You are building a multi-level deck. a. For each level, write a polynomial in standard form that represents the area of that level. Then write the polynomial in standard form that represents the total area of the deck. Level 1: Level 2: Total area: b. What is the total area of the deck when x=20? Total Area: ft2 c. A gallon of deck sealant covers 400 square feet. How many gallons of sealant do you need to cover the deck in part (b) once? gallons

The equivalent expressions of the given expression are ⁵√x³, and  [tex](x^3)^{1/5}[/tex]  . The correct answer would be options (B) and (D).

The expression is given in the question, as follows:

[tex]x^{3/5}[/tex]

We have to determine the equivalent of the given expression.

As per option (A),

³√x⁵ = [tex](x^5)^{1/3}[/tex] = [tex]x^{5/3}[/tex]

This is not equivalent to the given expression.

As per option (B),

⁵√x³ = [tex]x^{3/5}[/tex]

This is equivalent to the given expression.

As per option (C),

[tex](x^5)^{1/3}[/tex] = [tex]x^{5/3}[/tex]

This is not equivalent to the given expression.

As per option (D),

[tex](x^3)^{1/5}[/tex] = [tex]x^{3/5}[/tex]

This is equivalent to the given expression.

As per option (E),

(⁵√x)³ = [tex](x^{1/5}) ^3[/tex] = [tex]x^{1/75}[/tex]

This is not equivalent to the given expression.

As per option (F),

(³√x)⁵ = [tex]x^{1/243}[/tex]

This is not equivalent to the given expression.

Hence, the correct answer would be options (B) and (D).

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The measure of angle FAB is 13x6°-3° = 78°-3°=75°.

An angle is a figure formed when two straight lines, or rays, intersect at a single point. There are many different types of angles, including acute angles, obtuse angles, right angles, reflex angles, and straight angles. Angles are measured in degrees, with a full rotation being 360 degrees.

We know outer angle of a triangle is equal to the sum of the two opposite interior angles
So, from triangle ABC,
13x - 3 = 3x + 2 + 55°
So, 13x - 3x = 57° + 3°
So, 10x = 60°
So, x = 60°/10 = 6°
So, Angle FAB = 13 x 6° - 3° = 78° - 3° = 75°

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The common difference will be equal to 3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression. A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Given that the data for the arithmetic sequence is a₁= -10, an = 26, Sn = 80, and the total number is n = 13.

The common difference will be calculated as,

an = a₁ + d ( n - 1 )

26 = -10 + d ( 13 - 1 )

d = 36 / 12

d = 3

Hence, for the arithmetic progression, the common difference is 3.

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The respective exterior angles are 155°, 55°, 150°

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: The angles of the triangle as 30°, 25°, and 125°

We know that sum of an exterior angle is the sum of the two non-adjacent angles

Thus we have ∠DBC= 30+125=155°

∠ECA=30+25=55°

∠FAD=25+125=150°

Hence, The respective exterior angles are 155°, 55°, 150°

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The value of x and y in the equations are 0 and -1 respectively

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3.

-2y = 2-3x equation 1

-5y = 10 - 5x equation 2

rearranging the equations

3x-2y = 2

5x - 5y = 10

using elimination method

15x - 10y = 10 equation 3

15x - 15y = 15 equation 4

subtract equation 3 from 4

- 15y +10y = 5

-5y = 5

divide both side by -5

y = -1

substitute -1 for y in equation 1

-2(-1) = 2-3x

3x = 2-2

3x = 0

x = 0/3

x = 0

therefore the value of x and y are 0 and -1 respectively.

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Answer: One solution

Step-by-step explanation:

21x - 33 = 6x + 12

15x = 45

x = 3

One solution

The correct statement is -4<x<-3

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph of a polynomial function.

let the function be f(x) then from the graph we can clearly observe that

f(x)>0 for x∈[-4,-3)

Thus x lies between -4<x<-3

Hence, The answer is -4<x<-3

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Answer:

8z

.......................

Answer:

To compare the speaking rate of Lincoln and King, we need to find out how many words per minute each of them spoke.

First, we'll find Lincoln's speaking rate:

He gave a 272-word speech that lasted 2 minutes and 17 seconds.

we can convert 2 minutes and 17 seconds to seconds by multiplying 2 minutes by 60 seconds/minute and adding 17 seconds, which gives us 137 seconds.

Now we can divide the number of words by the number of seconds to find the words per second:

272 words / 137 seconds = 2 words/second

To convert words per second to words per minute we need to multiply by 60 seconds/minute:

2 words/second * 60 seconds/minute = 120 words/minute

Now we'll find King's speaking rate:

He gave a 1,667-word speech that lasted 17 minutes and 1 second.

