Give a algebra equation to represent this pattern

The correct ratios are

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex] ,  tan(C) =[tex]\sqrt{3}[/tex] , sin(B) = [tex]\frac{1}{2}[/tex]

Consider the below figure attached to this question.

In triangle ABC, ∠A=90°, ∠B=30° and ∠C=60°, AC=9 and BC=18.

Using Pythagoras' theorem we get

hypotenuse² = perpendicular² + base²

BC² = AB² + AC²

⇒(18)² = AB² + 9²

⇒324 - 81 = AB²

Taking square root on both sides.

⇒√243 = AB

∴ √3 =AB

Trigonometric ratios are

[tex]sin(C) = \frac{opposite}{hypotenuse} = \frac{AB}{BC} = \frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]

[tex]cos(B) = \frac{base}{hypotenuse} = \frac{AB}{BC} = \frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]

[tex]tan(C) = \frac{opposite}{basee} = \frac{AB}{AC} = \frac{9\sqrt{3} }{9} =\sqrt{3}[/tex]

[tex]sin(B) = \frac{opposite}{hypotenuse} = \frac{AC}{BC} = \frac{9 }{18} =\frac{1}{2}[/tex]

[tex]tan(B) = \frac{opposite}{base} = \frac{AC}{AB} = \frac{9 }{9\sqrt{3} } =\frac{1 }{\sqrt{3} }[/tex]

Therefore, the correct ratios are

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex] , tan(C) = [tex]\sqrt{3}[/tex] , sin(B) =[tex]\frac{1}{2}[/tex]

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The complete question is:

Which trigonometric ratios are correct for triangle ABC? Select three options.

1. sin(C) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction

2. cos(B) = StartFraction StartRoot 2 EndRoot Over 3 EndFraction

3. tan(C) = StartRoot 3 EndRoot sin(B) = One-half

4. tan(B) = StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction.

The equation of the tangent line to the circle through the point (-6,8) has equation = Y = 0.75x + 3.5

For circles that have a center at (0,0), the equation is  [tex]x^{2} + y^{2} = r^{2}[/tex]

[tex]x^{2} + y^{2} = 10^{2}[/tex]

[tex]x^{2} + y^{2}[/tex] = 100

We check if the point (-6,8) is a circle

[tex]x^{2} + y^{2}[/tex] = 100

[tex]-6^{2} + 8^{2}[/tex] = 36 + 64 = 100

So the point is exactly at circle line, as picture below

We solve the gradient of a normal line (n)

Mn = [tex]\frac{y2 - y1}{x2 - x1}[/tex] = [tex]\frac{8 - 0}{-6 - 0}[/tex]  = [tex]- \frac{8}{6}[/tex]

For perpendicular lines the gradient is

Mp = [tex]- \frac{1}{Mn}[/tex]  = [tex]\frac{- 1 }{-\frac{8}{6} }[/tex] = [tex]\frac{6}{8} = \frac{3}{4}[/tex]

The standard equation of a linear line is

Y =  mx + c

We need to find constant (c). We substitute x and y with point (-6,8)

So, x = -6 and y = 8

C = y - mx

C = 8 - ¾(-6) = 8 – [tex]\frac{18}{4}[/tex] = 3.5

With m = Mp =  [tex]\frac{3}{4}[/tex] and c = 3,5    

So, Y =  mx + c

      Y =     [tex]\frac{3}{4}[/tex] x + 3.5

      Y = 0.75x + 3.5

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8 is not a perfect number as sum of its proper divisors is not equal to 8.

A perfect number is a positive integer that is equal to the sum of its proper divisors, which are the divisors of the number excluding the number itself. In other words, a perfect number is a number that can be written as the sum of its divisors, excluding itself.

For example, the number 6 is a perfect number because its divisors are 1, 2, and 3, and 1+2+3 = 6.

8 is not a perfect number because it is not equal to the sum of its proper divisors. The divisors of 8 are 1, 2, 4, and 8, and 1+2+4 = 7, which is less than 8.

Therefore, 8 is not a perfect number. To this date, only 49 known perfect numbers have been found, they are all even numbers and the largest known perfect number is 2^(74,207,281) − 1, it has over 22 million digits.

