I'm having trouble with this problem, if anyone could help I would really appreciate it. Thank you :)

Answer:

Choice C; degree is 3

Step-by-step explanation:

The degree of the polynomial is the greatest of the exponents (powers) of its various terms.

So the degree of this polynomial is 3  which is choice C

We have the identity

[tex](a + b)^2 = a^2 + 2ab + b^2 = a^2 + ab + b (a + b) \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b (a + b)} \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}[/tex]

assuming [tex]a+b\ge0[/tex].

For the numerator, let [tex]b=1[/tex], so [tex]a\ge-1[/tex], which means

[tex]a^2 + a = x \implies a = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]

and so

[tex]\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}} = \dfrac{-1 + \sqrt{1 + 4x}}2 + 1 = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]

For the denominator, let [tex]b=-1[/tex] so that [tex]a\ge1[/tex]. Now

[tex]a^2 - a = x \implies a = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]

so that

[tex]\sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}} = \dfrac{1 + \sqrt{1 + 4x}}2 - 1 = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]

So, in the integral we can simplify and evaluate it to

[tex]\displaystyle \int_0^{2021} \frac{\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}}}{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{\frac{1 + \sqrt{1 + 4x}}2}{1 - \frac{1 - \sqrt{1+4x}}2} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{1 + \sqrt{1 + 4x}}{1 + \sqrt{1 + 4x}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} dx = \boxed{2021}[/tex]

Answer:

38

Step-by-step explanation:

[tex]3x {}^{2} y - x[/tex]

[tex] 3 \times ( - 2) { \\ }^{2} \times 3 - ( - 2)[/tex]

[tex]3 \times 4 \times 3+ 2[/tex]

[tex]36 + 2[/tex]

[tex]38[/tex]

Answer:

-1

Step-by-step explanation:

Answer:

-1 is the answer

Step-by-step explanation:

Increase in the length is 3.64 ft.

What is area of square?

The area of square is the product of side of the square.

i.e., Area of square =  side * side

Given that;

Yossi has garage whose area =262 ft²

And, 50% area is incremented.

Now, the New Area is calculated as;

Area = 262 × 150%

       = 393 ft²

As we know that;

Area of Square = (Length) × (Length)

Length = √393 = 19.82 ft

Also,

Length of garage = √262 = 16.18 ft

Hence, Increase in the length = 19.82 - 16.18 = 3.64 ft.

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Answer:

32

Step-by-step explanation:

1-295/2

Answer:

x>22/3 or x<-32/3

Step-by-step explanation:

Step 1 - add 6 to both side

Step 2 - divide both sides by two

Step 3 - Solve Absolute Value

We know either x+ 5/3 >9 or x+5/3<-9

Subtract 5/3 from both sides

Answer:

a diamond ♦ it as acute angles

Answer:29

Step-by-step explanation:14 multiplied by 29=406

Answer:

14 x 29 = 406

Step-by-step explanation:

so I believe it's 29

A baseball stadium has 45,000 seats. If tickets have been bought for 5/8 of the seats for the next game, then 45000−(5/8⋅45000)=16875 seats left.

We will subtract (5/8⋅45000) from 45000.

To subtract in mathematics is to take something away from a group or a number of things. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction problem are the minuend, subtrahend, and difference.

Subtraction is therefore the antithesis of addition. Thus, addition and subtraction are the polar opposites of each other. We could say that subtraction is the opposite of addition.

A subtraction number sentence is an equation that displays the result of subtracting one number from another. The first number is the minuend, the second number is the subtrahend, and the answer is the difference in a subtraction number sentence.

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Answer:

[tex]\mathrm{a + 4 = |+All~real~numbers|}[/tex] (+∞)

Any concerns please notify me, and have a great day!

Answer:

I believe its cubic polynomial because it has 3 degrees

Step-by-step explanation:

Answer:

quartic

Step-by-step explanation:

The degree of a polynomial is the highest exponent in the expression. Polynomials are classified by their degree

This polynomial has its highest exponent 4

Therefore the degree of this polynomial is 4

A polynomial with degree 4 is known as a quartic polynomial

Approximately 733395 babies were born in the UK in 2018.

Given,

In the UK in 2018 a baby was born every 43 seconds.

We have to find the total number of babies in the UK in 2018.

A baby in every 43 seconds.

There is 3600 seconds in an hour.

There is 24 hours in a day.

In 2018 there were 365 days.