We can convert 17 minutes and 1 second to seconds by multiplying 17 minutes by 60 seconds/minute and adding 1 second, which gives us 1021 seconds.

Now we can divide the number of words by the number of seconds to find the words per second:

1,667 words / 1021 seconds = 1.633 words/second

To convert words per second to words per minute we need to multiply by 60 seconds/minute:

1.633 words/second * 60 seconds/minute = 98.00 words/minute

Now we can subtract King's speaking rate from Lincoln's speaking rate to find out how many more words per minute Lincoln said than King:

120 words/minute - 98.00 words/minute = 22 words/minute

So Lincoln spoke 22 words per minute more than King.

You rewrite the expression with radical exponent as 4 ⁹√x²

A radical exponent is a notation used to indicate that a number or variable is being raised to a fractional power. It is written as the radical symbol (√) before the base and the fractional exponent written on top of the radical.

To rewrite the expression, you need to use simply the indices.

(64x^(2/3) )^(1/3) = 64^(1/3) × x^(2/3 ×1/3)

                          = (64)^(1/3) × x^(2/9)

                          = 4x^(2/9)

                          = 4 ⁹√x²

The exponent property used here depicts how to solve numbers with fractions as exponent.

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Explanation:

There are 17 people under age 25.

There are 17 people that got a B.

17+17 = 34 people so far in either group. However, notice that we double-counted the people who are both under 25 and got a B. There are 5 such people we double-counted here.

Subtract off 5 to correct for this erroneous double-counting

34-5 = 29

There are 29 people who either...

This is out of 48 people total.

To arrive at the probability we want to find, divide the two values we found: 29/48

Optionally you can convert that fraction to decimal form, but I think it's better to stick with the fraction (since it's most exact).

Answer: D, 128 boxes

Step-by-step explanation:

There are 8 cutting machines that each cut 12 boxes every 3/4 minutes. 8x12=96. Divide that by 3 which is 32 boxes a 1/4 minute. Then multiply that by 4 to get a whole minute which is 128 boxes.

Answer:

We can use algebra to solve this problem. Let's call the unknown number x.

We are given that 10% of x is 40, so we can write that as:

x * 10% = 40

x * 0.1 = 40

We are also given that 55% of x is 220, so we can write that as:

x * 55% = 220

x * 0.55 = 220

We can now use these two equations to solve for x.

From the first equation, x = 40 / 0.1 = 400

We can substitute that value of x into the second equation to check if it's true.

400 * 0.55 = 220

Now, we have the value of x, we can use it to find 65% of that number.

x * 65% = x * 0.65 = 400 * 0.65 = 260

So, 65% of that number is 260

Answer:

260

Explanation:

Formulate: 220+40

----------------------/\  You should know the answer by now

Therefore , the solution of the given problem of trapezium comes out to be they are similar , therefore each side of trapezium will be equal

so x = 3

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is known as Trapezium in the United Kingdom and other English-speaking countries. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's base is defined as its parallel sides. An identical one set of opposite sides that are parallel to one another define a trapezoid.

Here,

Given :

we have similar trapezium as a figure 1 and figure 2

So ,

We can see :

they are in ratio

as,

=> 10/6 = 5/x

=> x = 5*6/10

=> x =30/10

=> x =3

since they are similar , therefore each side of trapezium will be equal so x = 3

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On solving the provided question, we can say that the equation is, y = -48.3 ÷ (-7)=​48.3/7 = 6.9

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

the equation is, y = -48.3 ÷ (-7)=​48.3/7 = 6.9

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Answer:

y = -5x +77

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

77 - y = 5x

Subtract 77 from each side

77-y-77 = 5x-77

-y = 5x-77

Multiply each side by -1

y = -5x +77

Answer:

y = - 5x + 77

Step-by-step explanation:

Slope intercept form means,

Here,

m - slope of the line

c - y intercept

And now to write the given expression in slope intercept form you can simply make y the subject in the equation.

Let us write it now.

77 - y = 5x

Subtract 77 from both sides.

-y = 5x - 77

To make y value positive multiply the whole equation by -1.

y = - 5x + 77

If the 3 sides are given, then we can create only one unique triangle.

Here we want to see how many unique triangles can be formed with the given side lengths:

Notice that the 3 sides of the triangle are given. Then the triangle is completely defined, (remember the side-side-side criteria)

That is enough to conclude that only one unique triangle can be made with the given side lengths (though that triangle could be translated or rotated to get similar triangles).

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It is given that m∠AOB = 42° and m∠EOF = 66°. By the congruent rule m∠EOF ≅ m∠BOC. Therefore, m∠BOC = 66°. By the sum of m∠AOB and m∠BOC, m∠AOC = 108°, and by the supplementary rule m∠AOC + m∠COD = 180°. After application of the supplementary rule, m∠COD = 72°

Congruent angles are angles that have the same measure, in degrees and are often represented by the symbol "≅"

m∠EOF and m∠BOC are vertical angles and so they are equal and satisfy the congruent rule.