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Answer:

729

Step-by-step explanation:

3x3x3=27

27x27=729

Answer:

[tex](3^3)^{2}[/tex] = [tex]729[/tex]

Step-by-step explanation:

To solve this problem, you need to utilize this exponent property:

[tex](a^n)^m = a^{n*m}[/tex]

In this problem,

a = 3

n = 3

m = 2

Substitute these values into the property and compute.

∴ [tex](a^n)^m = a^{n*m}\\(3^3)^2 = 3^{3*2}\\(3^3)^2 = 3^6\\(3^3)^2 = 729[/tex]

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A 5 cm pentagon has a perimeter of 25 cm.

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length. A perimeter is the length of a two-dimensional shape's border. It is sometimes defined as the total of the lengths of all the object's sides. The perimeter of such form is the algebraic sum of the lengths of each side. We have formulae for the various geometric forms.

Here,

side of pentagon=5 cm

perimeter of pentagon=5*side

=5*5

=25 cm

The perimeter of a 5 cm pentagon is 25 cm.

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Answer:

So the solution is x = -0.57 and y = 30/7.

Step By Step Explanation:

To solve a system of linear equations, such as "x = 8 - 2y" and "3x + y = 6", we can use substitution or elimination method.

Using substitution method:

solve one equation for one variable

substitute the expression obtained in step 1 into the second equation

solve the equation obtained in step 2 to find the value of the variable that was solved for

substitute this value back into the first equation to find the value of the other variable.

x = 8 - 2y;

3x + y = 6;

solve for x in the first equation

x = 8 - 2y

substitute the value of x in the second equation

3(8-2y) + y = 6

solve the second equation obtained for y

24 - 6y + y = 6

25 - 6y = 6

-6y = -19

y = 19/6

substitute the value of y back in the first equation

x = 8 - 2(19/6) = 8 - (38/6) = 8 - (63/6) = 8 - (63/6) = 8 - 10.5 = -2.5

So the solution is x = -2.5 and y = 19/6

Alternatively, using elimination method:

Add or subtract one equation from the other to eliminate one of the variables.

Solve the resulting equation for the remaining variable.

Substitute this value into either of the original equations to find the value of the eliminated variable.

Multiply the first equation by -3

-3x = -24 + 6y;

Add the above equation to the second equation

-3x + y = 6

-24 + 6y + y = 6

-24 + 7y = 6

7y = 30

y = 30/7

substitute the value of y into the first equation

x = 8 - 2(30/7) = 8 - (60/7) = 8 - (60/7) = 8 - 8.57 = -0.57

So the solution is x = -0.57 and y = 30/7.

The length of Nathan's cat will be √27 inches.

Logic is the manipulation of all those concepts, whereas algebra is the study of abstract symbols.

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all referred to by the abbreviation PEMDAS. This strategy is utilized to provide an accurate and comprehensive solution to the issue.

A number is referred to as rational if the value of a numerical expression terminates, in which case it is a rational number, and irrational if the value of the expression does not terminate.

5/2, 1/3, 45, 59, 144, and so forth are examples of rational numbers.

The irrational numbers include, e,√27, and so forth.

Nathan's cat will be about √27 inches long.

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Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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A Riemann sum is a method used to approximate the definite integral of a function. A definite integral is a measure of the area between a function and the x-axis over a certain interval. The Riemann sum formula is used to approximate this area by breaking up the interval into a number of subintervals (or "rectangles") and summing the areas of each rectangle. The formula for a Riemann sum is given by:

∑ f(x_i) * Δx

where f(x) is the function being integrated, x_i is the right endpoint of the i-th subinterval, Δx is the width of the subinterval, and the sum is taken over all the subintervals.

The Riemann sum formula is defined with a limit, as the number of subintervals approaches infinity and the width of subintervals approaches zero, the Riemann sum formula becomes the definite integral.

There are different ways to calculate Riemann sum, such as Left Riemann Sum, Right Riemann Sum, Midpoint Riemann Sum, and Trapezoidal Riemann Sum, each one of them has different ways to calculate x_i, thus leading to different results, but all of them approach the definite integral as the number of subinterval increases.

