Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. The mean is always less than the median. All of the values in the data are used in calculating the mean. Σ(X-X)=0 i.e. the sum of the deviations is zero. There is only one mean for a set of data. The mean can be calculated for nominal data.

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Answer:

5.1

Step-by-step explanation:

ik i am in the future

Answer:

-0.6

Step-by-step explanation:

Answer:

⅗ as a decimal is -0.6

Answer:

120 degrees

Step-by-step explanation:

vertical angle of isoceles = 180 - 2(base angles) = 180 - 2(30) = 120

Answer:

isosceles triangle means both angle or sides equal so in this way

unknown angle + 30 + 30 = 180°

unknown angle+60=180

so unknown angle=120°

which is vertical angle

Answer:

B

Step-by-step explanation:

(y^(4))^(1/5)=y^(4/5)

Let numerator be x

ATQ

[tex]\\ \sf\longmapsto x+x+2=12[/tex]

[tex]\\ \sf\longmapsto 2x+2=12[/tex]

[tex]\\ \sf\longmapsto 2x=12-2[/tex]

[tex]\\ \sf\longmapsto 2x=10[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{10}{2}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Now the fraction is

[tex]\\ \sf\longmapsto \dfrac{x}{x+2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{5+2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{7}[/tex]

-- Their sum is 12.

-- If they were equal, each would be 6.

-- To make them differ by 2 without changing their sum, move 1 from the numerator (make it 5), to the denominator (make it 7).

Answer:

SOH-CAH-TOA

[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°

SOH = SIN = OPP/HYP

SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]

Step-by-step explanation:

Answer:

[tex]\huge\boxed{width=12cm}[/tex]

Step-by-step explanation:

[tex]l-length\\w-width\\P-perimeter[/tex]

The formula of perimeter of the rectangle:

[tex]P=2l+2w=2(l+w)[/tex]

Substitute:

[tex]l=6w\\\\P=168cm[/tex]

[tex]168=2(6w+w)\\168=2(7w)\\168=14w\qquad|\text{divide both sides by 14}\\\\\dfrac{168}{14}=\dfrac{14w}{14}\\\\12=w\Rightarrow w=12(cm)[/tex]

Answer:

Width of rectangle = 12 cm

Step-by-step explanation:

Let us assume that,

→ Length = 6x

→ Width = x

→ Perimeter = 168 cm

Perimeter of rectangle,

→ P = 2(L + W)

Forming the equation,

→ 168 = 2(6x + x)

Now the value of x will be,

→ 168 = 2(6x + x)

→ 2 × 7x = 168

→ 14x = 168

→ x = 168/14

→ [ x = 12 ]

Then the length and width is,

→ Length = 6x = 6(12) = 72 cm

→ Width = x = 12 cm

Hence, required width is 12 cm.

Answer:

b is the correct answer

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

12x^2-7x-12 = (4x+3)(3x-4)

4x+3=0. X = -3/4

3x-4=0. X = 4/3

(-3/4) (4/3) = -1

Answer:

x = 1

y=1.5

Step-by-step explanation:

3*1+2*1.5=6

The values of x and y in equation 6=3x+2y is for x is 1 and for y is 1.5.

We have given that,

x and y are integers and 0 < x < y.

6 = /3x+2y.

x=1 then

A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

6=3+2y

6-3=2y

3/2=y

y=1.5

3*1+2*1.5=6

Therefore we get the values of x and y is for x is 1 and for y is 1.5.

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Answer:

1/8

Step-by-step explanation:

Let "A" = the next call of a customer's complaint

Let "B" = the next call completed under 5 minutes

P(A) = 1/4

P(B) = 1/2

So ----> P(AB) = P(A) times P(B) P(AB)

                       = 1/4 times 1/2 = 1/8

Answer:

lol sorry i don't know. but i would try my best to find your answer

Answer:

This type of study is called a simulation

Step-by-step explanation:

Answer:

This would be a regular polygon.

Step-by-step explanation:

A regular polygon has congruent sides and interior angles.

An irregular polygon does not have congruent sides and all interior angles.

A convex polygon does not have a interior angle greater than 180°.

Lastly, a concave polygon has only one interior angle greater than 180°.

Using the process of elimination, it would not be a convex or concave polygon. Now we have either a regular or irregular polygon. This polygon can not be a irregular polygon because all the sides are congruent. This means that this polygon is a regular polygon!

The given polygon is a regular convex polygon.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. The interior of a solid polygon is sometimes called its body.

Given,

Polygon has 8 edges and 8 vertices.

1. Regular or Irregular:

A regular polygon has congruent sides and interior angles.

In the figure all sides are of equal length and the angle are same so, It is a regular polygon.

2. Convex or concave:

Convex polygon has all interior angles less than 180° while in concave polygon at least one interior angle should be greater than 180°.

In the given polygon all angles are less than 180°, so it is a convex polygon.

