If y*=y1/2(y2+1) then -3(16* - 9*) = -10.5y1(y2 + 1), called polynomial.
What is a polynomial?A polynomial is an expression that consists of variables, numbers, and operations (like addition, subtraction, multiplication, and division). It is similar to a mathematical equation, but instead of an equals sign, it uses coefficients and variables in a power form. The power of a polynomial is determined by the highest power of the variables in the expression.
For example, if the polynomial is x2 + 5x + 2, then the power is 2. Polynomials are used in many areas of mathematics, such as calculus, algebra, and number theory.
If y*= y1/2(y2+1) then -3(16* - 9*)
= -3(16(y1/2(y2 + 1)) - 9(y1/2(y2 + 1)))
= -3(8y1(y2 + 1) - 4.5y1(y2 + 1))
= -3(3.5y1(y2 + 1))
= -10.5y1(y2 + 1)
In this problem, 16* is equal to 16(y1/2(y2 + 1)) and 9* is equal to 9(y1/2(y2 + 1)). When -3 is multiplied to 16* - 9*, the result is -3 times the difference of 16* and 9*. The expression then simplifies to -10.5y1(y2 + 1).
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What is the missing numerator?
How to convert 89 cm to inches?
89 centimeter is approximately equal to 35.0394 inches ( rounded to four decimal places )
To convert 89 cm to inches, we can use the following formula:
1 cm = 0.393701 inches
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in inches = conversion factor × The length in centimeter
Substitute the values in the equation
89 cm = 89 x 0.393701
Multiply the numbers
= 35.0394 inches ( rounded to four decimal places )
Therefore, 89 centimeter is 35.0394 inches
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What is the conversion of 375 f to c ?
The value after conversion Fahrenheit to Celsius is equal to 375 Fahrenheit to 190.556 Celsius.
The unit which represents the measurement of the temperature in Standard form is given by Fahrenheit and Celsius.
Relation between Fahrenheit and Celsius is represented by the formula as written below
(°F − 32) × 5/9 = °C
Here Substitute the value 375 Fahrenheit in the above formula to get into Celsius ,
= ( 375°F − 32) × 5/9
= 343 × 5/9
= 1715 / 9
= 190.55555 Celsius
= 190.556 Celsius
Therefore, the converted value of 375 Fahrenheit into the Celsius is given by 190.556 Celsius .
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Please help!The monthly profit for a small company is represented by 250x³ - 42x² + 112x, where x is the
number of beds sold. Classify the polynomial by the number of terms. Then identify the degree.
The polynomial 250x³ - 42x² + 112x is a trinomial of degree 3.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.
The given polynomial is 250x³ - 42x² + 112x.
To classify this polynomial by the number of terms, we count the number of terms it has, which is three. Therefore, we can classify it as a "trinomial".
To identify the degree of this polynomial, we look at the highest power of x in the polynomial. In this case, the highest power of x is 3, which is the coefficient of the x³ term. Therefore, the degree of this polynomial is 3.
So, the polynomial 250x³ - 42x² + 112x is a trinomial of degree 3.
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A hemispherical bowl of radius R is placed in a uniform magnetic field that has magnitude B0 and is in the positive z direction. The open top of the bowl is in the xy plane.
Part A
Obtain an expression for the magnetic flux through the hemispherical surface of the bowl.
Express your answer in terms of some or all of the variables B0, R, and the constant ?.
The expression for the magnetic flux through the hemispherical surface of the bowl is EπR².
Hemisphere:
The word hemisphere can be divided into hemisphere and sphere. Hemisphere means half, and sphere means three-dimensional shape in mathematics. Thus, a hemisphere is a three-dimensional geometric shape that is a hemisphere that is flat on one side and a round bowl on the other. It is formed when a sphere is cut exactly down the center along its diameter, leaving two identical hemispheres.
The volume of a hemisphere is the number of unit cubes that can fit inside it. The units of volume are cubic units, such as m³, cm³, ft³ and so on.