So, the total number of babies born in 2018 in the UK:

= (Seconds in an hour × hours in a day × total days in 2018) ÷ 43

= (3600 × 24 × 365) ÷ 43

= 31536000 ÷ 43

= 733395.3488

≈ 733395

That is, in the UK in 2018 approximately 733395 babies were born.

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Macro bought 175 pens

The number of pens Macro bought can be calculated as follows

let x represent the number of pens bought

let y represent the number of pencils bought

x + y = 300.........equation 1

0.25x + 0.15y= 62.50.........equation 2

From equation 1

x + y= 300

x= 300-y

Substitute 300-y for x in equation 2

0.25(300-y) + 0.15y= 62.50

75 - 0.25y + 0.15y= 62.50

75 - 0.1y= 62.50

-0.1y= 62.50-75

0.1y= 12.5

y= 12.5/0.1

y= 125

Substitute 125 for y in equation 1

x + y= 300

x + 125= 300

x= 300-125

x= 175

Hence Marco bought 175 pens

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Considering the definition of perpendicular line, the equation of of perpendicular line is y= -3/4x + 5/2.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3y= 4x +7. Expressed in the form y = mx + b, you get:

y= (4x +7)÷ 3

y= 4/3x -+7/3

The line has a slope of  4/3. If you multiply the slopes of two perpendicular lines, you get –1, then:

4/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 4/3

slope perpendicular line= -3/4

So, the perpendicular line has a form of: y= -3/4x + b

The line passes through the point (6, -2). Replacing in the expression for parallel line:

-2= (-3/4)×6 + b

-2= -9/2 + b

-2+ 9/2= b

5/2= b

Finally, the equation of of perpendicular line is y= -3/4x + 5/2.

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Answer:

0.67

Step-by-step explanation:

Original price = $8.10

New price = $13.50

Increase in price = 13.50−8.10=$5.40

Ratio of the increase in price to the original price = 5.40 8.10=0.67

Answer:

[tex]\frac{-5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{-3}{4}[/tex] - [tex]\frac{-1}{3}[/tex]  Subtracting a negative number is the same as adding a positive

[tex]\frac{-3}{4}[/tex] + [tex]\frac{1}{3}[/tex]  Rewrite each fraction with a common denominator.  Let's use 12 as our new denominator.

[tex]\frac{-3}{4}[/tex] = [tex]\frac{-9}{12}[/tex]  multiple the top and the bottom of the first fraction by 3 to get the equivalent fraction [tex]\frac{-9}{12}[/tex]

[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{12}[/tex]  Multiple the top and bottom of the first fraction by 4 to get the equivalent fraction [tex]\frac{4}{12}[/tex].

Now, add the two fractions

[tex]\frac{-9}{12}[/tex] + [tex]\frac{4}{12}[/tex] = [tex]\frac{-5}{12}[/tex]  The denominator stays the same and you add the numerators.

Answer:

[tex]\sf A. \quad -3.5 < -\dfrac{10}{3}[/tex]

Step-by-step explanation:

Convert -3.5 into a fraction:

[tex]\implies \sf -3.5=-\dfrac{35}{10}=-\dfrac{\diagup\!\!\!\!5 \times 7}{\diagup\!\!\!\!5 \times 2}=-\dfrac{7}{2}[/tex]

Rewrite both fractions so that they have the same denominator:

[tex]\implies \sf -\dfrac{7}{2}=-\dfrac{7 \times 3}{2 \times 3}=-\dfrac{21}{6}[/tex]

[tex]\implies \sf -\dfrac{10}{3}=-\dfrac{10 \times 2}{3 \times 2}=-\dfrac{20}{6}[/tex]

[tex]\textsf{As }\: -\dfrac{21}{6} < -\dfrac{20}{6} \textsf{ then}:[/tex]

[tex]\sf \implies -3.5 < -\dfrac{10}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

If there are 13 men, then the ratio of men to the total is 13:26. If you simplify that, it would just be 1:2, so for every 2 students in the class, 1 of those students is a man. This would just be half.

Work Shown:

x = number of people in week 3

280/x = 4/3

280*3 = 4*x

x = 280*3/4

x = 210

The required solution of the given expression is -9.

A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Given:

The given expression is

-2-(+7)

According to given question we have

Number line is a line with 0 in the middle, and then increasing positive numbers to the right of the 0 and decreasing negative numbers to the left of the 0. The line is infinite in length and it's not possible to show the whole line, but we will illustrate where on the line 9 and -9 are located.

