2. Will you consider these mathematical phrases as polynomials? Why
or why not?​

Answer:

45:34

Step-by-step explanation:

1575:1190

Divide both numbers by 35:

45:34

The least common denominator is 4x^2.

Answer:

Step-by-step explanation:

the least common denominator is 4 x^2

(x+1)/4x

3(x+1)/2x^2

To find the common denominator, find the prime factors of each denominator

4x =2*2*x

2x^2 = 2*x*x

We need to take the greatest number of each term

2:  We have two 2's in the first term and one 2 in the second term so we will take two 2's

x: we have one x in the first term and two x's in the second term so we take two x's

common denominator; 2*2*x*x

                                     4x^2

the lateral surface area of the triangular prism with measurement of 5cm, 5cm, 4cm, 6cm and 12cm is 140 cm².

To find the lateral surface area of a triangular prism, we need to calculate the sum of the areas of all the rectangular faces of the prism. In this case, the triangular prism has two triangular faces and three rectangular faces. The triangular faces have dimensions of 5 cm (base) and 4 cm (height), while the rectangular faces have dimensions of 5 cm (width), 6 cm (height), and 12 cm (length).

To calculate the area of one of the triangular faces, we use the formula for the area of a triangle:

Area = (1/2) x base x height

In this case, the base is 5 cm and the height is 4 cm, so the area of one triangular face is:

Area = (1/2) x 5 cm x 4 cm = 10 cm²

Since there are two triangular faces, the total area of the triangular faces is: Total area of triangular faces = 2 x 10 cm² = 20 cm²

To calculate the area of one of the rectangular faces, we use the formula for the area of a rectangle: Area = length x width

In this case, the dimensions of the rectangular faces are 6 cm (height) x 5 cm (width) and 12 cm (length) x 5 cm (width), so the areas of these faces are: Area of one rectangular face = 6 cm x 5 cm = 30 cm²

Area of another rectangular face = 12 cm x 5 cm = 60 cm²

Since there are three rectangular faces, the total area of the rectangular faces is: Total area of rectangular faces = 30 cm² + 60 cm² + 30 cm² = 120 cm²

Finally, the lateral surface area of the triangular prism is the sum of the areas of the triangular and rectangular faces:

Lateral surface area = Total area of triangular faces + Total area of rectangular faces

Lateral surface area = 20 cm² + 120 cm² = 140 cm²

Therefore, the lateral surface area of the triangular prism is 140 cm².

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The optimal amounts of Gatorade and cookies to buy are 4 bottles of Gatorade and 4 boxes of cookies, which gives a total cost of 4(1) + 4(2) = 12, the maximum possible utility for this budget

To find the optimal amounts of Gatorade and cookies to buy in order to maximize utility with a budget of $12, we can use the method of Lagrange multipliers.

Let x be the number of bottles of Gatorade to buy, and let y be the number of boxes of cookies to buy. We want to maximize the utility function:

U(x,y) = xy

Subject to the budget constraint:

1x + 2y = 12

To apply the method of Lagrange multipliers, we form the Lagrangian function:

L(x,y,λ) = xy - λ(1x + 2y - 12)

Taking partial derivatives of L with respect to x, y, and λ and setting them equal to zero, we get:

δL/δx = y - λ= 0

δL/δλ  = x - 2λ= 0

δL/δλ = 1x + 2y - 12 = 0

Solving these equations simultaneously, we get:

x = 4

y = 4

λ = 2

Hence, the optimal amounts of Gatorade and cookies to buy are 4 bottles of Gatorade and 4 boxes of cookies.

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The sequence generated recursively by the rule is 1, 0.5, 0, -5, -2.5, 2, 7.25, ...

A recursive rule is a mathematical rule that describes how to calculate the value of a term in a sequence or function based on the values of previous terms. In other words, a recursive rule defines a sequence or function in terms of itself.

To apply a recursive rule, we start with one or more initial terms and then use the rule to generate the subsequent terms. The rule involves a formula that expresses each term in the sequence or function as a function of the previous terms. This process continues indefinitely, generating an infinite sequence or function.