The volume of a hemisphere = 2/3πr³
where
r is the radius of the hemisphere.
According to the Question:
Flux passing through the curved surface is equal to the flux passing through the flat surface.
Since flux through the flat surface
ϕ flat = E× Area
= E× πR²
The electric flux through a closed surface is 1/E₀ times the total charge unclosed.
By Gauss's law, flux ,
Since number of field lines entering from circular side is equal to number of field lines leaving the hemispherical surface, net flux is 0.
Therefore,
(Flux)h + (flux)c = 0 -------------------------(1)
[* (flux)h means flux from hemispherical surface and (flux)c means flux from circular surface]
Therefore,
(flux)h = - (flux)c ---------------------------- (2)
Flux = E.A [ Where E and A are vectors ]
Flux = E A cos θ
(Flux)c = EA cos π [ Because field and surface area vector are anti parallel]
(flux)c = E πR² (-1) ------------------------------ (3)
From equation (2) and (3)
(flux)h = - (- EπR²)
⇒ (Flux)h = EπR²
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what is big number calculator?
A big number calculator is a software application or program designed to perform arithmetic operations on large numbers that cannot be easily handled by standard computer hardware and software.
Big numbers are typically defined as numbers that are too large to be stored in the registers or memory of a typical computer processor.
In a big number calculator, arithmetic operations such as addition, subtraction, multiplication, and division are performed using algorithms that are specifically designed to handle large numbers. These algorithms may use techniques such as long division, long multiplication, and other mathematical strategies to perform the required computations.
Big number calculators are often used in scientific and engineering applications where very large numbers are encountered. They can also be useful in cryptography, where large prime numbers are used for encryption and decryption operations.
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What is the binary conversion of 2?
The binary conversion of 2 is 10.
In binary, there are only two possible digits, 0 and 1. Each digit in a binary number represents a power of 2, with the rightmost digit representing 2^0 (which is 1), the second digit representing 2^1 (which is 2), the third digit representing 2^2 (which is 4), and so on.
So in the binary number 10, the rightmost digit represents 2^0, which is 1, and the second digit represents 2^1, which is 2. Adding these two powers of 2 together gives a total value of 2 in binary.
To convert a decimal number to binary, you can divide the number by 2 and record the remainder at each step until the quotient is 0. Then, the binary number is simply the remainders read in reverse order. In this case, 2 divided by 2 is 1 with a remainder of 0, so the first digit of the binary number is 0. 1 divided by 2 is 0 with a remainder of 1, so the second digit of the binary number is 1. Therefore, the binary conversion of 2 is 10.
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Check that Han's answer is correct by calculating the product of 2. 43 and 13
The product of 2.43 and 13, which is the result of the multiplication operation, is 31.59.
What is the product of numbers?The product of two or more numbers is the result of the multiplication operation performed on the numbers.
Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
The multiplication operation involves the multiplicand, the multiplier, the multiplication operand (x), the equal symbol (=), and the result, known as the product.
2.43 x 13 = 31.59
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1. Tanya used 3(3/8) yards of fabric to maker her dress, and she used 1(1\3) yards of fabric to make her jacket. What was the total amount of yards?
A. 4(1/8)
B. 4(1/6)
C. 4(4/11)
D. 4(1/2)
E. 4(17/24)
The total amount of yards are 4(1/8).
To find the total amount of fabric Tanya used, we need to add the amount of fabric she used for the dress and the amount of fabric she used for the jacket.
Tanya used 3(3/8) yards of fabric for the dress and 1(1/3) yards of fabric for the jacket. We can add these two amounts by finding a common denominator for the fractions and adding the whole numbers:
3(3/8) + 1(1/3) = 3(9/24) + 1(8/24)
=> 3(17/24)
Therefore, Tanya used a total of 3(17/24) yards of fabric. This can be simplified to:
=> 3(17/24) = 4(1/8)
So the answer is A. 4(1/8).
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what is 55kg in lbs?
According to the conversion, 55 kg is equal to approximately 121.25 lbs.