-2-(+7)

=-2-7

=-9

Therefore, the required solution of the given expression is -9.

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a > 4 for which the solutions of the inequality are all real numbers.

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a  for the given inequality.

a(x+3) < 5x+15-x

a(x+3) < 4x +15

ax+3a < 4x+15

Subtract 3a from both sides

ax+3a -3a< 4x+15-3a

ax < 4x+15-3a

ax-4x < 15-3a

x(a-4) < 15-3a

[tex]x < \frac{15-3a}{a-4}[/tex]

Like there is a variable a in the denominator, a-4 >0, then a>4.

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Answer:

8a^5 - 28a^4 + 2a^3 +29a^2 + 6a - 9

Step-by-step explanation:

(4a3-5a-3) × (2a2-7a+3)

= 4a^3 × 2a^2 + 4a^3(-7a) + 4a^3 × 3 - 5a × 2a^2 - 5a(-7a) - 5a × 3 - 3 × 2a^2 - 3(-7a) - 3 × 3

= 8a^5 - 28a^4 + 2a^3 +29a^2 + 6a - 9

Another name for a zero sum pair is additive inverse.

A number's cumulative is its inverse number. When a number is multiplied by its cumulative , the sum of both figures equals zero. The straightforward approach is to convert a positive number to a negative number and vice versa. We formerly know that 7(- 7) Equals 0. Accordingly,-7 is the cumulative of 7, and 7 is the cumulative  of-7.

Inverse cumulative Property

When the sum of two real figures is zero, each is said to be the cumulative  of the other.

Inverse Complement of Real figures

A whole number, a natural number, an integer, a bit, a numeric, or any real number can be specified.

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If [tex]x[/tex] is positive, then [tex]\tan^{-1}(x)[/tex] is between 0 and π/2, which means [tex]\cos(\tan^{-1}(x))[/tex] is between 1 and 0.

Let [tex]\theta = \tan^{-1}(x)[/tex]. Then [tex]\tan(\theta) = x[/tex], and it follows from the Pythagorean identity that

[tex]\sin^2(\theta) + \cos^2(\theta) = 1 \implies \tan^2(\theta) + 1 = \sec^2(\theta) \\\\ ~~~~ \implies \sec(\theta) = \sqrt{1 + \tan^2(\theta)} \\\\ ~~~~ \implies \cos(\theta) = \dfrac1{\sqrt{1+\tan^2(\theta)}} \\\\ ~~~~ \implies \cos(\tan^{-1}(x)) = \boxed{\dfrac1{\sqrt{1+x^2}}}[/tex]

We took the positive square root when solving for [tex]\sec(\theta)[/tex] because we know [tex]\cos(\theta)[/tex] is non-negative, between 0 and 1.

Answer:

Step-by-step explanation: just mutiply 7x3 you get 21

Answer: DG and EF are parallel. DE=13

Step-by-step explanation:

DG and EF are parallel. They are both right angled triangles.
EF/DG=DE/CD

5/1.25=DE/3.25

4=DE/3.25

4*3.25=DE

13=DE

The algebraic expression of the mathematical statement three more than a number, multiplied by five more than the number is (3 + x) * (5 + x)

The mathematical statement is given as

Three more than a number, multiplied by five more than the number.

Let the number be represented with x.

So, we have the following illustration

Three more than a number, multiplied by five more than the number ⇒ Three more than x, multiplied by five more than x

More than means +

So, we have the following illustration

Three more than a number, multiplied by five more than the number ⇒ 3 + x, multiplied by 5 + x

Multiplied by means *

So, we have the following illustration

Three more than a number, multiplied by five more than the number ⇒ (3 + x) * (5 + x)

Hence, the algebraic expression of the mathematical statement three more than a number, multiplied by five more than the number is (3 + x) * (5 + x)

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Answer:

Step-by-step explanation:

Answer:

a farmer has 9 1/ 2 ha of land . He needs 11/4 ha for each crops

the no of different crop he can plant is ..

Step-by-step explanation:

Charles is correct as the solution of the mathematical operation (6 + 6) × 6 is also 72 as 12 × 6 = 72.

So, 12 × 6 = 72

Now, let's do what Charles say as follows:
Break 12 as 6 + 6.

Therefore, Charles is correct as the solution of mathematical operation (6 + 6) × 6 is also 72 as 12 × 6 = 72.

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