Recursive rules are often used in mathematics to define sequences and functions that have a recursive structure, such as the Fibonacci sequence or the factorial function. They can also be used to define algorithms for solving problems in computer science and other areas.

One advantage of recursive rules is that they can provide a concise and elegant way of defining complex sequences or functions. However, they can sometimes be difficult to work with, as they can lead to complicated and recursive formulas that are hard to evaluate or simplify.

To generate the sequence 1, 0.5, 0, -5, ... recursively, we can use the following rule:

a_n = (a_{n-1} - 3a_{n-2})/2

where a_n represents the nth term in the sequence.

Using this rule, we can generate the sequence as follows:

a_1 = 1 (given)

a_2 = 0.5 (given)

To find the next term, we use the recursive rule:

a_3 = (a_2 - 3a_1)/2 = (0.5 - 3(1))/2 = -1

Continuing in the same way, we can find the next terms:

a_4 = (a_3 - 3a_2)/2 = (-1 - 3(0.5))/2 = -2.5

a_5 = (a_4 - 3a_3)/2 = (-2.5 - 3(-1))/2 = 2

and so on. Thus, the sequence generated recursively by the rule is 1, 0.5, 0, -5, -2.5, 2, 7.25, ...

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$25 hourly is $52,000 per year.

To convert an hourly rate to an annual salary, we need to multiply the hourly rate by the number of hours worked per week, then by the number of weeks worked per year.

Assuming a standard work week of 40 hours and 52 weeks in a year, we can calculate the annual salary for an hourly rate of $25 as:

Annual salary = Hourly rate x Hours per week x Weeks per year

Annual salary = $25/hour x 40 hours/week x 52 weeks/year

Annual salary = $52,000

Therefore, an hourly rate of $25 is equivalent to an annual salary of $52,000.

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The angle of depression from the top of the taller building is equal to the angle of elevation from the top of the shorter building.

The angle of depression from the top of the taller building is the angle between the line of sight from the top of the taller building and the base of the shorter building. This angle is equal to the angle of elevation from the top of the shorter building, which is the angle between the line of sight from the top of the shorter building and the top of the taller building. Both angles are measured from the horizontal and are equal in b. This is because the two buildings are the same distance apart and the line of sight from the top of one building to the base of the other is the same as the line of sight from the base of one building to the top of the other.

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Using the strategy below, we can identify the lightest heart (the pure-hearted person) using the balance only twice, as required by the puzzle.

we can use the following strategy:

Divide the 8 people into 3 groups of 3, and leave 2 people aside.

Weigh any two of the three groups against each other using the balance.

If the two groups weigh the same, then the pure-hearted person must be in the remaining group of two that we left aside. Weigh one of the remaining people against another one from this group.

If they weigh the same, then the remaining person is the pure-hearted one. If one is heavier, then that person is a sinner, and the lighter one is the pure-hearted person.

If the two groups from step 2 are not of the same weight, then the pure-hearted person must be in one of these two groups. Take any two people from the group that weighs more and weigh them against each other.

If they weigh the same, then the pure-hearted person is in the remaining group that was not weighed, and we can find them by weighing one person from that group against another.

If one of the two people weighed in step 5 is lighter, then that person must be the pure-hearted person. If they are the same weight, then the pure-hearted person is in the other group that was not weighed, and we can find them by weighing one person from that group against another.

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Input x (0 1 2)-  Output y( 2 -1 -4) is ​represents the function y = -3x+2.The relationship between such a collection of input data and each output is how a function is defined.

A function is, to put it simply, a relationship between outputs in which each input is connected to exactly one output. For each function, there is a range, made the request, and domain. Typically, a function is written as f(x), where x stands for the output. It is possible for a function to be declared inside of a class, module, or other function.

To determine Function , we obtain,

y = -3x+2

y = -3(0)+2=2

y = -3(2)+2=-1

y = -3(2)+2=-4

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For some values, such as the speed of light or the separation between the Earth and the sun, scientists and mathematicians long ago realized they needed a simpler way to write and refer to these large numbers.

