find the degree of the polynomial 2x^6+x^3+5

Answer:

\(2 {x}^{2} + 5x - 3 = 0 \\ 2( {x}^{2} + \frac{5}{2} x - \frac{3}{2} ) = 0 \\ 2( {x}^{2} + \frac{5}{2} x + {( \frac{5}{4} )}^{2} ) - \frac{3}{2} - {( \frac{5}{4} )}^{2} ) = 0 \\ ( {(x + \frac{5}{4} )}^{2} = \frac{49}{16} \\ x + \frac{5}{4} = ± \frac{7}{4} \\ x = 0.5 \: \: and \: \: 3\)

Answer:

x= \(\frac{1}{2}\)     or     x= -3

Step-by-step explanation:

\(\boxed{x^{2} +kx=(x+\frac{k}{2})^{2} -(\frac{k}{2})^{2} }\)

First ensure that the coefficient of x² is 1.

x² +\(\frac{5}{2}\)x -\(\frac{3}{2}\)= 0

[x +(\(\frac{5}{2}\) ÷2)]² -(\(\frac{5}{2}\) ÷2)² -\(\frac{3}{2}\)= 0

(x +\(\frac{5}{4}\))² -(\(\frac{5}{4}\))² -\(\frac{3}{2}\)= 0

(x +\(\frac{5}{4}\))²- \(\frac{25}{16}\) -\(\frac{3}{2}\)= 0

(x +\(\frac{5}{4}\))² -\(\frac{49}{16}\)= 0

(x +\(\frac{5}{4}\))²= \(\frac{49}{16}\)

x +\(\frac{5}{4}\)= \(\sqrt{\frac{49}{16} }\)                (square root both sides)

x +\(\frac{5}{4}\)= ±\(\frac{7}{4}\)

x= -\(\frac{5}{4}\) +\(\frac{7}{4}\)       or       x= -\(\frac{5}{4}\) -\(\frac{7}{4}\)

x= \(\frac{1}{2}\)             or       x= -3

Answer:

P(pink) = 0.225

Step-by-step explanation:

We should ignore the spinner picture because it is a trick!

We need to use the data provided in the table

We need to find the probabilty of getting pink out of all the colors:

\(\frac{pink}{purple\ +\ pink\ +\ yellow\ +\ blue} = \frac{9}{12\ +\ 6\ +\ 9\ +\ 13}\\ = \frac{9}{40} = 0.225\ \ (22.5\%)\)

We use the probability notation:

P(pink) = 0.225

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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Answer:

(x, y) = (1, 4)

Step-by-step explanation:

Given:  x+y=5 and 2x-y=-2

Solve for y and x

x+y=5; solve for y

y = 5 - x; substitute into other equation

2x-y= -2

2x - (5 - x) = -2

2x - 5 + x = -2; combine x's

3x - 5 = -2; add 5 to both sides

3x =3; divide by 3

x = 1; use this to solve for y

x+y=5

1 + y = 5; subtract 1 from both sides

y = 4

(x, y) = (1, 4)

Answer:

B)34

Step-by-step explanation:

Answer:

B.34°

supplementary angles

their sum is 180

180=146+x

x=180-146=34

The expected number of coins that are heads at the end after Jennifer has tossed 64 fair coins and those that landed on tails were tossed again is 32. the expected number of coins that are heads at the end is 48.

Here is a detailed explanation:Jennifer tosses 64 coins, and each coin has an equal chance of landing on either heads or tails. Thus, the probability that any one coin lands on heads is 0.5, and the probability that it lands on tails is also 0.5.When Jennifer tosses the 64 coins, some of them will land on tails.

Those coins will be tossed again. However, the probability of getting heads or tails for these coins is still 0.5 since the coins are fair.Therefore, the probability that a coin that has already been tossed and landed on tails to land on heads the second time is also 0.5.

The same applies to the third toss. The probability that a coin will land on heads or tails is 0.5.The total number of coins that land on tails during the first toss is given by

64*0.5 = 32.

Since these coins are tossed again, the expected number of coins that land on tails for the second toss is given by

32*0.5 = 16.

The remaining coins that landed on heads during the first toss are not affected. Thus, the expected number of coins that landed on heads during the first toss is

64 - 32 = 32.

The total number of coins that landed on heads during the first toss is given by 32.

Adding the expected number of coins that land on heads during the second toss (16),

the expected number of coins that land on heads is

32 + 16 = 48.

