Write a proof for this statement

49^{1/2} and (8x)^{1/3} are correct in polynomial .

What is a polynomial, simply put?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

                           A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.

1)  [tex]49^{1/2}[/tex]  = √49

4)  [tex](8x)^{1/3}[/tex]   = ∛8x

option 1 and 4 is correct.

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The proportion is (y/x) = (26/20).

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

As per the given data:

Two figures below are similar figures.

All sides are given in the diagram.

If any two triangles are similar, then their corresponding sides are in the same proportion.

∴ (2.5 / x) = (1 / 1.5) = (3.25 / y)

= (5/2x) = (2/3) = (13/4y)

From cross-multiplication, we can find:

(y/x) = (26/20)

Hence, the proportion is (y/x) = (26/20).

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The day she will order both kinds of flowers on the same day is 12th day of the year.

LCM is the full form of least common multiple, it stands for the lowest common multiple. The least common multiple of two numbers can be mentioned as the smallest number that is a multiple of both of them.

here, we have,

Given:

Sunflower order = every 6 days

Daisies order = every 4 days

Find the lowest common multiple of 6 days and 4 days

6 days = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

4 days = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

The lowest common multiple of 6 days and 4 days is 12 days

Therefore, the day she will order both kinds of flowers on the same day is 12th day of the year.

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Answer:53

Step-by-step explanation:

The dimensions of the poster are approximately 10.64 inches by 1.15 inches.

What are dimensions of an objects?

Dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, breadth, and height.

According to the problem, the length of the poster is 8 more inches than two times the width, which can be expressed as:

length = 2x + 8

The area of the poster is given as 42 square inches, so we can set up the equation:

area = length * width

Substituting the expressions for length and width, we get:

42 = (2x + 8) * x

Expanding the right side, we get:

[tex]42 = 2x^2 + 8x[/tex]

Moving all terms to one side, we get:

[tex]2x^2 + 8x - 42 = 0[/tex]

Dividing both sides by 2, we get:

[tex]x^2 + 4x - 21 = 0[/tex]

We can solve for x using the quadratic formula:

x = (-4 ± √(4² - 41(-21))) / (2*1)

x = (-4 ± √88) / 2

x = (-4 ± 2√22) / 2

x = -2 ± √22

Since the width of the poster cannot be negative, we take the positive solution:

x = -2 + √22

Using this value, we can find the length of the poster:

length = 2x + 8 = 2(-2 + √22) + 8 = 2√22 + 4

Therefore, the length of the poster is approximately 10.64 inches (rounded to two decimal places).

Thus, the dimensions of the poster are approximately 10.64 inches by 1.15 inches.

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Answer: Unfortunately, the given information is not sufficient to answer the questions 1.1.1, 1.1.2, 1.1.3, and 1.1.4. However, I can provide some insights based on the given information.

1.1.1: B₁ is not defined in the given information. Without knowing what B₁ represents, we cannot determine its size.

1.1.2: We know that AB is parallel to QD, and CD = CB. Also, angle Ĉ = 110°. However, we don't know the location of point P, so we cannot determine the size of angle ABC.

1.1.3: We know that angle D₃ = 70°, but we don't know the location of point P, so we cannot determine the size of angle D₂.

1.1.4: We know that angle ₂ = 100°, but we don't know the location of point P, so we cannot determine the size of angle A₂.

Step-by-step explanation:

Answer:It has no solution

Step-by-step explanation:

Answer: No

Step-by-step explanation:

So you have to substitute the x and y with the numbers in the ordered pair.

y becomes 28.

x becomes 4.

So the equation 7 = y - 5x becomes 7 = 28 - 5(4).

Then, you solve.

7 = 28 - 5(4)

7 = 28 - 20

7 = 8

7 ≠ 8

So, the ordered pair is NOT a solution of the equation.

Hope this helps!!!

The differential of the function, f(x)=x^5 -8x is

df(x) = (5x^4 - 8) dx. That is dy = (5x^4 - 8) dx

From the question, we are to determine the differential of the given function

To find the differential of the function f(x), we use the formula:

df(x) = f'(x) dx

where f'(x) is the derivative of f(x) with respect to x, and dx is an infinitesimal change in x.

First, we need to find the derivative of f(x):

f'(x) = 5x^4 - 8

Now we can substitute this into the differential formula:

df(x) = (5x^4 - 8) dx

Hence, the differential of the function is

df(x) = (5x^4 - 8) dx

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Answer:25

Step-by-step explanation:39+26=65,

65-40=25,

39+26=25+40

Answer:

Step-by-step explanation:

65-40=25,

39+26=25+40

The range for both of the plots is same.

