locate the absolute extrema of the function
on the closed interval

The answer of the given question based on the relation is R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}.

Set listing notation is a way to represent a set by listing all of its elements between curly braces { }. If a set has a large or infinite number of elements, it may not be practical to list all the elements. In such cases, we can use set-builder notation to describe the set using a condition or a rule.

The "has the same parity as" relation on set A means that any two elements in A are related if they have the same parity (either both even or both odd).

So, we can write the relation R as a set of ordered pairs where each pair consists of two elements that have the same parity.

R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}

In this set, the ordered pair (x, y) indicates that x and y have the same parity. For example, (1, 3) is in R because 1 and 3 are both odd. Similarly, (2, 4) is in R because 2 and 4 are both even.

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The length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.

what is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Let's denote the length of the shorter leg by "x".

According to the problem statement, the length of the longer leg is 22cm more than six times the length of the shorter leg, so:

longer leg = 6x + 22

Also, the length of the hypotenuse is 23cm more than six times the length of the shorter leg, so:

hypotenuse = 6x + 23

Now, we know that this is a right triangle, so we can use the Pythagorean theorem to relate the side lengths:

shorter leg² + longer leg² = hypotenuse²

Substituting the expressions we found earlier, we get:

x² + (6x + 22)² = (6x + 23)²

Expanding the squared terms and simplifying, we obtain:

x² + 36x² + 264x + 484 = 36x² + 276x + 529

Subtracting 36x² + 276x + 529 from both sides, we get:

x² - 12x - 45 = 0

Now, we can solve for x by factoring the quadratic equation:

(x - 15)(x + 3) = 0

So, either x = 15 or x = -3. Since we're dealing with lengths, we discard the negative solution and take x = 15.

Therefore, the length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.

So the side lengths of the right triangle are 15cm, 112cm, and 113cm.

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Answer:

50.23

Step-by-step explanation:

To calculate the difference between the offensive and defensive values, we simply subtract the defensive value from the offensive value:

81.8 - 31.57 = 50.23

The difference between the offensive and defensive values is 50.23.

According to the solution we have come to find that, The sum of the given vectors u and v is (1, 0).

In mathematics, a vector is a mathematical object that has both magnitude (or length) and direction. It is usually represented as a directed line segment, where the length of the segment corresponds to the magnitude of the vector, and the direction of the segment represents the direction of the vector.

A vector can be specified in terms of its components or coordinates, which are typically expressed as a sequence of numbers or symbols. For example, a two-dimensional vector can be written as (x, y), where x and y are the components of the vector along the x-axis and y-axis, respectively.

To find the sum of two vectors, we simply add their corresponding components.

So, for the given vectors u = (8, 1) and v = (-7, -1), their sum u + v can be computed as:

u + v = (8, 1) + (-7, -1) = (8 - 7, 1 - 1) = (1, 0)

Therefore, the sum of the given vectors u and v is (1, 0).

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The wholesaler's markup is the difference between the selling price and the cost price, which is $80.43 - $73 = $7.43.

The markup rate can be found by dividing the markup by the cost price and multiplying by 100 to get a percentage:

markup rate = (markup / cost price) x 100%

markup rate = ($7.43 / $73) x 100%

markup rate = 10.17%

Therefore, the wholesaler's markup rate is 10.17%, rounded to the nearest hundredth.

I hope this helps but i am not sure about the last qn.

Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 7

Colby spends 29 minutes making her collage.

50 is the total amount of minutes and 21 minutes is a part of that total.

This means we have to subtract.

50 - 21 = 29.

The length of the ramp is approximately 4.95 meters and the angle the ladder makes with the ground is approximately 58.21 degrees.

To solve x^2 + 8x - 20 = 0 using the Zero Product Property, we first need to factor the quadratic equation into two linear factors:

So, we have

(x + 2)(x - 10) = 0

This gives

x = -2 and x = 10

To find the length of the ramp, we can use the trigonometric ratio of tangent.

We know that the vertical height (opposite side) of the ramp is 1.8 meters and the angle between the ramp and the ground (angle of elevation) is 20

So, we have

tan(20) = opposite / adjacent

tan(20) = 1.8 / adjacent

This gives

adjacent = 1.8/tan(20)

Evaluate

adjacent = 4.95

Therefore, the length of the ramp is approximately 4.95 meters.

We know that the ladder is 20 feet long and reaches a point 17 feet up the wall.

Let the angle the ladder makes with the ground be θ.

Using the trigonometric ratio of sine, we have:

sin(θ) = opposite / hypotenuse

sin(θ) = 17 / 20

Taking the arc sine of both sides, we get:

θ = sin^(-1)(17/20)

Using a calculator, we get:

θ ≈ 58.21 degrees

Therefore, the angle the ladder makes with the ground is approximately 58.21 degrees.