The angles m∠AOB and m∠BOC form the larger angle m∠AOC so;

m∠AOC = 42° + 66° = 108°

The supplementary rule states that if two angles add up to 180°, they are considered supplementary angles, thus m∠AOC + m∠COD = 180° is correct as m∠AOC and m∠COD both lie on a straight line AD.

Therefore, application of the supplementary rule will give the size of the angle m∠COD = 72° as follows:

108° + m∠COD = 180°

m∠COD = 180 - 108°

m∠COD = 72°.

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Considering the definition of an inequality, the required inequality is for x ≤  4.6 and the number of people who can go to the amusement park must be less than 4.

An inequality is an inequality between two algebraic expressions of one or more unknowns, connected through the signs:

The inequality between the two algebraic expressions only holds, or rather, is only true for certain values of the unknown.

Being "x" the number of people who can go to the amusement park, and considering that:

the inequality that expresses the previous relationship is

10.50 + 32.50x ≤ 160

Solving:

32.50x ≤ 160 - 10.50

32.50x ≤ 149.5

x ≤ 149.5÷ 32.5

x ≤ 4.6

Finally, the required inequality is for x ≤  4.6 and the number of people must be less than 4.

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The size of the actual car is 186 inches

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Represent the size of the actual car by x and the size of the model car by y

then y = 1/24 of x

y = x/24

now, y = 7.75

x = 7.75 ×24

x= 186 inches

Therefore if the model size is 7.75 inches, then the size of the actual car is 186 inches

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The actual length of the car is 0.32 inches

A model car is 1/24 the size of the actual car

The length of the model car is 7.75 inches

Therefore the length of the actual car can be calculated as follows

1/24 × 7.75

= 7.75/24

= 0.32

Hence the actual car is 0.32 inches long

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Answer:

1 3 5 15 and its a composite

Step-by-step explanation:

i went online

Step-by-step explanation:

15 can be factorised as ,

1 × 15

3 × 5

5 × 3

15 × 1

so all the factors of 15 are 1 , 3 , 5 and 15

since 15 has more than 2 factors that is more than 1 and itself, so it is composite number.

And we are done!

- Rishabh

The difference between two natural numbers is greater than 6 and less than 11. The greater of the two numbers is 14. There are 5 possible values for the unknown number.

These integers that start at 1 and go all the way up to infinity are known as natural numbers or counting numbers. You can use numbers to count things, represent or exchange money, determine the temperature, tell the time, and many other things. Since they are used to count things, these numbers are known as "natural numbers." It may be 5 glasses, 6 books, 1 bottle, and so on while counting the objects. Thus, counting numbers is a different term for natural numbers. Natural numbers are a group of all whole integers other than 0. These numbers are crucial to daily interactions and communication.

Let's call the unknown number x. We know that:

x - 14 > 6 and x - 14 < 11

x > 20 and x < 25

Now we can see that there are 5 possible values for x: 21, 22, 23, 24 and 25.

Therefore, there are 5 possible values for the unknown number.

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Answer:None

Step-by-step explanation:

Upon solving the given polynomial equation, Correct option is C, [tex]\frac{- 2(x + 6)}{(x + 4)(x-4)}[/tex]

An equation with many terms made up of integers and variables is referred to as a polynomial equation. Exponents for polynomials can range in value. A polynomial's degree is represented by its highest exponent. How many roots can be found in a polynomial problem is indicated by the degree. For instance, the equation has three roots if the largest exponent is 3.

The values of x where y = 0 are the roots of the polynomial equation. The polynomial equation can be written using its roots if we are aware of them.

Given ,

[tex]\frac{x}{x^{2} - 16 } - \frac{3}{x - 4}[/tex]

Taking [tex]\frac{1}{(x - 4)}[/tex] as common factor,

[tex]\frac{1}{(x - 4)} (\frac{x}{x + 4} - 3 )[/tex]

Taking LCM,

[tex]\frac{1}{(x - 4)} (\frac{x - (3 \times (x+4)}{x + 4} )[/tex]

[tex]\frac{x - 3x - 12}{(x + 4)(x-4)}[/tex]

[tex]\frac{- 2x - 12}{(x + 4)(x-4)}[/tex]

[tex]\frac{- 2(x + 6)}{(x + 4)(x-4)}[/tex]

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The values from the evaluation of the quartic function, f(x) = x⁴ + 3·x³ - 15·x² - 19·x + 30, are as follows;

Part A: x-intercepts; x = -5, -3, 1, 3

y-intercept; y = 30

The x- and y-intercepts are found using f(x) = 0, and x = 0, respectively

Part B: Local minimums; (-3.87062, -70.7), (2.18282, -194.93)

Local maximum; (-0.5622, 35.5)

Part C: The graph is W shaped with f(x) increasing to ∞ as x increases to -∞ and +∞

The function is neither even nor odd

A quartic function is a polynomial of degree 4.