A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain.

The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.

Use the graphs of f(x)= and g(x) =3/x+3,  log2(x+3) to determine which of the following x+3 features they have in common.

The range is the same for all the plots.

For both cases the range is (-∞,∞)

Hence The range for both of the plots are same.

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Answer:60 cents per taco

Step-by-step explanation:

120/2=60

180/3=60

300/5=60

480/8=60

Answer:

1. 12

2. 6

3. 4.5

4. 7

Don't quite under #5

Explanation:

Sample mean = ΣX / n

1. 108 / 9 = 12

2. 72 / 12 = 6

3. 2 + 7 + 9 + 4 + 5 + 3 + 0 + 6 = 36 / 8 = 4.5

4. 8 + 2 + 5 + 7 + 12 + 9 + 11 + 3 + 6 = 63 / 9 = 7

Answer:

The new size of the diagram would be 28 cm by 16.8 cm. This is calculated by multiplying the original dimensions of 16 cm and 12 cm by the ratio of 7:4. Therefore, the new width of the diagram would be 16 cm x 7 = 112 cm and the new height would be 12 cm x 4 = 48 cm. The new size of the diagram is therefore 112 cm by 48 cm, which can be simplified to 28 cm by 16.8 cm

Step-by-step explanation:

A photocopier that enlarges in the ratio 7:4 will increase the size of the diagram by a factor of 7/4. To find the new size of the diagram, we can multiply the original measurements by the factor of enlargement.

The new width of the diagram will be:
16 cm × 7/4 = 28 cm

The new height of the diagram will be:
12 cm × 7/4 = 21 cm

Therefore, the new size of the diagram will be 28 cm by 21 cm.

Answer: The new size of the diagram will be 28 cm by 21 cm.

The amount of interest he has earned is $438

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

A = P ( 1+r/100) ^t

A is the amount after year t

P is the principal and r is the rate

800 = P( 1+ 12/100)⁷

800 = P( 1+ 0.12)⁷

800 = P ( 1.12)⁷

800 = P( 2.21)

P = 800/2.21

P = $362

A = P+ 1

I = A-P

I =800 - 362

I = $438

therefore the interest he earned is $438

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The inequality for this graph is given as follows:

y < 2.

The four inequality symbols, along with their meaning, are presented as follows:

For the graph in this problem, the inequality is composed by the values that are below y = 2, with an open interval as the line is dashed and not solid, hence it is defined as follows:

y < 2.

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Answer:

Option 1 is the correct choice

Step-by-step explanation:

All possible outcomes are represented with the exception of {HHT}

This would correspond to x

Option 1 is the correct choice

Therefore, the probability that X is between 5.5 and 7.5 is approximately 0.0808.

If a company creates apparel and sells it to people directly through an online site, it may be using direct distribution.

To solve this problem, we need to standardize the distribution of X to a standard normal distribution. This is done using the following formula:

Z = (X - μ) / σ

where Z is the standard normal variable, X is the normally distributed variable, μ is the mean of X, and σ is the standard deviation of X.

Using the given values, we have:

Z1 = (5.5 - 2.6) / 2.2 = 1.318

Z2 = (7.5 - 2.6) / 2.2 = 2.682

We can then find the probability using the standard normal distribution table or a calculator with a built-in normal distribution function.

Using the table or calculator, the probability is:

P(5.5 ≤ X ≤ 7.5) = P(1.318 ≤ Z ≤ 2.682) = 0.0808 (rounded to four decimal places)

Therefore, the probability that X is between 5.5 and 7.5 is approximately 0.0808.

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Answer:

To solve the problem, we simply need to multiply 1 4/5 (or 9/5) by 500:

1 4/5 gallons x 500 ft²/gallon = 9/5 gallons x 500 ft²/gallon = 4500/5 ft² = 900 ft²

Therefore, 1 4/5 gallons of paint will cover 900 square feet. The answer is D.

Answer:

You need a rizz god????

Step-by-step explanation:

The equation that represents Anthony's reading ⁵/₆ hours each day for 2 days is B. 2 × ⁵/₆ = 10 × ¹/₆.

An equation is an algebraic statement that two or more mathematical expressions share equality or equivalence.

Unlike mathematical expressions which combine variables with the mathematical operands, equations are depicted using the equal symbol (=) to show that the expressions are equal or equivalent.

2 × ⁵/₆ = 10 × ¹/₆

= 10/6 hours or 100 minutes (10/6 × 60)

or 1 hour 40 minutes.

