Enter the next three numbers of the repeating decimal produced by the fraction 5/6.
0.833333...

Answer: k = 5/3

Step-by-step explanation:

    To solve, we will isolate the variable, k, by using inverse operations.

   Given:

2/5k + 1/6 = 3/10k + 1/3

   Subtract 1/6 from both sides of the equation:

2/5k = 3/10k + 1/6

   Subtract 3/10k from both sides of the equation:

1/10k = 1/6

   Divide both sides of the equation by (1/10), which is the same as multiplying both sides by 10:

k = 5/3

Answer:

k=5/3

Step-by-step explanation:

2/5k+1/6=3/10k+1/3

Move the 3/10k to the left side with subtraction

1/10k+1/6=1/3

Move the 1/6 to the right with subtraction

1/10k=1/6

Divide the 1/10 from each side

Getting K=5/3

The median distance is 5km.

The median distance, symbolized by δM, is the median value of the distance among any two node pairs. This is measured over each network's largest linked component, and takes into account pairs including of the same node.

In this case, the dots in the picture (attached) represent the number of matches.

So, if we write it all down here, the data will be:

3, 4, 4, 5, 5, 5, 5, 7, 7

Since the total of values in the data is odd number, that is 9, then the formula for the median distance will be:

Median = (n + 1) / 2

with n = 9

Thus, the median distance in this case:

= (n + 1) / 2

= (9 + 1) / 2

= 10 / 2

= 5

Hence, the median distance is 5km.

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Answer:

yes?

Step-by-step explanation:

1) The triangle classified according to their sides is given as follows:

a) Isosceles triangle - It has two equal sides

b) Scalene Right Angled Triangle.

c)  obtuse scalene triangle -Has an angle that is over 90 degrees, as well as three unequal sides

d) Equilateral Triangle - Three equal sides and three equal angles

e) Isosceles Right Angled Triangle - Right angle with two equal sides and two equal angles

f) Scalene Triangle - Three unequal sides and three unequal angles.

g) Equilateral Triangle - Three equal sides and three equal angles

h) Obtuse Isosceles Triangle - has two equal sides with an angle measuring above 90 degrees.

2) Note that the value of x is 6, JK is 83, KL is 83 and JL is 83.

As indicated above, an Equilateral Triangle is one whose sides are equal. Thus,

JK = KL = JL

That means 13x + 5 = 17x -19 ..............1

Simplifying 1 by collecting like terms:

17x - 13x = 19 + 5

4x = 24

x = 24/4

x = 6

We can proceed to find the sides now

JK = 13x + 5

13 x 6 + 5

= 78 + 5

= 83

JK = 83

KL = 17x - 19

= 17 x 6 - 19

= 102 - 19

= 83

KL = 83

JL= 8x + 35​

= 8 x 6 + 35

= 48 + 35

= 83

JL = 83

Therefore, the value of x is 6, JK is 83, KL is 83 and JL is 83.

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There are 51 trees, 41 weeds, and 16 grasses that are significant pollen producers.

In the context of beekeeping, the phrase "pollen source" refers to flowering plants that provide pollen to bees and other insects. Bees gather pollen to use as a source of protein for their young.

G, W, and T should stand for the number of grasses, weeds, and trees that serve as significant pollen sources.

According to information provided, state A is home to 80 significant sources of pollen. This data can be represented as follows in an equation:

G + W + T = 108......(1)

According to what is said, there are 7 times as many weeds as there are grasses. This data can be represented as follows in an equation:

W = 3G - 7......(2)

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

T = 3G + 3

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

G + W + T = 108

G + 3G - 7 + 3G + 3 = 108

7G - 4 = 108

7G = 112

G= 112/7

G = 16

Therefore, there are 16 grasses that are major pollen sources.

Number of weeds that are major pollen sources:

W = 3G - 7  = 3(16) - 7  = 48 - 7 = 41

Therefore, there are 41 weeds that are major pollen sources.

Number of trees that are major pollen sources:

T = 3G + 3  = 3(16) + 3  = 48 + 3  = 51

Therefore, there are 51 trees that are major pollen sources.

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Answer:

[tex]b=3/11[/tex]

Step-by-step explanation:

[tex]-3b+11=8b+8 \\ \\ 11b+8=11 \\ \\ 11b=3 \\ \\ b=3/11[/tex]

Answer:

A)  f(x) = tan(2x - π)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.3cm}\underline{Standard form of a tangent function}\\\\$f(x)=A \tan(B(x+C))+D$\\\\where:\\\\\phantom{ww}$\bullet$ $A=$ vertical stretch\\ \\\phantom{ww}$\bullet$ $\dfrac{\pi}{|B|}=$ period\\\\\phantom{ww}$\bullet$ $C=$ horizontal shift (positive is to the left)\\\\\phantom{ww}$\bullet$ $D=$ vertical shift\\\end{minipage}}[/tex]

The parent tangent function is:

[tex]f(x)=\tan(x)[/tex]

The period of the parent tangent function is π.

