write out cayley tables for groups formed by the symmetries of a rectangle and for . how many elements are in each group? are the groups the same? why or why not?

Answer: 4 / 3

Step-by-step explanation:

Soh Cah Toa

In this case, we'll use Toa

Tangent = Opposite / Adjacent

Tan A = 40 (opposite) / 30 (adjacent)

Tan A = 40 / 30 = 4 / 3 (simplified)

Answer:

              The correct scale faction the first pentagon dilated by to create the second pentagon is 1.25.

Step-by-step explanation:

              Since the second pentagon is a dilation of the first pentagon, we can conclude these pentagons are similar, meaning the shape retained all of its previous angles, and all the corresponding sides are dilated by a common scale factor. Since we know the values of a pair of corresponding sides, we can use those to find the scale factor of dilation.

             The corresponding side of the original pentagon is 4 units, and the corresponding side of the dilated pentagon is 5 units. Since the first pentagon dilated to become the second, in order to solve the scale factor the pentagon dilated by, we'd have to divide the side given on the second pentagon by the corresponding side of the first, which will be 5 ÷ 4 = 1.25. Therefore, that will be the scale factor the pentagon dilated by.

Have a great day! Feel free to let me know if you have any more questions :)

Answer: 29.8 feet

Step-by-step explanation:

To solve this, the first step is to make the imaginary triangle (look at the picture below). Now, we use the basic trigonometry functions. Since we have to find tge base part of the triangle (which is the adjacent one to the angle, and we already have the opposite to the angle. So, now we know we have to use the tan ratio. We now solve it with the following method:

[tex]tan(Angle) = \frac{Opposite}{Adjacent} \\[/tex]

Now we sub in our values and use the calculator to solve it:

[tex]tan(40) = \frac{25}{x}\\\\x = \frac{25}{tan(40)} \\\\x = 29.8 (1 d.p)[/tex]

Answer:

Non-linear

Explanation below

Step-by-step explanation:

The relationship is clearly non-linear

If it where a linear relationship then the temperature change per hour would be constant throughout the time period when the observations were made.

The resultant graph would be a straight line

Here the graph rises at a decreasing rate until it almost flattens out. This means the temperature reaches a maximum and stays at that maximum.

Therefore , the solution of the given problem of function comes out to be  f(x) = 1.1f(x + 1) is the solution for the graph.

The study of mathematics includes looking at numbers, their variables, the world around us, buildings, and both real and imagined places. An illustration of the relation between the quantity of inputs and the appropriate outputs for each is called a function. A function, simply described, is a group of inputs who, when combined, provide distinct outputs for each input. Every function has a city, province, or scope—also referred to as a domain—assigned to it. Functions are usually indicated with the letter f. (x). The input contains an x.

Here,

Given:

The parent function f(x) is translated left by one unit and slightly stretched vertically to form g(x).

=>g(x) is:

=> f(x) = 1.1f(x + 1)

Thus , f(x) = 1.1f(x + 1) is the given function which is graphed here.

Therefore , the solution of the given problem of function comes out to be  f(x) = 1.1f(x + 1) is the solution for the graph.

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The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.

The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.

The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.

Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.

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Answer: 360 = 7n + 12 + 13x — 16 + 6xx = 146 * 14 = 84°

Answer:

a)

 x  y

-2  6

-1   1

0  0

1   3

2  10

b)  Curve B matches all the values.

Step-by-step explanation:

See attached worksheet.

a)  Enter the x values into the equation to find the corresponding values of y.

b)  Mark these x,y values on the graph to identify the curve that matches all points.  That is curve B.

The simplified product of - (2/5).(2/5) is equal to - 4/25.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A product of two fractions - 2/5 and 2/5 is given.

We know in the product of fractions numerator is multiplied by the numerator and the denominator is multiplied by the denominator.

Therefore, - (2/5).(2/5).

= - (2×2)/(5×5).

= - 4/25.

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The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%

To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.

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Answer:

[tex]1) p = 205 - 3 = 202 \ 2)2x \div 7 = 4 \\ 2x = 28 \\ x = 14 \\ \\ 3)3y - 6 = 9 \\ 3y = 9 + 6 \\ 3y = 15 \\ y = 5[/tex]

To find three additional polar representations of the point (2, 3π/4), we can add or subtract 2πk to the angle, where k is an integer. Using this method, we get:

   (2, -5π/4) - subtract 2π

   (2, 11π/4) - add 2π

   (2, -3π/4) - subtract 2π

To find the smallest and largest values of the angle, we need to consider the interval −2π < θ < 2π. The given angle of 3π/4 lies in the second quadrant. Adding or subtracting 2π to this angle will give us angles in the third and fourth quadrants. Therefore, the smallest value of the angle is −3π/4, and the largest value is 5π/4. Thus, the polar representations are:

   (2, 3π/4)

   (2, -5π/4)

   (2, 11π/4)

   (2, -3π/4)

   (2, 5π/4)

The required standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is y = -2x² + 12x - 17.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

To find the quadratic function that has the vertex (3, 1) and passes through the point (5, -7), we can use the vertex form of the quadratic function: y = a(x - h)² + k, where (h, k) is the vertex.