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The length of the longest side of AABC is 4 units, and the area of AABC is equal to the area of ADEF.

An angle is the figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. The measure of an angle is usually given in degrees or radians and is determined by the amount of rotation between the two rays or lines. Angles are used in geometry and trigonometry to study shapes, distances, and other properties of objects.

Since AABC is similar to ADEF, the corresponding sides of the two triangles are proportional. Let the longest side of AABC be x. Then:

x/4 = 1/10 (since the ratio of the perimeters is 1:10)

Solving for x, we get:

x = 4/10 * 10 = 4

Therefore, the length of the longest side of AABC is 4 units.

Since the ratio of the areas of AABC to ADEF is 1:100, and we know that the longest side of ADEF measures 4, we can use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths:

Area of AABC / Area of ADEF =[tex](x/4)^2 = 1/100[/tex]

Substituting x = 4, we get:

Area of AABC / Area of ADEF[tex]= (4/4)^2 = 1[/tex]

So, the area of AABC is equal to the area of ADEF.

Therefore, The length of the longest side of AABC is 4 units, and the area of AABC is equal to the area of ADEF.

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the first term of the geometric series is approximately 105.294.

How to solve the problem?

The formula for the sum of a geometric series is given by:

Sn = a1(1 - rⁿ)/(1 - r)

where a1 is the first term, r is the common ratio, n is the number of terms, and Sn is the sum of the series.

We are given that Sn = 3045, r = 2/5, and An = 120, where An is the nth term of the series. We can use these values to solve for a1.

First, we can use the formula for the nth term of a geometric series:

An = a1 * rⁿ⁻¹

Substituting An = 120 and r = 2/5, we get:

120 = a1 * (2/5)ⁿ⁻¹

We also know that the sum of the series is Sn = 3045. Substituting the formula for Sn and solving for n, we get:

3045 = a1(1 - (2/5)ⁿ)/(1 - 2/5)

12180 - 4(2/5)ⁿ = 5a1

a1 = (12180 - 4(2/5)ⁿ)/5

Now we can substitute this expression for a1 into the equation we obtained for An:

120 = [(12180 - 4(2/5)ⁿ)/5] * (2/5)ⁿ⁻¹

Simplifying and solving for n, we get:

n = log(12/5) / log(2/5)

Substituting this value of n back into the expression for a1, we get:

a1 = (12180 - 4(2/5) power (log(12//log(2/5))) / 5

Using a calculator, we can evaluate this expression to get:

a1 ≈ 105.294

Therefore, the first term of the geometric series is approximately 105.294.

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Value of side x in equilateral triangle is 6units.

An equilateral triangle is a type of triangle in which all three sides are of equal length. Equilateral triangles are also equiangular, meaning all three angles are of equal measure and are each 60 degrees. Because all three sides and angles are equal, equilateral triangles are symmetric about their center point, and their three medians, altitudes, and angle bisectors are all the same line.

Area of equilateral triangle = √3/4×a²

Given side length=12

So, area of equilateral triangle =√3/4×12²=62.35383

We know that

Area of triangle= ½×base×height

Given

Base=12

let height of triangle be=y

Area=½×12×y

62.35383=½×12×y

y=10.39

Using pythagoras' theorem,

c²=a²+b²

122=x²+10.392

x=√144-107.95

x=6

Hence, value of side x in equilateral triangle is 6units.

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Answer:  9.01

Step-by-step explanation:  8.5*0.02= 0.17 *3= 0.51+8.5=9.01

Answer:

the circumcenter of triangle RST is (-4, 3).

Step-by-step explanation:

To find the circumcenter of a triangle, we need to find the intersection of the perpendicular bisectors of its sides.

Let's first find the midpoints of the sides RS, ST, and RT.

Midpoint of RS:

x-coordinate = (-2 + (-6))/2 = -4

y-coordinate = (5 + 5)/2 = 5

Midpoint of RS is (-4, 5).

Midpoint of ST:

x-coordinate = (-6 + (-2))/2 = -4

y-coordinate = (5 + (-1))/2 = 2

Midpoint of ST is (-4, 2).

Midpoint of RT:

x-coordinate = (-2 + (-2))/2 = -2

y-coordinate = (5 + (-1))/2 = 2

Midpoint of RT is (-2, 2).

Now, let's find the equations of the perpendicular bisectors of RS and ST, and then find their point of intersection.

Perpendicular bisector of RS:

The slope of RS is (5 - 5)/(-6 - (-2)) = 0.