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The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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The correct answer is:

C. True. If O is an eigenvalue of A, then the equation Ax=0x has only the trivial solution. The equation Ax=0x is equivalent to the equation Ax=0X and Ax=0 has only the trival solution if and only if A is not invertible.

What is an eigennvalue?

An eigenvalue is a scalar value associated with a square matrix. For a given matrix A, an eigenvalue λ represents a special scalar value such that when multiplied by a corresponding eigenvector v, the result is equal to the matrix A multiplied by that eigenvector.

This statement is a direct consequence of the definition of invertibility and the properties of eigenvalues. If 0 is an eigenvalue of A, it means that there exists a non-zero vector x such that Ax = Ox. In this case, A is not invertible because the existence of non-trivial solutions to Ax = Ox indicates that the system of equations represented by the matrix A  does not have a unique solution.

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Answer:

1.06 cups

Step-by-step explanation:

250 grams is equivalent to  1.06 cups

250 grams in cups is what?

⁠ One cup is equal to 250 grams of water.

160 grams, which is equal to 2/3 cup, or 5 2/3 oz.

- Some measuring spoons and cups have also ounce measurements for cooking.

You can use 8 4/5 oz in place of 250g to convert to ounces.

You divide the amount of grams by 28.35 to convert grams to ounces.

What is a gram ?

1/1000 kilogram is equal to one gram, which is also about equivalent to the mass of one cubic centimeter of water at its densest.

Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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Answer:

Step-by-step explanation:

To the nearest thousand the answer is 0.

If you meant thousandth then the second 4 to the right of the decimal point occupies the thousandth place. so that 4 is followed by a 3, that 4 is not changed.

The answer is 44.544

but it does depend on what you meant.

Answer:

287500

Step-by-step explanation:

Multiply 5 by 0.03 by 250000

Then add the results

Answer:37500 not 100% sure so becareful with ur grade

Step-by-step explanation:

Answer:

x = 1

y = -1

Step-by-step explanation:

A*B= (4y-8 3x-3)

1-) (4×2)+(3×y)= 3y+8

2-) (4×x)+(3×(-1))= 4x-3

AB=C

(3y+8 4x-3)=(5 1)

So

3y+8=5 ; y= -3/3 = -1

4x-3=1 ; x=4/4 =1

Answer:

4

Step-by-step explanation:

2(-3)=-6

(-6+(-2))/-2

(-6-2)/-2

-8/-2

4

Answer:

-30

Step-by-step explanation:

f(x) = 3 so f(-8) = 3;

g(x) = 5x + 7, so g(-8) = 5(-8) + 7 = -33

Then (f + g)(-8) = 3 - 33 = -30

This is the sum of two functions both evaluated at x = -8.

We have that f(x) exists described for all real values of x, except for \($x=x _0$\). \($\lim _{x \rightarrow x 0} f(x)$\)

The graph shows a rising trend when the derivative's sign is positive. In all cases where x > 0, the derivative's sign is positive.

A function is increasing, decreasing, or constant on an interval if the derivative is positive, negative, or zero on that interval.

It is possible to determine the slope of a tangent line to a curve at any time using a function's first derivative. The first derivative of a function provides us with a wealth of information about the function as a result of this definition. Obviously increasing if is positive. is decreasing if it is negative.

Remember that when we are taking the limit we are not evaluating the function in \($x_0$\), instead, we are evaluating the function in values really close to \($x_0$\) (values defined as \($\mathrm{xO}^{+}$\)and \($\mathrm{xO}^{-}$\), where the sign defines if we approach from above or bellow).

And because f(x) is defined in the values of x near \($x_0$\), we can conclude that the limit does exist if:

\($\lim _{x \rightarrow 0+} f(x)=\lim _{x \rightarrow 0-} f(x)$\)

if that does not happen, like in f(x) = 1 / x where \($x_0=0$\)

where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.

The complete question is:

Suppose that a function f(x) is defined for all real values of x, except x = xo. Can anything be said about LaTeX: \displaystyle\lim\limits_{x\to x_0} f(x)lim x → x 0 f ( x )? Give reasons for your answer.

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Answer:

A

Step-by-step explanation:

it should be A

The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

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In this case, the nurse should perform a complete physical exam to determine the cause of the patient’s symptoms. The nurse should also assess the patient's vital signs, including heart rate, blood pressure, and temperature.