Hence, by the above explanation, the given polygon is regular convex polygon.

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Answer:

i think its all real numbers

Step-by-step explanation:

i think!! im not so sure

Answer:

–10m4n3 + 8m2n6 + 3m4n3 – 2m2n6 – 6m2n6 = -7m4n3

⇒It is a monomial with a degree of 7 is correct

Step-by-step explanation:

Let's take any 2 points from the line.

1. (-4,-2)

2. (-2,-7)

[tex]slope \\ = \frac{Δy}{Δx} \\ = \frac{y_{2} - y_1}{x_{2} - x_1} \\ = \frac{ 7 - ( - 2)}{ - 2 - ( - 4)} \\ = \frac{5}{2} \\ = 2 \frac{1}{2} \\ = 2.5[/tex]

The simplification of the expression is  [tex]\frac{15\sqrt{2} }{4}[/tex]

First, find the factors of the number that ahs square root

Given,

= [tex]\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}[/tex]

Multiply the numerators by the surd of the denominators

= [tex]\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}[/tex]

Multiply through and find their square root

= [tex]\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}[/tex]

To simply, we have

= [tex]\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}[/tex]

Find the LCM

= [tex]\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}[/tex]

Add through

= [tex]\frac{75\sqrt{2} }{20}[/tex]

= [tex]\frac{15\sqrt{2} }{4}[/tex]

Thus, the simplification of the expression is  [tex]\frac{15\sqrt{2} }{4}[/tex]

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Answer:

13. 10

14. 51

Step-by-step explanation:

Answer:

13. 10

14. 51

Step-by-step explanation:

Answer:

147.3

Step-by-step explanation:

this is an hendecagon there is 11 sides the total interior measure is 1,620 if you divide that by each side which would be 11 you get 147.272727 which would ultimately round up to be 147.3

9514 1404 393

Answer:

  c = 14

  no extraneous solutions

Step-by-step explanation:

You can subtract the right-side expression, combine fractions, and set the numerator to zero.

  [tex]\dfrac{c-4}{c-2}-\left(\dfrac{c-2}{c+2}-\dfrac{1}{2-c}\right)=0\\\\\dfrac{c-4}{c-2}-\dfrac{1}{c-2}-\dfrac{c-2}{c+2}=0\\\\\dfrac{(c-5)(c+2)-(c-2)^2}{(c-2)(c+2)}=0\\\\\dfrac{(c^2-3c-10)-(c^2-4c +4)}{(c-2)(c+2)}=0\\\\\dfrac{c-14}{(c-2)(c+2)}=0\\\\\boxed{c=14}[/tex]

__

Check

  (14 -4)/(14 -2) = (14 -2)/(14 +2) -1/(2 -14) . . . . substitute for c

  10/12 = 12/16 -1/-12

  5/6 = 3/4 +1/12 . . . . true

There is one solution (c=14) and it is a solution to the original equation. There are no extraneous solutions.

Answer:

AED 972

Step-by-step explanation:

Area of the wall = 9² = 81 m²

each m² costs AED 12

so 81 m² will cost 12×81 = AED 972

Answer:

It's Micheal because he started with 6 and added 15 and he divided them into 3 piles

Answer:

not enough info

Step-by-step explanation:

Answer:

x = 3

y = 2

Step-by-step explanation:

3x - y = 7   ------------(i)

2x - 2y = 2 ---------(ii)

Multiply equation (i) by (-2)

(i)*(-2)          - 6x + 2y = -14

(ii)                 2x  - 2y =2     {Add both equation. now y will be eliminated}

                    -4x         = -12          {Divide both sides by -4}

                             x = -12/-4

x = 3

Plug in x = 3 in equation (i)

2*3 - 2y = 2

6 - 2y = 2    

Subtract 6 from both sides

 -2y = 2 - 6

  -2y = -4

Divide both sides by 2

      y = -4/-2

y = 2

Answer:

x = 3, y = 2

Step-by-step explanation:

Given the 2 equations

3x - y = 7 → (1)

2x - 2y = 2 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the y- term

- 6x + 2y = - 14 → (3)

Add (2) and (3) term by term to eliminate y

- 4x + 0 = - 12

- 4x = - 12 ( divide both sides by - 4 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3(3) - y = 7

9 - y = 7 ( subtract 9 from both sides )

- y = - 2 ( multiply both sides by - 1 )

y = 2

solution is (3, 2 )

Answer:

Step-by-step explanation:

Let's write that out completely:

[tex]ln_e(x)=7[/tex] The rule for going from log to exponential is what I call the "circular rule" in my classes and the kids never forget it. Take the base of the log, raise it to the power of the number on the other side of the equals sign, and then circle back to set it equal to the argument.

e is the base. Raise e to the 7th and circle back to set the whole thing equal to x (x is called the argument):

[tex]e^7=x[/tex] choice C.