First, we substitute the vertex (5, -7) into the vertex form to find a:

y = a(x - 3)² + 1

-7 = a[2]² + 1
a = -2

Since a = -2, the standard form of the quadratic function is:

y = -2x² + bx + c

Substitute the point (5, -7) into the standard form y = -2x² + bx + c to find b and c:

-7 = -2x² + b(5) + c

-7 = -50 + 5b + c

43 = 5b + c - - - - -(1)

Substitute the point (3, 1) into the standard form y = -2x² + bx + c to find b and c:

1 = -18 + b(3) + c

19 =3b + c - - - - -(2)

Solving equations 1 and 2 we get
43 - 19 = 2b
b = 12 and c = -17

Put a,b and c in the standard equation,
y = ax² + bx + c
y = -2x² + 12x - 17

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Solution:

Area=15400mm^2

Now,

Area=pi×r^2

or,15400=22/7×r^2

or,15400×7=22×r^2

or,107800=22r^2

or,107800/22=r^2

or,4900=r^2

or,r=70

Also,

Diameter (d)=r×2

=70×2

=140

The coordinates of the intercepts of the depreciation equation are (9, 0) and (0, 22,995).

The x intercept is the x coordinate of a point where the line touches the X axis.

The y intercept is the y coordinate of a point where the line touches the Y axis.

Here, there are two variables.

The independent variable x is the number of years.

The dependent variable y is the value of the car.

x intercept is the year when the value of the car is 0.

Given that, model of a car loses all of it's marketable value after 9 years.

x intercept = 9

y intercept is the value of the car in the 0th year.

Initial value of the car = $22,995

y intercept = 22,995

Hence the intercepts are (9, 0) and (0, 22,995).

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The system of equations is:

y = 19 + 4*x

y = 15 + 6x

And the solution is x = 2 and y = 27.

We know that red is using a 19-kilogram bar, increasing the amount of weight he lifts by 4 kilograms on each set. Then after x sets he will be lifting:

y = 19 + 4*x

kilograms.

And his partner, meanwhile, started out using a 15-kilogram bar and is upping the weight by adding 6 kilograms on every set. Here we can write:

y = 15 + 6x

Then we need to solve the system of equations at:

y = 19 + 4*x

y = 15 + 6x

Using substitution, wecan write:

19 + 4x = 15 + 6x

19 - 15 = 6x - 4x

4 = 2x

4/2 = x

2 = x

They will lift the same weight after 2 sets, and the weight is:

y = 19 + 4*2

y = 19 + 8 = 27

They will be lifting 27 kilograms.

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The value of x for the equation is -10.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given equation,

-3/4(x + 2) = 6

both sides multiply by -4/3

-3/4(x + 2) * -4/3 = 6 * -4/3

x + 2 = -8

subtract 2 from both sides

x + 2 - 2 = -8 - 2

x = -10

Hence the value of x is -10.

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Answer:

To find the dimensions that would guarantee the greatest possible area, we can use the formula for the area of a rectangle, which is A = l * w, where l is the length and w is the width.

Since one side of the garden is already boarded by a river, we only need to use 600ft of fencing for the other three sides. This means that the length and width of the garden must add up to 600ft. We can write this as:

l + w = 600

Since we want to find the dimensions that would give us the greatest possible area, we want to maximize l * w. Using the formula for the area of a rectangle, we can write this as:

A = l * w = l * (600 - l) = 600l - l^2

To find the maximum area, we can differentiate this equation and set it equal to zero:

dA/dl = 600 - 2l = 0

Solving for l, we get:

l = 300/2 = 150ft

So, the shorter side is 150ft and the longer side is 450ft (600 - 150).

Finally, we can use the formula for the area of a rectangle to find the greatest possible area:

A = 150 * 450 = 67,500ft^2

Therefore, the greatest possible area for the garden is 67,500ft^2 when the shorter side is 150ft and the longer side is 450ft.

Step-by-step explanation:

The equation of the parabola is x² - 8x + 16 = 0

To find the equation of the parabola with focus (4, -3) and directrix y = -3, we can use the definition of a parabola.

A parabola is the set of all points that are equidistant to the focus and the directrix.

The distance from a point (x, y) to the directrix y = -3 is simply the vertical distance between the point and the line, which is |y - (-3)| = |y + 3|.

The distance from a point (x, y) to the focus (4, -3) can be found using the distance formula:

d = √[(x - 4)² + (y + 3)²]

Since the point is equidistant to the focus and the directrix, we have:

d = |y + 3|

Squaring both sides, we get:

(x - 4)² + (y + 3)² = (y + 3)²

Simplifying, we get:

(x - 4)² = 0

Thus, the equation of the parabola is simply:

x² - 4x - 4x + 16 = 0

x² - 8x + 16 = 0

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The unit rate of the shirt is $1.50 per shirt.