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The perimeter of the triangle formed by ABC is 26.56

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.In order to make it simple to identify the points, a cartesian plane divides the plane space into two dimensions.

Here,

The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axes of the coordinate plane. The origin is the place where these coordinate axes connect, and they split the plane into four quadrants (0, 0). Additionally, each point in the coordinate plane is denoted by the coordinates (x, y), where x represents the point's location in relation to the x-axis and y represents its position in relation to the y-axis.

The points on the plane are

A (1,-2) , B(8,-5) and C (5,5)

The length of AB is

=> (81)2+(-5+1)2 = √72 +42

= √65

The length of BC is

(8-5)2+(-5-5)2 -

= /32+102 =

✓109

And Length of AC is

√(1 − 5)2 + (−2 −5)2 = √42 +72 = √65

The perimeter of the triangle is √65+ √65+√109 = 26.56

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It take him to 7 minutes reach the ground. You can calculate the tangent  height of an object using the distance and angles

By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can determine the height of the object of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 metres if theta is 50 degrees and D is 40 metres.

rate of descent=30 feet per minute

Height of climb=250 feet

Since he jumped 40 feet in no time,

hence,

new height=250-40=210

Time taken to reach ground=height/rate of descent

Time taken=210/30

Time taken=7 minutes

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Answer:

(f ⋅ g)(3) = 100, the distance in miles the bus traveled

Step-by-step explanation:

The product of (miles/hour) and (hours) is (miles), so only answers with units of distance are applicable. The numbers are ...

 f(3) = 2·3² +2 = 20 . . . . miles per hour

 g(3) = 3+2 = 5 . . . . hours

so (f·g)(3) = f(3)·g(3) = 20·5 = 100 . . . . miles

Answer:

(f ⋅ g)(3) = 100, the distance in miles the bus traveled.

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=2x^2+2\\g(x)=x+2\end{cases}[/tex]

To calculate the composite function (f ⋅ g)(3), multiply function f(3) by function g(3).

[tex]\begin{aligned}(f \cdot g)(3)&=f(3) \cdot g(3)\\&=(2(3)^2+2)(3+2)\\&=(2(9)+2)(3+2)\\&=(18+2)(3+2)\\&=(20)(5)\\&=100\end{aligned}[/tex]

If function f(x) represents the rate of a bus travelling in miles per hour,

and function g(x) represents the time the bus travelled in hours:

[tex]\implies f(x) \cdot g(x)=\rm miles/hour \cdot hour=\dfrac{miles}{hour} \cdot hours=miles=distance[/tex]

Therefore, (f ⋅ g)(3) = 100 represents the distance in miles the bus traveled.

The sum of the measures of the interior angles of a quadrilateral is 360°. The sum of the measures of the exterior angles of a quadrilateral is 360°.

What is a quadrilateral?

A quadrilateral is a closed shape that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The sum of quadrilateral interior angles is always 360 degrees.

Assume that ABCD is a quadrilateral.

The sum of the interior angle and the corresponding exterior angle is 180°.

The exterior angle of A is E. The exterior angle of B is F. The exterior angle of C is G. The exterior angle of D is H.

Thus ∠A + ∠E = 180°  .....(i)

∠B + ∠F = 180°  ......(ii)

∠C + ∠G = 180° ......(iii)

∠D + ∠H = 180° ......(iv)

Add equations (i), (ii), (iii), (iv):

∠A + ∠E + ∠B + ∠F + ∠C + ∠G +  ∠D + ∠H = 180°+180°+180°+180°

(∠A+∠B + ∠C +∠D) + ∠E +∠F +  ∠G + ∠H = 720°

The sum of all interior angles of quadrilateral is ∠A+∠B + ∠C +∠D = 360°.

360°+  ∠E +∠F +  ∠G + ∠H = 720°

∠E +∠F +  ∠G + ∠H = 720° - 360°

∠E +∠F +  ∠G + ∠H =  360°

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On solving the provided question we can say that by coordinates-  (4,-8)(4,−8) ; y - y1 = m(x-x1) => y - x 12 = 0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

by coordinates-

(4,-8)(4,−8)

y - y1 = m(x-x1)

y +8 = x - 4

y - x 12 = 0

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When the capacity and radius are stated as 37.68 cubic inches and 1.5 inches, respectively, the height of the soup can is 5.34 inches.