Once the assessment is completed, the nurse should immediately initiate fluid resuscitation to prevent dehydration and hypovolemic shock. The nurse should also administer pain medication as ordered and elevate the head of the bed to relieve abdominal distention.In this case, the patient is exhibiting symptoms of dehydration, including vomiting and minimal intake, which may result in hypovolemic shock. The patient is also experiencing severe abdominal distention and pain, which may indicate a gastrointestinal obstruction or perforation. These symptoms can be life-threatening and require immediate intervention by the nurse. Therefore, the nurse should perform a complete physical examination to determine the cause of the patient's symptoms. This examination should include a detailed abdominal assessment, such as auscultation for bowel sounds, palpation for tenderness and rigidity, and percussion for the presence of ascites. The nurse should also assess the patient's vital signs, including heart rate, blood pressure, and temperature. The nurse should also monitor the patient's urine output to ensure adequate fluid replacement and to detect any signs of renal failure. The nurse should administer pain medication as ordered and elevate the head of the bed to relieve abdominal distention.

In conclusion, the nurse should perform a complete physical exam to determine the cause of the patient’s symptoms. The nurse should also assess the patient's vital signs, including heart rate, blood pressure, and temperature. Once the assessment is completed, the nurse should immediately initiate fluid resuscitation to prevent dehydration and hypovolemic shock. The nurse should also administer pain medication as ordered and elevate the head of the bed to relieve abdominal distention.

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Answer:

500 shots

Step-by-step explanation:

the question is 8% of what number is 40?

we can use this proportion:  is/of = %/100

let 'g' = number of goals

40/g = 8/100

cross-multiply to get:

8x = 4000

x = 500

Answer:

3n + 8 ≤ 32

Step-by-step explanation:

You multiply the 3 and the n together then add the 8 and it can't be more than 32 but it can be equal to 32

Answer:

infinite solutions

Step-by-step explanation:

2x-6 = 3x+1-X-7

Combine like terms

2x-6 = 3x-x +1-7

2x-6 = 2x -6

subtract 2x from each side

-6 = -6

Since this is a true statement, x can be any real number

Answer:

Mom drove for 18 hours.

Dad drove for 6 hours.

Step-by-step explanation:

Given that:

Number of hours for the driving duty = 24 hours

Speed at which the mom drove = 75 miles per hour

Speed at which the dad drove = 60 miles per hour

Total distance driven by both of them = 1710 miles

To find:

Number of hours for which each person drive for ?

Solution:

Let number of hours driven by dad = \(x\) hours

Let number of hours driven by mom =  (24 - \(x\)) hours

Let us have a look at the formula for Distance in terms of Speed and Time.

\(Distance = Speed \times Time\)

Distance traveled by Mom = \(75 \times x =75x \ miles\)

Distance traveled by dad = \(60(24-x) =144-60x\) miles

As per question statement:

\(75x+1440-60x=1710\\\Rightarrow 15x=1710-1440\\\Rightarrow 15x = 270\\\Rightarrow x = 18\ hours\)

So, Mom drove for 18 hours.

Dad drove for 6 hours.

John purchased 24 chocolates for Rs.96. How many chocolates can be purchased for Rs.72?

John purchased 24 chocolates = Rs.96.

Chocolates can be purchased for Rs.72 = x

24:96 = x:72

Means = Extreams

96 × x = 24 × 72

( 12 × 2 = 24, 12 × 8 = 96 )

(8 × 1 = 8, 8 × 9 = 72)

Therefore, 18 chocolates can be purchased for Rs.72

answer : the sum so obtained is rupees 300

Answer:

7.28

Step-by-step explanation:

You have to know the same rate for $4.16 for 4 tomatoes. Think about it

Answer:

x2-20x+100

Step-by-step explanation:

You have to factor the expression in order to get your answer

Do this by expanding out the expression: (x-10)(x-10) Then factor by multiplying each of the components! Use the FOIL acronym to help you. FOIL stands for First, Outer, Inner, Last. Meaning multiply the first numbers of the expressions together, then the outers, then the inner two numbers, then the last two numbers of the expression.

Multiply x and x to get  , multiply x and -10 to get -10x, multiply -10 and x to get -10x, multiply -10 and -10 to get 100. Add them all together:  . Then combine like terms

The required trinomial in standard form is x²+20x+100.

Important information:

Using the formula \((a+b)^2=a^2+2ab+b^2\), we get

\((x+10)^2=(x)^2+2(x)(10)+(10)^2\)

\((x+10)^2=x^2+20x+100\)

Therefore, the required trinomial in standard form is x²+20x+100.

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Answer:

A) On a graph, points (4, 10) and (6, 1) are outside of the cluster.

Answer:

A) The first option

Step-by-step explanation: