Find the degree of this polynomial: ?
5x8 – 8x4 + 4

Using it's concept, it is found that the sample space of T and S is:

{{8, [850-1500]}, {9, [850-1500]}, {10, [850-1500]}, {11, [850-1500]}, {12, [850-1500]}, {13, [850-1500]}, {14, [850-1500]}}

The sample space is the set that contains all possible outcomes for an experiment.

In this problem:

Considering that for each time, the cost will be between $850 and $1500, the sample space for T and S is:

{{8, [850-1500]}, {9, [850-1500]}, {10, [850-1500]}, {11, [850-1500]}, {12, [850-1500]}, {13, [850-1500]}, {14, [850-1500]}}

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We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

what is  vertex ?

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. It is a common term used in geometry, graph theory, and other areas of mathematics.

In the given question,

We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

To see why, suppose there exists a walk w of odd length starting and ending at v, and suppose w is the shortest such walk. If w does not repeat any vertices, then we have found an odd cycle that does not repeat any vertices, and we are done.

Suppose instead that w repeats some vertex v' (not equal to v). Then we can split w into two walks, w1 and w2, where w1 starts at v, goes to v', and then returns to v, and w2 is the rest of w starting and ending at v'. Since v' is not equal to v, both w1 and w2 are walks of odd length, and both are strictly shorter than w. By the minimality of w, both w1 and w2 must contain odd cycles that do not repeat any vertices. We can then combine these cycles to form an odd cycle that does not repeat any vertices in G, and we are done.

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Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

B. 168 students

Step-by-step explanation:

Given that there are a total of 600 students.

28% of the students pack their lunch.

To find:

Total number of students who pack their lunch = ?

Solution:

Percentage of a given number is calculated using the following method.

\(y\%\) of a number \(x\) is given by:

\(x \times \dfrac{y}{100}\)

i.e. multiply the number by percentage to be found and divide by 100.

So, we have to find 28% of 600 here, to find the answer to the question.

\(\therefore\) Number of students who pack their lunch is given as: (Multiply the given number 600 with 28 and divide by 100.)

\(600 \times \dfrac{28}{100}\\\Rightarrow 6 \times 28\\\Rightarrow \bold{168}\)

So, the correct answer is:

B. 168

Answer:

The integer is 1

Step-by-step explanation:

Required

Translate and solve

Let the positive integer be x.

So, we have;

The square of the integer is: x^2

Plus 5 times its consecutive integer is: x^2 + 5(x + 1)

Equals 11 is: x^2 + 5(x + 1) = 11

So, we have:

\(x^2 + 5(x + 1) = 11\)

Open bracket

\(x^2 + 5x + 5= 11\)

Subtract 11 from both sides

\(x^2 + 5x -6= 0\)

Expand

\(x^2 + 6x - x-6= 0\)

Factorize:

\(x(x + 6) - 1(x+6)= 0\)

Factor out x + 6

\((x - 1) (x+6)= 0\)

Split

\(x - 1 = 0\ or\ x + 6 = 0\)

Solve for x in both cases

\(x = 1\ or\ x = -6\)

Since the number is positive, then \(x = 1\)

The hοle needs tο be 39 inches deeper.

A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.

The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).

Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:

6 feet - 2.75 feet = 3.25 feet

Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:

3.25 feet x 12 inches/1 fοοt = 39 inches

Therefοre, the hοle needs tο be 39 inches deeper.

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Answer:

ok so they purchased price of the car is $1000 and the asking price will be 20% of $1000 so $1000 is a 100% so to get 20% of $1000 it will be 100% + 20% to get 120 percent so the asking price is 120 per cent of $1000 so 120 percent of $1000 is equals to 1200 dollars then you are told that he could not sell it by that price so he reduced it by 20% so this $1200 is 100% so he reduced it by 20% so it will be 100% - 20% to get 80% so this person sold his car at 80% so we will get 80% of $1200 and we will get $960 so he made a loss of $40

Answer:

hope this helps and have a great dayyyyyy

Answer:

yes what we should by you

Step-by-step explanation:

rhsoba

Answer:

79 degrees

Step-by-step explanation:

180 - 73 - 28 = 79

Because a line is 180 degrees

Answer:

200% increase

Step-by-step explanation:

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

1. Muliplication Property of Equality

2. Simplifying

3. Addition Property of Equality

4. Simplifying

Step-by-step explanation:

First, get x-7 by itself by multiplying 2 on both sides. Simplify both sides to get x-7=-22. Add 7 to both sides to get x by itself to get x=-15.

The expression tan(arcsec(x/3)) can be written   \(1/3 \sqrt{x^2-9}\)  in algebraic form.

The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.

The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to \(1/3 \sqrt{x^2-9}\).

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The image of the rectangle is attached below.

The rectangle has a length of 2 cm and a width that is 2 times less, which means the width is 1 cm. To calculate the perimeter of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2(L + W), where P is the perimeter, L is the length, and W is the width.

Substituting the values, we get P = 2(2 + 1) = 2(3) = 6 cm.

Therefore, the perimeter of the rectangle is 6 cm.

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The inequality equation that models the situation is given as

           $9z + $15.50y ≥$410

According to the question we have been given that

   Money Alice has to earn at least = $410

   Money she gets for 1 hour in grocery store = $9

  Money she gets for 1 hour in tutoring = $15.50

We need write an inequality equation for these situation.

Let the number of hours she work at grocery store be z

Let the number of hours she works tutoring be y

As it is an inequality equation the inequality sign will be greater than that is '≥'.