It is also known as the object's capacity. The fundamental equation for volume is length, width, and height, as opposed to the fundamental equation for the area of a rectangular shape, which is length, breadth, and height. The math is the same regardless of how you refer to the different dimensions. For example, you can substitute "depth" for "height." Volume is used to describe an object's capacity.Volume can also be used to describe how much space a three-dimensional object occupies.

given

volume of a can of soup = 37 .68 cubic inches

length of radius = 1.5 inches

v = 37 .68 cubic inches

r = 1.5 inches

v = [tex]\pi r^{2} h[/tex]

37.68 = 7.06 * h

h = 5.34 inches

When the capacity and radius are stated as 37.68 cubic inches and 1.5 inches, respectively, the height of the soup can is 5.34 inches.

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Rationales that may be involved : [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex] and real roots in reason: [tex]$1,-1,-\frac{15}{2} \mathrm{~}$[/tex] .

We can use the theorem of rational zeros since all coefficients are integers.The constant term's coefficient, or trailing coefficient, is 15, and The plus and minus signs can be used to find its components. [tex]$\pm 1, \pm 3, \pm 5, \pm 15$[/tex]  . The options for p are as follows. The maximum degree of the term's coefficient, or the leading coefficient, is -2.

The plus and minus signs can be used to find its components. [tex]$\pm 1, \pm 2$[/tex] . The possible possibilities for q are as follows.

Discover each potential value for [tex]$\frac{p}{q}: \pm \frac{1}{1}, \pm \frac{1}{2}, \pm \frac{3}{1}, \pm \frac{3}{2}, \pm \frac{5}{1}, \pm \frac{5}{2}, \pm \frac{15}{1}, \pm \frac{15}{2}$[/tex]

These could be the rationale for the following: [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex]                                                      rationales that may be involved: [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex] .

real roots in reason: [tex]$1,-1,-\frac{15}{2} \mathrm{~}$[/tex].

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Answer:

Step-by-step explanation:

2.25

In 1 hour one cycle and 1/4th of the second cycle can be assembled. or 1.25 cycles can be assembled.

The division is a mathematical operation among the 4 fundamental mathematical operations. It is the process of dividing a group of items into smaller groups and used for equal distribution.

Divisions are used very often in our daily life like dividing food items, dividing money for people calculating averages, etc.      

Here we have

John was able to assemble 10 bicycles in 8 hours.  

Given that he is consistently assembling each bicycle  

To find the number of cycles that can be assembled in 1 hr

Divide given number of cycles by the given time  

Number cycles can be assembled = 10/8 = 1.25    

This means John can assemble 1 cycle and 1/4 of the 2nd cycle.

Therefore,

In 1 hour one cycle and 1/4th of the second cycle can be assembled. or 1.25 cycles can be assembled.

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option A The inequity x ≥   3 indicates how many days it will take Rebecca to finish her orders.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

given

180x3=540 is the value.

0x3=0 3x8 =24

Add 1+2 tens and the tens on top of the one to obtain 540.

so option A The inequity x ≥   3 indicates how many days it will take Rebecca to finish her orders.

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1 - √5x is not a polynomial.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics.

Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial.

A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Hence, 1 - √5x is not a polynomial.

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Therefore , the solution of the given problem of  proportionality relationship comes out to be  it is not proportional relationship.

Relationships are regarded to as proportional when they continuously have the same ratio. For instance, the number of trees in an airport and the number of apples in a harvesting of apples depend on the average number of apples produced by each tree. A linear relation between two number or variables is referred to as being proportional in mathematics. If the initial quantity doubles, the other amount also does so. Whenever one of the parameters is reduced to 1/100th of the its previous value, the other decreases as well.