Unit rate is a measure of the relationship between two quantities, where the second quantity is expressed as a unit of one. It is often expressed as a ratio, with the unit of the second quantity being 1. Unit rate helps us compare different quantities and make sense of their relative sizes.

The unit rate for the shirts can be calculated by dividing the total cost by the number of shirts. In this case, the unit rate would be:

$6.00 ÷ 4 shirts = $1.50/shirt

So, the unit rate for the shirts is $1.50 per shirt.

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Answer:

the answer is E

Step-by-step explanation:

your welcome

Answer: 5n+30

( The problem was incomplete on my end )

( Hope this helps )

Trapezoidal Rule: [tex](b-a)^3 / 96n^2,[/tex] Simpson's Rule: [tex](b-a)^5 / 2880n^4\\[/tex].  Both approximations have error of 0.0208.

For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get [tex]|E| ≤ 2^3/12(4)^2(2)[/tex] or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get[tex]|E| ≤ 2^5/180(4)^4(2)[/tex] or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.

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Answer:

Both triangles are congruent by S A S congruent.

Step-by-step explanation:

     In ΔHIG & ΔKJG,

HG = KG                Given

∠GHI ≅ ∠GKJ       Alternate interior angles, HI // KJ and KH is transversal

    HI = KJ               Given

ΔHIG  ≅ ΔKJG       Side Angle Side congruency

Using a system of equations, the unit cost of one roll of plain wrapping paper and one roll of holiday wrapping paper is as follows:

A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.

A system of equations is otherwise known as simultaneous equations.

                         Plain Wrapper   Holiday Wrapper     Total Cost

Cody sales               5                           8                      $174.00

Aliyah                       5                          10                      $210.00

Let the unit cost of Plain Wrapper = x

Let the unit cost of Holiday Wrapper = y

5x + 8y = 174... Equation 1    

5x + 10y = 210... Equation 2

Subtract Equation 1 from Equation 2:

5x + 10y = 210

-

5x + 8y = 174

2y = 36

y = 18

y = $18

Substitute y = 18 in either equation:

5x + 8y = 174

5x + 8(18) = 174

5x +144 = 174

5x = 174 - 144

5x = 30

x = 6

x = $6

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The fraction cannot be worked out, given the information on the numerator being even and the denominator being odd.

When fractions are said to be in their simplest forms as 1 / 1, then it means that both the numerator and the denominator are the same. This way, they can divide each other and leave one.

For such a situation to happen, the numbers will have to either both be even numbers, or odd numbers. The numerator cannot be even while the denominator is odd.

This fraction therefore cannot be worked out.

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According to algebra property of power of a power, the following results are listed below:

Case 1: (x⁵)³ = x¹⁵ (Correct choice: 1)

Case 2: (x⁸)⁷ = x⁵⁶ (Correct choice: 4)

Case 3: (x⁷)¹⁰ = x⁷⁰ (Correct choice: 2)

Case 4: (x¹⁴)³ = x⁴² (Correct choice: 3)

In this question we find four cases of power of a power, whose solution is described by the following algebra property:

(xᵃ)ᵇ = xᵃᵇ, where x, a and b are real numbers.

Now we proceed to determine the solution to each case:

Case 1

(x⁵)³ = x¹⁵

Case 2

(x⁸)⁷ = x⁵⁶

Case 3

(x⁷)¹⁰ = x⁷⁰

Case 4

(x¹⁴)³ = x⁴²

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Answer:

6,072

Step-by-step explanation:

5,600 - 4,420 = 1,180

They gained 1,180 people over 5 years.  Now we need to find how many people they gain every year (roughly).

Since it's 5 years, we are going to divide.

1,180 / 5 = 236

They gained 236 people over 1 year.  Since 1998 is two years is before 2000, we're going to multiply 236 by 2.

236 x 2 = 472

Now we add this to the 1998 population.

5,600 + 472 - 6,072

The population in the year 2,000 is 6,072

To find the area of the base of the column, we need to find the expression for the radius of the column, r, in terms of x.

The volume of a column can be calculated as V = πr²h, where r is the radius, h is the height, and π is pi.

Using the given expression for the volume of the column, we can write:

πr²h = x³ + 37x² - 110x + 400

Since h = x + 40, we can substitute to get:

πr²(x + 40) = x³ + 37x² - 110x + 400

Dividing both sides by π(x + 40) gives us:

r² = (x³ + 37x² - 110x + 400) / (π(x + 40))

Finally, taking the square root of both sides gives us the expression for the radius in terms of x:

r = √((x³ + 37x² - 110x + 400) / (π(x + 40)))

So, the expression that approximates the area of the base of the column in terms of x and π is:

A = πr² = π √((x³ + 37x² - 110x + 400) / (π(x + 40)))²