The midpoint of RS is (-4, 5).

So, the equation of the perpendicular bisector of RS is x = -4.

Perpendicular bisector of ST:

The slope of ST is (5 - (-1))/(-6 - (-2)) = -3/2.

The midpoint of ST is (-4, 2).

So, the equation of the perpendicular bisector of ST is y = (-3/2)(x + 4) + 2, which simplifies to y = (-3/2)x - 1.

Now, let's find the point of intersection of these two lines.

x = -4 for the perpendicular bisector of RS, so we substitute that into the equation of the perpendicular bisector of ST:

y = (-3/2)(-4) - 1 = 4 - 1 = 3.

Therefore, the circumcenter of triangle RST is (-4, 3).

Answer: I thank it is 200 point in 2 hour

Step-by-step explanation:

Answer: x = -2.5

Step-by-step explanation:

I think you meant 6x^2 + 15x = 0

6x^2 + 15x = 0

3x(2x + 5) = 0

2x + 5 = 0

2x = -5

x = -2.5

The premise is that both of my next-door neighbors and I have brick homes. So, all of the homes in our area are brick construction. A good illustration of inductive reasoning is this.

2. Given that the pattern appears to be multiplying by 3, then 6, then 9, then 12, and so on, the next multiplication fact is probably 37 x 15 = 555.

3.

(A) The number 101 comes next in the list.

(b) The following digit in the series is -10.

4. According to the formula n(n+1)/2, the first n positive integers are added together. Hence, 48(48+1)/2 = 1176 is the sum of the first 48 positive integers.

5.

(A) The formula n(3n-1)/2 yields the nth pentagonal number. Thus, 6(3x6-1)/2 = 91 is the sixth pentagonal number.

(b) The expression n(n+1)/2 yields the nth triangular number. Hence, 8(8+1)/2 = 36 is the eighth triangular number.

6. There are ten ways to use the four nickels, three dimes, and two quarters to make a 30-cent purchase from the vending machine.

7. The first week, Ronnie had $12 to his name.

8.a.The ones digit in the number 24000 is 6.

(b) 341's units digit is 3.

9. 19 rungs make up the ladder.

10. Catwoman owns 42 felines.

11. 58 nests would require 8 birdhouses, plus 2 additional nests.

12. A total of 60 pupils received an A or a B.

13.

(a) 550 cups are anticipated to be consumed in 2004.

(b) The year 2003 exhibits the biggest decline in cups.

14. Since 2001, the typical class size has risen.

15. During 2001 and 2002, as well as between 2004 and 2005, the average class size increased. From 2001 to 2003, the average class size grew by two pupils.

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Since the two equations represent the same line, there are infinitely many solutions to the system.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, each containing one or more terms, separated by an equal sign. The terms may contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. Equations are used to represent relationships between variables and to solve problems in mathematics, science, engineering, and many other fields. They can be classified based on their degree, number of variables, and the types of functions they involve. Linear equations, for example, involve only first-degree terms and are used to represent straight lines; quadratic equations involve second-degree terms and are used to represent parabolas.

Here,

To determine whether the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point, we can first put the equations in slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.

10y + 8x = 10

10y = -8x + 10

y = (-4/5)x + 1

5y - 5 = -4x

5y = -4x + 5

y = (-4/5)x + 1

Notice that the two equations have the same slope of -4/5 and the same y-intercept of 1. Therefore, the two lines are identical and intersect at every point on the line.

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Answer: To find the amount of border needed to put wallpaper around a rectangular bedroom, the formula for the perimeter of a rectangle is needed. The formula for the perimeter of a rectangle is:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width of the rectangle.

Step-by-step explanation:

Therefore, the sum of the first 6 terms of this arithmetic sequence is 57.

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant number to the previous term. The fixed constant number is called the common difference (d) of the sequence.

Here,

To find the sum of the first 6 terms of this arithmetic sequence, we can use the arithmetic sum formula:

Sn = n/2 * [2a + (n - 1)d]

where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

In this case, we have:

a = 2 (the first term)

d = 3 (the common difference, since each term is 3 more than the previous term)

n = 6 (the number of terms)

Substituting these values into the formula, we get:

S6 = 6/2 * [2(2) + (6 - 1)3]

= 3 * [4 + 15]

= 3 * 19

= 57

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In a perfectly competitive market, firms are price takers, meaning they have no market power and must accept the market price for their output.

A market price is the price at which a good or service is sold in a specific market. The forces of supply and demand determine market price in a competitive market.

Firms in a perfectly competitive market are price takers, which means they lack market power and must accept market prices for their output.