Here,

Given :

x= 1 , y=6

x=2,y=12

So , the equation is :

=> y =2x

The proportional relationship says that the line of the given equation passes through origin ,

=> y =2x

=> y = 2(0)

=> 0 =0

Thus , x =0 and y=0  because this line  pass through origin it is proportional relationship.

Therefore , the solution of the given problem of  proportional relationship comes out to be  it is not proportional relationship.

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Answer: i’m the biggest bird

Step-by-step explanation:

i’m the biggest bird

A conclusion or a hypothesis presented on an unproven foundation in mathematics is referred to as a conjecture, conjectures 6,it is divisible by 2,4,9,12.

Therefore the result is 6,it is divisible by 2,4,9,12.

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The situation below that has a positive rate of change between variables: "The height of a building increases by 10 feet for every story added".

A positive rate of change indicates that the amount under consideration is rising over time, whereas a negative rate of change indicates that it is declining with time. Change rates can be positive or negative. This corresponds to a change in the y -value between the two data points. The term zero rate of change refers to a quantity that does not fluctuate over time. An growing function's average rate of change is positive, whereas a declining function's average rate of change is negative.

Here,

The case below that exhibits a positive rate of change between variables: "The height of a building grows by 10 feet for every floor added".

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If there were only 5 coin tosses, the answer would be p5, where p= 0.6.

Now,

18 - 5 + 1 = 14 consecutive sequences of 5 flips contained in 18 flips. So it's tempting to say the answer is 14p5 ≈ 1.08, but it's also wrong. This is actually the number of expected 5-sticks, not the probability of at least one 5-stick. The problem is that since these sequences overlap, the events are not mutually exclusive, so we cannot sum them to get the overall probability. We have to subtract out all the possibilities of generating multiple 5 streaks, but calculating that probability is very complicated.

This post on stack swapping suggests an elegant approach that can be adapted to this problem. Let's define a sequence P(n). where P(n) is the probability of at least one consecutive heads after a total of n rollovers. So the answer of the question is P(18).

Clearly, P(0) = P(1) = P(2) = P(3) = P(4) = 0. This is because he can't get 5 heads in a row unless he flips the coin 5 times. P(5) is easy to compute, it only happens if all 5 flips are heads, so P(5) = p5 = 2433125 = 0.07776 .

Well, the length of the discontinuous part is n - 6, so the probability is

(1 −P(n−6)). The T,H,H,H,H,H part is the probability (1−p)p5 =(0,4)(0,6)5, and since these are independent events, the probability of THHHHH [not consecutive first letters] is (1−P( n −6))( 1−p) p5 .

Putting, All together:

P(n) = P(n−1) + (1−P(n−6))(1−p) p5.

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Answer: 5:12< 7:9

Step-by-step explanation: (5:12) x3=   15:36  <  21:36  (7:9)x3=21:36

Answer:

[tex]\frac{5}{12} < \frac{7}{9}[/tex]

Step-by-step explanation:

[tex]5:12[/tex]  [tex]7:9[/tex]

[tex]5*9[/tex]  [tex]7*12[/tex] (using cross multiply)

[tex]45 < 84[/tex]

Therefore your answer is [tex]\frac{5}{12} < \frac{7}{9}[/tex]

Extra:

I hope this helped at all.

Note: (Please don't delete this answer moderators.)

The common ratio is 18/23.

What is the geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed number, called the common ratio. To find the common ratio of a geometric sequence, we can divide each term by the previous term.

It's important to note that in a geometric sequence, the quotient of any two consecutive terms is always constant and that is the common ratio.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is.

aₙ= a₁ rⁿ⁻1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.

Given the geometric sequence: 28, 23, 18

We can find the common ratio by dividing each term by the previous term:

r = 23/28 = 18/23

Therefore, the common ratio is 18/23.

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The solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:

y < 2x + 4.

ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.

iii) | x + 3 | = y, you can split this into two cases:

i. x + 3 = y

ii. -(x + 3) = y

iv) |2x – 6| + 2 = y, you can split this into two cases:

i. 2x - 6 + 2 = y

ii. -(2x - 6) + 2 = y

We can use these equations to plot the graph on a coordinate plane.

Hence, the solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

To learn more about the graph of a function visit,

brainly.com/question/25950034

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