A tangent function is discontinuous when cos(x) = 0, so it has vertical asymptotes whenever cos(x) = 0.

Therefore, the parent tangent function has vertical asymptotes at:

[tex]x=\dfrac{\pi}{2}+\pi n[/tex]

and so its domain is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{2}+\pi n\right\}[/tex]

If the domain of the given tangent function is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{4}+\dfrac{\pi}{2}n\right\}[/tex]

then its vertical asymptotes are when:

[tex]x =\dfrac{\pi}{4}+\dfrac{\pi}{2}n[/tex]

Therefore, its period is π/2.

[tex]\implies \dfrac{\pi}{|B|}=\dfrac{\pi}{2}[/tex]

[tex]\implies B=2[/tex]

And it has been horizontally shifted by π/2:

[tex]\implies f(x)=\tan\left(2\left(x-\dfrac{\pi}{2}\right)\right)[/tex]

[tex]\implies f(x)=\tan\left(2x-\pi\right)[/tex]

Function g(x)

[tex]g(x)=\tan(x- \pi)[/tex]

Function h(x)

[tex]h(x)=\tan \left(x-\dfrac{\pi}{2}\right)[/tex]

Function j(x)

[tex]j(x)=\tan \left(\dfrac{x}{2}- \pi \right)[/tex]

Answer:

-6, 19, 29

Step-by-step explanation:

Range = y

Domain = x

The equation is y = 5x + 4

we plug x into the equation:

5 (-2) + 4 = -6

5 (3) + 4 = 19

5 (5) + 4 = 29

The area of rectangle in the simplest Form is: [tex]= 45[/tex]

What is the area of a rectangle?

The area of a rectangle of length (L) and width (W) is given by the multiplication of the dimensions, as follows:

Area of rectangle = Length (L) * Width (W)

Given:

Area of rectangle =[tex]\sqrt{15*9*5*3}[/tex]

                              ⇒[tex]\sqrt{3*5*3*3*5*3}[/tex]

                              ⇒3*5*3

                              ⇒45

Therefore, the area of rectangle in the simplest Form is: 45

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The radius of the hemisphere with volume 3839cm³ is 11.9cm

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units.

The volume of a hemisphere is given as ⅔πr³

Where r is the radius

V = ⅔×3.14r³

3839 = 2/3× 3.14r³

r³ = (3839× 3)/3.14×2

r³ = 11517/6.28

r³ = 1833.9

r = cube root of 1833.9

r = 11.9cm

Therefore the radius of the hemisphere is 11.9cm

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The opposite sides are parallel to each other if diagonals of the quadrilateral bisect each other.

The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.

AC and BD bisect each other.

We know that in a quadrilateral if the diagonal of the quadrilateral bisect each other then the opposite sides are parallel to each other.

AC = BD         (Equal diagonal)

Then the side AB and CD are parallel to each other. And similarly, the sides BC and AD are also parallel to each other.

AB || CD or BC || AD

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The value of k  for the point on the line is 63

We can find the value of k by using the slope formula. The slope of a line can is given by:

Slope = (y2-y1)/(x2-x1)

Since the pass through the origin (0,0), (k,7) and (-81,-9). we can write:

x1 = 0, y1 = 0 and x2 = -81, y2 = -9

Slope = (-9-0)/(-81-0) = 1/9

Also, we can write:

x1 = k, y1 = 7 and x2 = -81, y2 = -9. And the slope is still the same

1/9 =  (-9-7)/(-81-k)

1/9 = -16/(-81-k)

1/9(-81-k) = -16

-9 - k/9 = -16

-k/9 = -16 + 9

-k/9 = -7

-k = -7 × 9

-k = -63

k = 63

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In the parallelogram HIJK, the measure of angle J and K are 45 degrees and 135 degrees respectively.

You should know that a parallelogram is a quadrilateral whose opposite sides are parallel.  The given parameters for the solution are

m<H = 45 degrees

Having said this, the m<K will be:

Produce the line H to P

This implies that <JKP is = 45 degrees ........... corresponding angles

It there means that  <HKJ = 180-45 = 135 degrees

Also; <JKP = <IJK   ................ corresponding angles

Therefore m<J is 45 degrees.