In the world of mathematics, measurement plays a vital role in determining the quantity, weight, and size of any object. The standard units of measurement are different in various countries, and knowing how to convert from one unit to another is essential.
The question posed is, "What is 55 kg in lbs?" Here, 'kg' is a unit of mass, commonly used in the metric system, whereas 'lbs' stands for pounds, which is a unit of weight in the Imperial system. To convert from kg to lbs, we need to multiply the given value by a conversion factor.
1 kg is equal to 2.20462 pounds. Hence, we can use this conversion factor to convert 55 kg to lbs as follows:
55 kg x 2.20462 lbs/kg = 121.2542 lbs (rounded off to two decimal places)
In conclusion, understanding measurements and being able to convert from one unit to another is a fundamental aspect of mathematics. In this case, we used the conversion factor of 2.20462 lbs/kg to convert 55 kg to lbs.
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Rey's total payment for his student loan was $24,506. What was his monthly payment if he paid it off after making 120 monthly payments?
Johnny has 24 pairs of shoes which is 4 less than two thirds the amount of shoes Ralph has. How many pairs of shoes Ralph have?
Answer: Really?
Step-by-step explanation:
what is inverse tangent derivative?
Answer:
(tan-1x)' = 1/(1 + x2)
Step-by-step explanation:
The differentiation of tan inverse x is the process of finding the derivative of tan inverse x with respect to x.
361 divided by 2,510
0.14382470119, rounded to 0.14, is the answer.
Answer: 0.1438 (to 4 decimal places)
A doctor finds that patients inhales once every 3 seconds. The same patient's heart beats 82 times per minute while at rest. How many times does this patient inhale in a 24-hour day?
Using arithmetic operations it is obtained that the patient inhales approximately 29,520 times in a 24-hour day.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
We can start by converting the patient's breathing rate from seconds to minutes, since we have the heart rate in minutes.
Use the arithmetic operation of multiplication and division -
The patient inhales once every 3 seconds, which is equivalent to -
(1 inhale / 3 seconds) x (60 seconds / 1 minute) = 20 inhales per minute
Next, we can use the patient's heart rate to find the number of breaths per heartbeat, and then multiply by the heart rate to get the total number of breaths per minute -
Breaths per heartbeat = 1 inhale / 4 heartbeats (since each heartbeat corresponds to 4 phases of the cardiac cycle, during which the patient inhales and exhales once)
Breaths per minute = (Breaths per heartbeat) x (Heart rate)
= (1/4) x 82
= 20.5
So the patient takes approximately 20.5 breaths per minute.
Multiplying this by the number of minutes in a day (24 hours x 60 minutes per hour = 1440 minutes) gives -
Breaths per day = (Breaths per minute) x (Minutes per day)
= 20.5 x 1440
= 29,520
Therefore, the number of inhales is 29,520.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
2.1
D
4
to
E
Answer:
[tex]31.7^\circ[/tex]
Step-by-step explanation:
We use the property that the sin of the angle of a right triangle is the ratio of the side opposite that angle divided by the hypotenus
Therefore
[tex]\begin{aligned}\sin x & = \dfrac{2.1}{4}\\& = 0.525\\\end{aligned}\\\begin{aligned}x &= sin^{-1}(0.525)\\& = 31.7^\circ \end{aligned}[/tex]
Which equation does the graph of the systems of equations solve?
• -x^2+2x+3=x^2-4x+3
•x^2-2x+3=2x^2-4x+3
•x^2-2x+3=2x^2-4x-3
•-x^2-2x+3=x^2-4x+3
The equation that the graph of the systems of equations solve is:
x^2 - 2x + 3 = 2x^2 - 4x + 3
This is the second equation listed.
Ashley and Alexandro have to determine if the two lines, y = -2x + 7 and 6x + 3y = 21, are parallel, perpendicular, or neither. Ashley thinks the lines are parallel. Alexandro thinks the lines are neither. Who is correct?
