polynomial function with the standard polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, we can say aₙ = 15, and a₀ = 3.

By rational root theorem, we know that all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.

Therefore, we can say that p = {factors of ±3} and q = {factors of ±15},

or, p = {±1, ±3}, q = {±1, ±3, ±5, ±15}.

Now, we can write all potential roots by calculating p/q.

p/q = {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}

Therefore, all potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational roots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.

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Answer:

(-1, -4)

Step-by-step explanation:

y = -x² - 2x - 5

y = -1(x² + 2x + 5)

y = -1(x² + 2x + 1 - 1 + 5)

y = -1(x² + 2x + 1) - 4

y = -(x + 1)² - 4

Answer:

Sweater: 392 [tex]\frac{6}{7}[/tex]

Hat: 78[tex]\frac{4}{7}[/tex]

Scarf: 83[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

Set the sweater = x

The hat = [tex]\frac{1}{5}[/tex] x

The scarf = [tex]\frac{1}{5}[/tex] x + 5

x + [tex]\frac{1}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x + 5 = 555

Combine like terms

1[tex]\frac{2}{5}[/tex] x + 5 = 555

Subtract 5 from both sides

1[tex]\frac{2}{5}[/tex] x = 550

Divide by 1[tex]\frac{2}{5}[/tex]

x = 392 [tex]\frac{6}{7}[/tex] This is how much wool was used for the sweater.

Divide by 5 to get the hat = 78 [tex]\frac{4}{7}[/tex]

Add 5 to that to get the scarf: 83[tex]\frac{4}{7}[/tex]

Congruent triangles are exact copies of each other. The correct options are 1, 2, 3, and 4.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes the length of line segment AB, and so on for others).

The following details about the two given congruent triangles TUV and WXY can be written,

[tex]\rm m\angle T = m\angle W \: or \: \: \angle T \cong \angle W\\\\\rm m\angle U = m\angle X\: or \: \: \angle U \cong \angle X \\\\\rm m\angle V = m\angle Y \: or \: \: \angle V \cong \angle Y \\\\\rm |TU| = |WX| \: \: or \: \: TU \cong WX\\\\\rm |VU| = |YX| \: \: or \: \: VU \cong VU\\\\\rm |TV| = |WY| \: \: or \: \: TV \cong TV[/tex]

Hence, the correct options are 1, 2, 3, and 4.

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Answer: A,,B, C, D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ray can be defined as a part of a line that has a fixed starting point but no end point.

The starting point is B and on its way to infinity, it passes through point A.

Correct sign is

[tex]\huge\boxed{\overrightarrow{BA}}[/tex]

The income elasticity for the household is -1.05.

Income elasticity measures how quantity demanded changes when there is a change in the income of a person / household

Income elasticity = percentage change in quantity demanded / percentage change in income

Income elasticity = -21% / 20 = -1.05

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Answer:b

Step-by-step explanation:

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:

[tex]x \to y[/tex]

[tex]f(x) \to x[/tex]

[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]

x · (y + 7) = - 2 · y + 2

x · y + 7 · x = - 2 · y + 2

2 · y + x · y = - 7 · x + 2

y · (2 + x) = - 7 · x + 2

[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

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The x-coordinates are -4 and 0.

Answer:

y = 38 + 12x

Step-by-step explanation:

38is fixed cost per month and since the charge is $12 per GB, the variable cost is 12x where x is the GB used

Answer:

50.007131355

Step-by-step explanation:

A calculator lol?

The value of x from the given diagram is -6

Line is defined as the distance between two points. Given the line RP with the following measures

RP = 17

RQ = x + 14

QP = x + 15

Using the expression

RP = RQ + QP

Substitute

17 = x + 14 + x + 15

17 = 2x + 29

Determine the value of x

2x = 17 - 29
2x= -12

x = -6

Hence the value of x from the given diagram is -6

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Answer:

10

Step-by-step explanation:

square root of 6^2 + 8^2

Answer:

nmj

e

w

w

w

w

w

w

w

w

w

wej i2v82v2ivw8q

Step-by-step explanation:

h2iwv282vw8wvq

The total length of the wire needed to make this shape is 162cm

The perimeter of a triangle is the sum of the external side of the triangle.