The specified function  is presented as follows;

f(x) = x⁴ + 3·x³ - 15·x² - 19·x + 30

Part A: The x-intercept is the point the graph intersects the x-axis. Therefore, at the x-intercept, using an online tool, we get;

f(x) = 0 = x⁴ + 3·x³ - 15·x² - 19·x + 30 = (x - 1)·(x + 3)·(x - 3)·(x + 5)

The points at which the function, intersects the x-axis are therefore. where;

(x - 1) = 0, and (x + 3) = 0, (x - 3) = 0, (x + 5) = 0

The coordinates of the x-intercepts are; (1, 0), (-3, 0), (3, 0), (-5, 0)

The y-intercepts are the point where the function intersects the y-axis, which is the point x = 0

The y-intercept is therefore;

x = 0, f(0) = 0⁴ + 3 × 0³ - 15 × 0² - 19 × 0 + 30 = 30

Part B: The local maximum and local minimums are the points where the derivative of the function is zero, which is found as follows;

f'(x) = 4·x³ + 9·x² - 30·x - 19 = 0

The solution obtained using an online tool are;

x ≈ -0.5622, x ≈ 2.18282, x ≈ -3.87062

The second derivative is; f''(x) = 12·x² + 18·x - 30 = 0

The values at the second derivative, we get;

f''(-0.5622) = 12×(-0.5622)² + 18×(-0.5622) - 30 ≈ -36.3

f(-0.5622) = (-0.5622)⁴ + 3×(-0.5622)³ - 15×(-0.5622)² - 19×(-0.5622) + 30 = 35.5

Therefore;

f''(2.18282) = 12×(2.18282)² + 18×(2.18282) - 30 ≈ 66.5

f(2.18282) = (2.18282)⁴ + 3×(2.18282³ - 15×(2.18282)² - 19×(2.18282) + 30 = -194.93

f''(-3.87062) = 12×(-3.87062)² + 18×(-3.87062) - 30 ≈ 80.1

f(-3.87062) = (-3.87062)⁴ + 3×(-3.87062)³ - 15×(-3.87062)² - 19×(-3.87062) + 30 = -70.7

Therefore, the function increases in the interval, -3.87062 ≤ x < -0.5622

The function decreases in the interval; -0.5622 < x < 2.18282

Part C; The shape of the quartic function, f(x) = x⁴ + 3·x³ - 15·x² - 19·x + 30, in which the coefficient of x⁴ is 1 is the shape of a W.

The end behaviour is that as x approaches -∞ and +∞, the function, f(x), approaches +∞

The even and odd function test for the function is as follows;

f(x) = x⁴ + 3·x³ - 15·x² - 19·x + 30

f(-x) = (-x)⁴ + 3·(-x)³ - 15·(-x)² - 19·(-x) + 30 =  x⁴ - 3·x³ - 15·x² + 19·x + 30

Therefore, f(x) ≠ f(-x), the function is not even

Similarly, -f(x) ≠ f(-x), the function is not odd

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monthly payments for the student loan will be $212.66.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

student loan totaling $63,800 when you graduate from college.

The interest rate is APR = 4%, and the loan term is 25 years.

S = 63,800*4*25/100 =63800

Monthly it will take 63800/12*25 =  $212.66

Hence, monthly payments for the student loan will be $212.66.

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Answer:

21

Step-by-step explanation:

12 plus 9

Akifumi is correct because both yield the same answer. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

All real numbers can be expressed using four basic mathematical operations, and these are:

1. The addition operator ('+') is used to calculate the sum of the numbers.

2. Subtraction with the sign "-," which yields the numbers' differences.

3. When the outcome is the product of the numbers, multiply ('×').

4. Division ('÷'), which results in the quotient of the numbers.

In order to find whether Akifumi is correct or not, we will find the answer of both.

So, 1½ times as much as 20 can be represented as

1.5 * 20 = 30

So, we get the total of 30.

The quotient of 20 and 2 comes out to be 10.

Now, adding 20 to this, we get

10 + 20 = 30

So, we get the total of 30.

Hence, Akifumi is correct because both yield the same answer.

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Answer:

8.60cm

Step-by-step explanation:

a/sinA=b/sinB

15/sin90⁰=x/sin35⁰

cross multiply

15sin35⁰=xsin90⁰

8.6036=x

x=8.60cm