Thus, the correct equation of Anthony's reading time for 2 days is Option B.

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Equation B. 2 × ⁵/₆ = 10 × ¹/₆ is the option that represents Anthony's reading ⁵/₆ hours each day for 2 days.

Answer: Without a perpendicular cut, we cannot determine the height of the triangle directly. However, we can use the Pythagorean Theorem to find it indirectly.

Let's assume that Francine has cut the paper into a right triangle ABC, where AB and BC are the legs of the triangle, and AC is the hypotenuse. Let x be the length of AB and y be the length of BC. We can then use the Pythagorean Theorem to find the length of AC:

AC^2 = AB^2 + BC^2

We don't know the exact values of AB and BC, but we do know that the area of the triangle is given by:

Area = (1/2) * AB * BC

We can use this formula to find the area in terms of x and y:

Area = (1/2) * x * y

Now we need to eliminate one of the variables (either x or y) so that we can express the area in terms of the other variable and AC. We can do this by rearranging the Pythagorean Theorem to solve for one of the variables:

x^2 = AC^2 - y^2

y^2 = AC^2 - x^2

Let's solve for y:

y^2 = AC^2 - x^2

y = sqrt(AC^2 - x^2)

Now we can substitute this expression for y into the formula for the area:

Area = (1/2) * x * sqrt(AC^2 - x^2)

To find the maximum possible area, we need to maximize this expression. We can do this using calculus, by taking the derivative of the expression with respect to x, setting it equal to zero, and solving for x. However, since we only need an approximate answer to the nearest tenth of a square centimeter, we can use trial and error to find the value of x that gives the maximum area. We can start by trying different values of x, and using a calculator to evaluate the expression and find the corresponding area.

Let's try a few values of x:

If x = 0, then the area is 0.

If x = AC/2 (i.e., if the triangle is isosceles), then the area is (1/8) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.

If x = AC/sqrt(3) (i.e., if the triangle is equilateral), then the area is (1/4) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.

Since the area is maximized when the triangle is equilateral, we can assume that the piece of paper is an equilateral triangle, and use the formula for the area of an equilateral triangle:

Area = (sqrt(3)/4) * side^2

where side is the length of one of the sides of the triangle. To find the side length, we need to know the length of AC. We don't know the exact value of AC, but we can estimate it by measuring the length of the longest side of the piece of paper (assuming that it is the hypotenuse of the triangle). Let's say that the longest side is 30 cm. Then, by the Pythagorean Theorem, we can find the length of the other two sides:

x^2 + y^2 = 30^2

x^2 + (sqrt(AC^2 - x^2))^2 = 30^2

2x^2 + AC^2 - x^2 = 900

x^2 = (900 - AC^2)/

Step-by-step explanation:

Answer: $17,788.20

Step-by-step explanation:

To calculate the monthly payment, we can use the loan formula:

P = (r * A) / (1 - (1 + r)^(-n))

where:

P is the monthly payment

A is the loan amount, which is the sale price of the car ($16,000) in this case

r is the monthly interest rate, which is the annual percentage rate (APR) divided by 12 (4% / 12 = 0.003333...)

n is the total number of payments, which is the number of years of the loan multiplied by 12 (5 years * 12 = 60)

Substituting these values into the formula, we get:

P = (0.003333... * $16,000) / (1 - (1 + 0.003333...)^(-60))

P ≈ $296.47

Therefore, the monthly payment is approximately $296.47, which is within the budget of $300/month.

To calculate the total cost of the car after the loan has been paid in full, we can multiply the monthly payment by the total number of payments (60) and add the original sale price of the car:

Total cost = P * n + A

Total cost = $296.47 * 60 + $16,000

Total cost = $17,788.20

Therefore, the total cost of the car after the loan has been paid in full is approximately $17,788.20.

Answer:

181

Step-by-step explanation:

Answer:

181

Step-by-step explanation:

Just Cause.

Answer:

7863

Step-by-step explanation:

i donk know soeet

The two lines are intercept of each other and can intersect each other and are perpendicular to each other.

With examples, what is line intercept sampling?

To calculate the cover of specified classes in the landscape, such as forests or different types of forests, line intercept sampling is utilized.

                                        Over the region of interest, line samples are randomly placed, and it is then examined what percentage of each sample line falls into the target area class.

The points at which a line crosses an axis are known as the xxx-intercept and the yyy-intercept, respectively.

Thus, the two lines are intercept of each other and can intersect each other and are perpendicular to each other.  

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