Given the following parameters

Length of one side of the outside shape = 24cm

The side length of the smaller triangle = 24/4 = 6cm

The perimeter of the smallest triangle  3(6) = 18cm

The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm

Total length of wire needed. = 3(24) + 3(18) + 36

Total length of wire needed = 72 + 54 + 36

Total length of wire needed = 162cm

Hence the total length of the wire needed to make this shape is 162cm

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Answer:

?

Step-by-step explanation:

because there is no picture or option

Answer:

The graph of the circle is not a function

The segment length is 14 (square root)2

Given that Triangle ABC is right angle triangle

The vertex marked is B where side AC is the hypotenuse

The side of AC is at Vertex B is 14

The dash segment from vertex B to point D on side AC

Angle BDA is marked right angle .

Angles A and C both marked 45 degrees.

As shown in diagram

Triangle ABC is drawn according to the statement where B is vertex

The side lengths are 14  

Now to find Another side length that is x

So , the equation formed is

x*cos45 = 14

x/√2 = 14

x = 14√2

Hence the length of the segment is 14√2

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Answer:

Step-by-step explanation:

The segment length is 14 (square root)2

Given that Triangle ABC is right angle triangle

The vertex marked is B where side AC is the hypotenuse

The side of AC is at Vertex B is 14

The dash segment from vertex B to point D on side AC

Angle BDA is marked right angle .

Angles A and C both marked 45 degrees.

As shown in diagram

Triangle ABC is drawn according to the statement where B is vertex

The side lengths are 14  

Now to find Another side length that is x

So , the equation formed is

x*cos45 = 14

x/√2 = 14

x = 14√2

Hence the length of the segment is 14√2

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The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.

Volume is the space occupied by a three dimensional object .

The concentration of solution required is 22% acid

The concentration of solution available is 10% and 30%

The total volume required is 15 liters

The formula for making a mixture is

Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)

22 = (10 * x + 30 *(15 -x))/( 15)

10 x + 450 - 30x =330

-20x = -120

x = 6

The volume of 10% solution will be 6 l

and 9 litre of the 30 % solution will be taken.

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Answer:

  [c] The value of w cannot be a negative number.

  [d] Substitution is used to replace the variable l with a value of 20.

  [e] The subtraction property of equality is used to isolate the term with the variable w.

Step-by-step explanation:

     To figure out which steps of the solution are true, let us solve.

2 l plus 2 w equals 62 -> 2l + 2w = 62

----

2l + 2w = 62

2(20) + 2w = 62  <- Substitution is used to replace the variable l with a value of 20.

40 + 2w = 62

2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.

w = 11

     This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.

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Answer:

the angles of a triangle always equal 180 so

34+x-5+4y=180

simplify

29+x+4y=180

-29

x+4y=151

-4y

x=-4y+151

then put this into the original equation

29-4y+151+4y=180

simplify

29+151=180

so this proves that this works

-1/4x-151=y

Hope This Helps!!!

Answer:

1m=100cm

1m squared=100cm×100cm

1msquared= 10000cm squared

She has to multiply 10000 to convert square centimetres to square meters. Hence option D is correct.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

We know that 1 meter is equal to 100 cm now for a 1-meter square the centimetres will be calculated as,

1m=100cm

1m squared=100cm×100cm

1msquared= 10000cm squared

Hence option D is correct.

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The equation of the transformed function is h(x) =  4(x - 7)² - 19 option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

g(x) =  4x² - 16

The above function shifted 7 units to the right and 3 down.

Applying transformation:

x → (x - 7)

G(x) =  4(x - 7)² - 16

G(x) → G(x) - 3

h(x) =  4(x - 7)² - 16 - 3

h(x) =  4(x - 7)² - 19

Thus, the equation of the transformed function is h(x) =  4(x - 7)² - 19 option (C) is correct.

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