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The correct question:

In parallelogram HIJK, the measure of angle H is 45∘.

Find the measure of angle J. Explain how you know.

Find the measure of angle K. Explain how you know.

Answer:

APR stands for Annual Percentage Rate, which is the interest charged on a loan expressed as a yearly rate. In this case, we are given the interest rate for a loan over 10 days.

To calculate the APR, we need to determine the annualized interest rate, which is the interest rate multiplied by the number of times the interest is compounded per year.

We know that the interest on the loan is $200. The loan amount is $800 and the loan period is 10 days.

First we need to calculate the daily interest rate:

Interest/Loan amount = 200/800 = 0.25

To find the annualized interest rate, we need to multiply the daily interest rate by the number of days in a year:

0.25* 365 = 91.25%

To the nearest percent the APR for this loan is 91%

The correct answer is B.We can find by complex number by using complex form.

Complex numbers are the numbers that are expressed in the form of a+ib where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example 2+3i is a complex number where 2 is a real number (Re) and 3i is an imaginary number (Im).

Every real number is a complex number when the imaginary part is zero. But remember that every complex number is not a real number. For example we can write 5 as 5+0×(i). Hence Every Real Number is a Complex Number.

Now

A complex number is of the form a+ b(i)

 =8/3 +[tex]\sqrt{-7/3}[/tex]

 =8/3 +[tex]\sqrt{7/3}[/tex] [tex]\sqrt{-1}[/tex]

=8/3+[tex]\sqrt{7/3}[/tex] (i)

The second option is a complex number because it can be rewritten in the form

a + b(i).

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The height of the triangular pyramid will be 154 cm.

A pyramid with a triangle base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids contain four vertices.

Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.

The volume of the triangular pyramid will be,

Volume = 1/2 x Base x h

11120 = 1/2 x ( 17 x 17 /2 ) x h

h = ( 11120 x 2 x 2 ) / ( 17 x 17 )

h = 44480 / 289

h = 154 cm

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Based on the given set of real numbers, a list of all the rational numbers in the set include the following: B. √4, -2/3, 1, 9/8, √(9/4), 2.4. Therefore, the correct answer option is: B. square root of 4 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

In this scenario, the rational numbers include all of the following:

However, -√2 and √10 would not be classified as rational numbers because they cannot be obtained when an integer is divided by another integer.

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The best step to use in getting angle ECA is the exterior angle property which gives us; Angle ECA =  154°

In a triangle geometry, we know that the exterior angle is always equal to the sum of the interior opposite angles. This property is referred to as  the exterior angle property. This tells us that any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.

Now, in this question, we are trying to find the measure of angle ECA which is an exterior angle given by the expression 166 - 6x.

Now, the interior opposite angles are (100x - 59) and (6x + 1). Thus;

Applying the exterior angle property, we will have the first step as;

(100x - 59) + (6x + 1) = 166 - 6x

106x - 58 = 166 - 6x

112x = 166 + 58

112x = 224

x = 224/112

x = 2

Thus;

Angle ECA = 166 - 6(2) = 154°

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The given polynomial does not have x - 3 as its factor.

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The remaining factors of the polynomial can be found by dividing it by the same factor.

The polynomial is given as P(x) = 2x¹ − 5x³ - 4x² + 4.

In order to check whether x - 3 is a factor, evaluate P(3) as below,

P(3) = 2 × 3¹ - 5 × 3³ - 4 × 3² + 4

⇒ -161

Since, P(3) ≠ 0, x - 3 is not a factor of P(x).

Hence, the given expression is not a factor of P(x).

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The cost of a pack of gum is equal to $2.1.

In order to determine the cost of a pack of gum, we would assign variables to the cost of a pack of gum and cost of a candy bar respectively, and then translate the given word problem into an algebraic equation as follows:

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation which models this situation is;

4c + 2g = 9.80    ......equation 1.

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation 2.

c = 2g/3     ......equation 3.

Substituting equation 3 into equation 1, we have:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

Cost of a pack of gum, g = 29.4/14

Cost of a pack of gum, g = $2.1

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Complete Question:

Brock bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?

The ordered pair of the equation of line is given by

A ( 6 , 6 ) , B ( 0 , 2 ) , C ( -2 , -6 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be A ( 6 , 6 )

Let the second point be B ( 0 , 2 )

The slope of the line m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 6 ) / ( 0 - 6 )

Slope m = -4 / -6

Slope m = 2/3

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = 2/3 ( x - 6 )

On simplifying the equation , we get

y - 6 = ( 2/3 )x - 4

Adding 6 on both sides of the equation , we get

y = ( 2/3 )x + 2

Therefore, the value of A is y = ( 2/3 )x + 2

Hence , the equation of line is y = ( 2/3 )x + 2

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The way that they could calculate the point that is equidistant from all three gates is; By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.