As a result, in a perfectly competitive market, the demand for multiple variable inputs is derived from the marginal product of each input.

The marginal product is the extra output generated by adding one more unit of an input while holding all other inputs constant.

Thus, the value of the marginal product, which is the marginal product multiplied by the market price of the output, is the demand for an input.

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The equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, x, can be represented as y = 2x + 125, where 2x represents the total amount she saves from her allowance and 125 represents the initial amount she saved.

This is a linear equation in slope-intercept form, where the slope of the line is 2, indicating that she saves $2 per day, and the y-intercept is 125, indicating that she had already saved $125 before starting to save from her allowance. To graph this equation, we can plot the y-intercept at (0, 125) and use the slope to find other points on the line. For example, after 5 days, she would have saved y = 2(5) + 125 = 135 dollars, giving us the point (5, 135). Plotting this point and connecting it with the y-intercept will give us a straight-line graph.

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Choose Download as ePub or Download as PDF from the Personal Books screen's export icon. The Apple Ibooks icon will say Transfer to Books when you select Open in.

A book is a device for storing data in the form either writing or images. Books are often made up of several pages that are bound together and covered in reeds, parchment, vellum, or paper.

Books are important in life, especially for young people. Reading books helps pupils learn more, improves their intelligence, and raises their awareness of the diverse nations and civilizations throughout the world.

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The correct order of the steps is:

1. Create a new document using a book template.
2. Add text to the book, then tap the More button in the upper-right corner.
3. Enter EPUB information, then tap Export.
4. Tap Export, then choose EPUB.
5. Choose Copy to Books to open the EPUB book in the Books app

.Your answer: To create an EPUB book and open it in the Books app, follow these steps in the correct order: 1. Create a new document using a book template. 2. Add text to the book, then tap the More button in the upper-right corner. 3. Tap Export, then choose EPUB. 4. Enter EPUB information, then tap Export. 5. Choose Copy to Books.

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Answer:

Jake's father can carry 10 and 5/7 lb of wood.

Step-by-step explanation:

Jake carried 6 and 1/4 lb of wood.

Let's convert this to an improper fraction:

6 and 1/4 = (4 * 6 + 1)/4 = 25/4

So, Jake carried 25/4 lb of wood.

Jake's father can carry 1 and 5/7 times as much as Jake.

Let's convert this to a fraction:

1 and 5/7 = (7 * 1 + 5)/7 = 12/7

So, Jake's father can carry 12/7 times as much as Jake.

To find out how many pounds Jake's father can carry, we need to multiply Jake's weight by 12/7:

Jake's father can carry = (25/4) * (12/7)

= (25 * 12) / (4 * 7)

= 300/28

= 10 and 5/7 lb (when simplified to a mixed number)

The distance between point A (6,3) and A' (2,1) is half of the original distance between A and B (6,3) and (15,3). Therefore, the scale factor is one half.

To determine the scale factor used to create the image of the second polygon A'B'C'D' from the original polygon ABCD, we can compare the side lengths of the two polygons.

The scale factor used to create the image is one half. This is because the distance between each vertex in the original polygon and the corresponding vertex in the image polygon is half of the original distance. For example,
Let's take the horizontal sides:
Side AB in polygon ABCD has length 15 - 6 = 9 units.
Side A'B' in polygon A'B'C'D' has length 5 - 2 = 3 units.

Now, we can find the scale factor by dividing the side length of A'B' by the side length of AB:
Scale factor = (A'B') / (AB) = 3 / 9 = 1/3

So, the scale factor used to create the image is one third.

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Answer:

S ========================= 9

because 9+ 1= 10

simple

Answer:

s=3

Step-by-step explanation:

3s+1 = 10

To solve for s in this two step equation, we must first subtract 1 from each side.

3s+1-1 = 10-1

3s = 9

Then divide by 3 on each side.

3s/3 = 9/3

s=3

Answer:

[tex]x {}^{ \frac{5}{8} } [/tex]

Step-by-step explanation:

[tex]1. \: \sqrt{x {}^{ \frac{5}{4} } } \\ 2. \: x {}^{ \frac{5 \times 1}{4 \times 2} } \\ 3. \: x {}^{ \frac{5}{4 \times 2} } \\ 4. \: x {}^{ \frac{5}{8} } [/tex]

The distance between town 1 and 2 is 83 miles

Word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

The distance between Town 1 and 3 is 110 miles and the distance between Town 2 and town 3 is 27miles.

Therefore the distance between town 1 and 2 is the difference between distance between town 1 and 3 and distance between town 2 and 3

This means that distance between town 1 and 2 = 110-27 = 83 miles.

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