They developed/created scientific notation at that time.

For us to estimate the order of magnitude:

Firstly, write the number in scientific notation.

Secondly, Round up to the nearest integer times a power of ten or power of ten.

Thirdly, Apply these estimates to your calculations.

Fourthly, If possible, compare the result to the exact one.

Example question, How many orders of magnitude are there in one million, for instance?

Answer will be, In order to represent the number 1,000,000, we will move the decimal to the left, stopping just before the first digit. The order of magnitude is determined by the quantity of left moves you make. Since we moved it six times, there are six orders of magnitude between ten and one million, which means that ten times six is equal to one million.

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The total number of miles that Parker would have to run is given as follows:

88.41 miles.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

As the number of miles increases by 5% each week, the common ratio is obtained as follows:

100% + 5% = 105% = 1.05.

Hence the number of miles each week is given as follows:

Then the total number of miles is given as follows:

16 + 16.8 + 17.64 + 18.52 + 19.45 = 88.41 miles.

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The value of 1 dollar is 0.94 Euro

The United States dollar (symbol: $; code: USD; also abbreviated US dollar or US dollar to distinguish it from other dollar-denominated currencies; called dollar, US dollar, American dollar or colloquially alone) is the  currency of the United States dollar. United States and several other countries. The Coinage Act of 1792 established the American dollar along with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of dollar and cent coins. US banknotes are issued as Federal Reserve notes, often called greenbacks because they are predominantly green.

US monetary policy  is managed by the Federal Reserve System, which serves as the nation's central bank.

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The simplest form is (-2 ±√12)/2.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: x = (-4 ±√48)/4

We have to simplify the given term.

x = (-4 ±√48)/4

x =  (-4 ±√12×4)/4

x =(-4 ±2√12)/4

Now, we take 2 as common and get

x = (-2 ±√12)/2

Hence, the simplest form is (-2 ±√12)/2.

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Answer:1st and 3rd

Step-by-step explanation:

Answer: (-4, -2) and (-13, 0)

Used a calculator

The inequality for solving the problem is d * cost per day + 275 * $0.10 ≤ $140

To solve this problem, we need to write an inequality that represents the total cost of renting the car and driving the planned miles. The total cost is the sum of the daily rental fee (d times the cost per day) and the cost of driving the planned miles (275 times $0.10 per mile). We can write the inequality as follows:

d * cost per day + 275 * $0.10 ≤ $140

Next, we need to solve for d, the number of days Salma can afford to rent the car. To do this, we can rearrange the inequality to isolate d on one side:

d * cost per day ≤ $140 - 275 * $0.10

d ≤ ($140 - 275 * $0.10) / cost per day

Now we can plug in the given cost per day for the car rental and solve for d. For example, if the cost per day is $30, we would have:

d ≤ ($140 - 275 * $0.10) / $30

d ≤ ($140 - $27.50) / $30

d ≤ $112.50 / $30

d ≤ 3.75

Since Salma cannot rent the car for a fraction of a day, we need to round down to the nearest whole number. Therefore, Salma can afford to rent the car for at most 3 days while staying within her budget.

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The value of the converting 148 pounds to kilograms is given by               ( 67.1328 ) kilograms.

One kilograms is equal to 2.20462 pounds.

⇒ 2.20462 pounds = One kilograms

⇒ One pounds = ( 1 / 2.20462 ) kilograms

⇒ One pounds = ( 0.4536 ) kilograms

Substitute the required value we have,

⇒ 148 pounds = ( 148 × 0.4536 ) kilograms

⇒ 148 pounds =  ( 67.1328 ) kilograms

Therefore, the conversion of the 148 pounds to kilogram is equal to  ( 67.1328 ) kilograms .