The circumcenter of a triangle is defined as the locus of point equidistant from the three vertices of a triangle.

From the image attached showing the location of the three gates, the first step to take is to join all the three entry points of the friends in order to form a triangle.

The second step to take now, will be to find the centroid of the triangle, such that all three friends must start moving in the direction of the midpoint of the opposite side.

Finally, following that procedure, the point equidistant from all the three gates can be calculated.

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The profit the company would make over the course of its 5 years of operation, given the starting annual profit and the constant increase in the profit, is $ 998, 329.34

To find the total profit that the company would make over the first 5 years of the operation, use the future value formula :

= First profit x Future value interest factor of annuity, 27%, 5 years

First profit = $ 117, 000

Rate of increase = 27 %

Number of years = 5 years

The profit in 5 years is:

= 117, 000 x 8.53272941

= $ 998, 329.34

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1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

The idea of area is essential to contemporary mathematics. A two-dimensional shape, figure, or planar lamina in a plane will occupy a specific amount of space, which is denoted by the area.

The area can be simply defined as the volume of cloth, or other material with the specified thickness, required to construct a model of the shape, or as the volume of paint required to completely cover the surface of the shape in a single layer, or "coat," of paint.

It is a two-dimensional illustration of the length of a curve or the volume of a solid, where length is a one-dimensional concept and volume is a closely related concept that exists in three dimensions.

Area of national park = 9,542 miles²

14% of the area of the park is reserved for animal preservation

= 9542 × 14

= 9542 × 14/100

= 9542 × 0.14

=  1335.88 miles²

Thus, 1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

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Answer:

x = -11.2

Step-by-step explanation:

hope it helps

Answer:fsjcc

Step-by-step explanation:

8473274+5487643=593fdj

]

Answer:

y + y + y + y + y + y

Step-by-step explanation:

6y =

6 * y =   ==> add y 6 times

Hence, 6 * y = y + y + y + y + y + y

X xcm 6cm 8cm is equal to 10cm if the area of the trapezium underneath is 40%2cm2.

Provide A B C D. trapezium the length of the sides excluding the base is 10,

[tex]$$\therefore \mathrm{AD}=\mathrm{DC}=\mathrm{CB}=10 \mathrm{~cm} \text {. }$$[/tex]

Draw a parallel DP & CQ on AB.

Let [tex]$\mathrm{AP}=x \mathrm{~cm}$[/tex]

In symmetry

[tex]$$\mathrm{QB}=x \mathrm{~cm}$$[/tex]

Consider area A of the trapezium. A B C D

[tex]$$\begin{aligned}& \left.A=\frac{1}{2} \text { (Sum of parallel sides }\right) \times(\text { Height }) \\& A=\frac{1}{2}(D C+A B) \times \text { DP } \quad \ldots(1)\end{aligned}$$[/tex]

Therefore, DPCQ creates a rectangle because DP & CQ are perpendicular to A B and C D were parallel to A B.

[tex]$$\therefore \mathrm{PQ}=\mathrm{DC}=10 \mathrm{~cm}$$[/tex]

Thus,

[tex]$$\begin{aligned}A B & =A P+P Q+Q B \\& =x+10+x \\& =2 x+10\end{aligned}$$[/tex]

Use the equation A r e a = h 2 (a + b) to determine a trapezium's area. The distance between a and b, which are two parallel sides, is denoted by the letter h. To put it another way, add the two parallel sides together, divide by 2, and then multiply this number by the separation between the parallel sides. The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y.

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The height of the mountain is derived to be 410 m approximately to 2 significant figure using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the length from point B to the foot of the mountain with x and the height of the mountain with h so that:

the distance from a to the foot of the mountain = 400m + x

tan 32° = h/(400 + x)

h = tan 32° (400 + x) {by cross multiplication}

h = 400 × tan 32° + xtan 32°

h = 249.9477 + xtan 32°

also;

tan 58° = h/x

h = tan 58° × x {by cross multiplication}

h = xtan 58°

so;

xtan 58° = 249.9477 + xtan 32°

xtan 58° - xtan 32° = 249.9477 {collect like terms}

x(tan 58° - tan 32°) = 249.9477

x(0.9755) = 249.9477 {divide through by 0.9755}

x = 249.9477/0.9755

x = 256.2252

h = 256.2252 × tan 58°

h = 410.9460.

Therefore, the height of the mountain is 410 m approximately to 2 significant figures using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

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