Thus the inequality equation is given as

           $9z + $15.50y ≥$410

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Answer: 9x + 15.5y ≥ 410

She earns $9 per hour at the grocery store and $15.50 per hour while tutoring. At each job, the number of hours multiplied by the hourly wage will give the amount of money earned.

The amount earned at the grocery store

9x plus amount earned tutoring 15.5y is at least 410

The inequality that models this situation is therefore

9x+15.5y≥410

Answer:

120 cm²

Step-by-step explanation:

Volume = length x wight x height

Volume = 6 x 4 x 5

Volume = 120 cm²

Answer:

c = 22

d = 11

Step-by-step explanation:

11sq rt 3 = 19.05

sin 60 = 19.05/c

0.8660 = 19.05/c

0.8660c = 19.05

c = 22

using Pythagorean theorem

d^2 + (11sq rt 3)^2 = 22^2

d^2 = 484 - 363 = 121

d = 11

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

D) 675 units per day.

Step-by-step explanation:

We can write a function to model the situation.

The company is currently producing 275 units per day.

And it will increase its production by 50 units after each year.

Therefore, after y years, its production in units per day will be:

\(f(y)=275+50y\)

Then 8 years from now, the company will be producing:

\(f(8)=275+50(8)=275+400=675\text{ units per day.}\)

Our answer is D.

Answer:

y = 63360x

Step-by-step explanation:

we know 1 mile = 63360 inches

So: y = 63360x

x mile

& y inch

Answer:

  10

Step-by-step explanation:

The general term of an arithmetic sequence is given by ...

  an = a1 +d(n -1) . . . . where a1 is the first term and d is the common difference

__

This formula can be used to find the value of d. The first term is given as 1, and the 5th term (a5) is given as 41. The value of n for the 5th term is 5.

  an = a1 +d(n -1)

  41 = 1 +d(5 -1) . . . . . substitute known values

  40 = 4d . . . . . . . subtract 1, simplify

  10 = d . . . . . . divide by 4

The common difference of this sequence is 10.

Answer:

10

Step-by-step explanation:

Answer:

8x

Step-by-step explanation:

thats not the answer

The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).

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The solution of the trigonometric equation  are, \(x=\frac{\pi}{2},\frac{3\pi}{2}\)

Given equation are,

           \(cos(\frac{\pi}{4} -x)=\frac{\sqrt{2} }{2}sinx\)

We know that,  \(cos(A-B)=cosA cosB+sinAsinB\)

         \(cos(\frac{\pi}{4} -x)=\frac{\sqrt{2} }{2}sinx\\\\cos\frac{\pi}{4} *cosx+sin\frac{\pi}{4} *sinx=\frac{\sqrt{2} }{2}sinx\\\\\frac{\sqrt{2} }{2}cosx+\frac{\sqrt{2} }{2}sinx=\frac{\sqrt{2} }{2}sinx\\\\\frac{\sqrt{2} }{2}cosx=0\\\\cosx=0\\\\x=\frac{\pi}{2},\frac{3\pi}{2}\)

Hence, The solution of the trigonometric equation  are, \(x=\frac{\pi}{2},\frac{3\pi}{2}\)

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1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1.

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem.

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'.

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares. One square is attached to the side of the triangle with length 'a', and the other square is attached to the side of the triangle with length 'b'. These squares are constructed by transforming the previous image, specifically by adding the squares and adjusting their positions accordingly.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1. The length of the bottom side of figure 5 is equal to 'a' (the length of the side of the triangle in image 1), and the length of the right side of figure 5 is equal to 'b' (the length of the other side of the triangle in image 1).

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a^2 + b^2). In this case, figure 5 represents side 'a' and figure 6 represents side 'b'. So, their lengths squared (a^2 and b^2) added together equal the length of figure 7 squared (c^2).

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'. When we combine these two figures and the square attached to the hypotenuse (c), we see that they perfectly fill the large square in figure 10. This shows that the area of the square on the hypotenuse (c^2) is equal to the sum of the areas of the squares on the other two sides (a^2 + b^2). This visual representation provides a clear and tangible demonstration of the Pythagorean Theorem.

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Answer:

P=$254

Step-by-step explanation:

let Hot N' Spicy be x

and Mild Mannered be y

  the objective function is

38x+35y=P

the constraints are

1. tomato sauce

2x+3y=18--------1

2. hot peppers

2x+y=10--------2

solving 1 and 2 we have

using substitution method

2x+y=10--------2

y=10-2x

put y=10-2x in eqn 1

2x+3(10-2x)=18

2x+30-6x=18

2x-6x=18-30

-4x=-12

x=12/4

x=3

put x=3 in eqn 2 we have

2(3)+y=10

6+y=10

y=10-6

y=4

He should make 3 gallons of Hot N' Spicy

and 4 gallons Mild Mannered

38(3)+35(4)=P

114+140=P

254=P

P=$254

1. Two angles are adjacet when they are next to each other, that is, the share a side and the vertex.

2. Two angles anre supplementary when their sum equals 180º

3. Two anfgles are vertical angles when they share the vertex but no side, they are usually formed when two lines cross each other formin an X shape.

4. Linear pair angles are formed when two lines cross each other at one point and both angles are over the same line. These angles are always supplementary.

5. Complementary angles are those that add up to 90º.

For angles ∠D and ∠E, they share one side and vertex, so they are adjacent, and they add up to 90º |_, so they are complementary.