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Answer:

x+y-200=0

Step-by-step explanation:

ax = x

by = y

c = 200 but we convert it to negative 200 after moving it from the RHS to LHS

So x+y=200 will be x+y-200=0 in the form ax + by + c =0

The factorial of a number n is the product of all positive integers up to and including n

The factorial function is typically represented using the "!" symbol, such that n! represents the product of all positive integers up to and including n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To represent the factorial function using product notation, we can write:

n! = ∏_{i=1}^n i

This means that we take the product of all positive integers from 1 to n, which is equivalent to computing n!. For example, using this notation, we can write:

5! = ∏_{i=1}^5 i = 1 x 2 x 3 x 4 x 5 = 120

Note that the product starts at i=1 and goes up to n, which includes all the positive integers we want to multiply together.

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None of the given equations gives the correct answer, the answer is none of the options.

The equation from the calculation is:

y = 375(0.9834)ˣ

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=". Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

The data gives the relation between time and temperature.

We are asked to find the time and temperature relation as an equation.

We are given five equations as options.

a) T(x) = 375(0.5)ˣ

x is time and T is temperature.

Now we will give the value of x = 10 in this equation.

T(10) = 375 * 0.5¹⁰ = 0.366

This is not the value given in the table.

So this is not the equation.

b) T(x) = -50x + 375

  T(10) = -50 * 10 + 375 = -500 + 375 = -125

This is not the equation.

c) T(x) = -25x² + 375

   T(10) = -25 * 10 * 1 0 + 375 = -2500 +375 = -2125

This is not the equation.

d) T(x) = 50x - 375

   T(10) = 50 * 10 - 375 = 500 - 375 = 125

This is not the equation.

e) T(x) = 25x² -75x + 375

  T(10) = 25 * 10 * 1 0 -75 * 10 + 375 = 2500 -750 +375 = 2125

The general form of the exponential equation is:

y = abˣ

375 = ab⁰= a

325 = ab¹⁰

275 = ab²⁰

275/325 = b¹⁰

b = 0.9834

So the equation for this data is:

y = 375(0.9834)ˣ

Since none of the given equations gives the correct answer, the answer is none of the options.

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When t = 4, the expression 3⋅2ᵗ evaluates to 48.

Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the given expression, all of which are separated by the arithmetic sign +.

An expression consists of one or more numbers or variables along with one more operation.

When t=4, the expression 3⋅2ᵗ evaluates to:

3⋅2⁴ = 3⋅16 = 48

Hence, when t = 4, the expression 3⋅2ᵗ evaluates to 48.

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The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is π/77 (243 - 9sqrt(3)).

To find the volume of the solid obtained by rotating the region bounded by the curves about the x-axis, we can use the method of cylindrical shells. This involves integrating the circumference of a cylindrical shell times its height to obtain the volume of each shell, and then adding up the volumes of all the shells to get the total volume.

First, let's find the points of intersection of the two curves:

2/7 x^2 = 9/7 - x^2

9/7 = 9/7 x^2 + 2/7 x^2

9/7 = 11/7 x^2

x^2 = 9/11

x = ±sqrt(9/11)

The solid we obtain by rotating this region about the x-axis will have cylindrical shells with height dx, radius x, and circumference 2πx. Therefore, the volume of each shell will be:

dV = 2πx × h × dx

where h is the difference between the y-values of the curves at x:

h = (9/7 - x^2) - (2/7 x^2) = 9/7 - 9/7 x^2

Therefore, the total volume of the solid will be:

V = ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) 2πx * (9/7 - 9/7 x^2) dx

V = 2π/7 ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) x(9 - 9x^2) dx

We can simplify the integrand by setting u = 9x^2:

du/dx = 18x

dx = du/18x

Substituting:

V = 2π/7 ∫(from u = 9/11 to u = 81/11) (1/2)u^(1/2) (9/2) (du/18x)

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / x du

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / sqrt(9/11 - u/11) du

This integral can be evaluated using a trigonometric substitution. Let u = 9/11 sin^2 θ, then:

du/dθ = (18/11) sin θ cos θ dθ

Substituting:

V = π/7 ∫(from θ = π/6 to θ = π/2) (81/121) sin^3 θ dθ

V = π/7 [(81/121) * (3/4) - (9/121) × (sqrt(3)/2)]

V = π/77 (243 - 9sqrt(3))

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Answer: we can't help you

Step-by-step explanation:

Sorry but it appears that there is an image that goes with this question but you didnt attach it so we can't answer your question

The solution for n of the expression in this problem is given as follows:

n = 5.

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

The mistake in the solution was applying the distributive property to 3(2n - 7), as 3 has to multiply both terms, 2n and -7, hence:

3(2n - 7) = 6n - 21.

Thus the solution to the expression is obtained as follows:

6n - 21 = 9

6n = 30

n = 30/6

n = 5.

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Answer: The value of sinB is b/c

Step-by-step explanation:since sinB =P/H

Here, P=perpendicular

         H=hypotenuse

so here, P=b and H=c

sinB=b/c

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The surface area of the given prism above would be = 606cm²

To calculate the surface area of the given prism is to add all the area of the faces.

The area of the two triangles = 2(1/2 base×height)

where base = 12 cm

height = 8cm

area = 1/2× 12×8

= 48 × 2 = 96cm²

Area of rectangle =3( l×w )= 3(17×10)

= 3×170 = 510cm²

Therefore the surface area of the prism = 96+510 = 606cm².

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The mode would remain the same because 24 is already a part of the set.

Mode is a measure of central tendency, or an average, in a set of numerical data. It is the most frequently occurring value in a set of data.

For example, consider the following set of numbers: 1, 2, 2, 3, 3, 3, 4, 4, 5. In this set, 3 is the mode since it appears most often. It occurs three times, while the other numbers occur fewer times.

Mode can be used with both continuous and discrete data. Continuous data can be divided into classes, and the mode is the most frequent class. For example, if the numbers above were in the following classes: 1-2, 3-4, 5-6, then 3-4 would be the mode since it occurs the most often.

Mode can also be used with categorical data. In this case, the mode is the most frequent category.

For example, if the data set consists of the categories blue, green, and red, and blue occurs most often, then blue is the mode.

24 is the most frequently occurring number in the set of 24, 58, 24, 24 53. So it is the mode. It appears 3 times, which is more than any other number.

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The value of the exponential equation is A = ( 8/7 ) x ^ -15/2

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = 8 / ( 7√x¹⁵ )   be equation (1)

On simplifying the equation , we get

The value of √x¹⁵ = x ^ 15/2

Now , the equation will be

A = ( 8/7 ) x ^ -15/2

Hence , the exponential equation is A = ( 8/7 ) x ^ -15/2

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The actual distance from Ferris to Butte is 10 miles shorter than the distance found by Wayne.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The actual distance is the hypotenuse of the right triangle, hence it is obtained as follows:

d² = 15² + 20²

d = sqrt(15² + 20²)

d = 25 miles.

The distance found by Wayne from the diagram is of 15 + 20 = 35 miles, then the difference is of:

35 - 25 = 10 miles.

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The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

The set of values that can be satisfies the given condition in the equation is known as the solution.  We can solve the equation by adding or subtracting the same integer from both sides. Here adding or subtracting doesn't change the value of the equation.

Here we have

√(x - 1) - 5 = x - 8  

Solve the above equation to get the solutions

√(x - 1) - 5 = x - 8    

Add 5 on both sides

√(x - 1) - 5 + 5 = x - 8 + 5

√(x - 1)  = x - 3  

Do squaring on both sides

[√(x - 1) ]² = (x - 3)²    

[ x - 1 ] = (x² + 9 - 6x)    

x² + 9 - 6x - x + 1 = 0

x² - 7x + 10 = 0  

Now factorize the above equation

x² - 5x - 2x + 10 = 0      

x(x - 5) - 2(x - 5) = 0

(x - 5) (x - 2) = 0

(x - 5) = 0     and     (x - 2) = 0

x = 5                       x = 2      

at x = 2 => √(2 - 1) - 5 = 2 - 8    

=> √1 - 5 = 2 - 8    

=>   - 4 = -6 [ which is not true ]

at x = 5 => √(5 - 1) - 5 = 5 - 8      

=> √(4 - 1) - 5 = - 3  

=> 2 - 5 = -3  [ which is true ]

Therefore,

The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

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