Ashley thinks the lines are parallel is correct. Meanwhile, Alexandro is wrong, he thinks the lines are neither.
The two lines, y = -2x + 7 and 6x + 3y = 21, are parallel because they have the same slope.
To determine if two lines are parallel, we need to check if their slopes are equal.
The slope of the first line, y = -2x + 7, is -2.
The slope of the second line, 6x + 3y = 21, can be found by rearranging the equation to solve for y:
3y = -6x + 21, divided by 3
y = -2x + 7
The slope of the second line is also -2. Since the slopes are equal, the lines are parallel.
However, to determine if two lines are perpendicular, we need to check if the product of their slopes is -1. The slope of the first line is -2, and the slope of the second line is -2.
The product of their slopes is (-2)(-2) = 4, which is not equal to -1. Therefore, the lines are not perpendicular.
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PLEASE HELP ME WITH THIS QUESTION
A square fits exactly inside a circle with each of its vertices
being on the circumference of the circle.
The square has sides of length x cm.
The area of the circle is 56^2cm.
Work out the value of x.
Give your answer in 3 significant figures.
The value of x to 3 significant figures is approximately 18.9 cm.
What is area of circle ?Area of circle can be defined as the product of pi and square of radius of circle.
The area of a circle is given by the formula[tex]A = πr^2[/tex], where r is the radius of the circle.
Since the area of the circle is 56^2 cm, we can set up the equation:
[tex]πr^2 = 56^2[/tex]
Solving for r, we get:
[tex]r = √(56^2/π) ≈ 13.37 cm[/tex]
Since the square fits exactly inside the circle, its diagonal is equal to the diameter of the circle, which is 2r. Therefore:
x√2 = 2r
Substituting the value of r, we get:
[tex]x√2 = 2(√(56^2/π))[/tex]
x√2 ≈ 26.74
Dividing both sides by √2, we get:
x ≈ 18.94
Therefore, the value of x to 3 significant figures is approximately 18.9 cm.
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A recipe requires 1 1/2, cups of milk for every 1/2 of a cup of flour. What is the ratio of
cups of milk to one cup of flour?
Answer:
So the ratio of cups of milk to one cup of flour is 3:1.
Step-by-step explanation:
We can start by multiplying the denominator by 2 to get a denominator of 1:
1/2 * 2 = 1
Now we need to multiply the numerator by 2 as well to keep the ratio the same:
1 1/2 * 2 = 3
Line l passes through the points (-8, 8) and (-4, 0). Write the equation of the image of
after a dilation with a scale factor of 1, centered at the origin.
Write your answer in slope-intercept form.
y =
57 cars pass through an intersection in 3 hours. Select all the correct responses to complete the statement
Answer:
Step-by-step explanation:
i ate my dog than did the math
19 cars will pass the intersection in 1 hour.
What is division?Division is used to split a number into equal parts.
Given is that 57 cars pass through an intersection in 3 hours.
It is given that 57 cars pass through an intersection in 3 hours.
So, we can write that in 1 hour, the number of cars that will pass are -
{x} = 57/3
{x} = 19
Therefore, 19 cars will pass the intersection in 1 hour.
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For each set of given information complete the missing information in the table
The missing information in the table is $290,000 for Firm 1 and $18,562,433 for Firm 2
The premium of a bond can be calculated by taking the coupon rate and subtracting the yield, and then multiplying the result by the face value of the bond.
For Firm 1, the premium is given by (7.00% - 8.00%) × $300,000 = -$10,000.
The proceeds of Firm 1 can then be calculated by
=> $300,000 – $10,000 = $290,000.
For Firm 2, the yield and coupon rate that is as interest are both given as 3.00%. This means that the bond will be sold at par value, so the face value and proceeds of the bond will be the same.
The face value of Firm 2 can be calculated by taking the proceeds given and dividing by the bond’s yield.
Thus, Firm 2’s face value is given by $556,853 / 3.00% = $18,562,433.
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Complete Question:
Complete the missing information in the table below. Assume that all bonds pay interest semiannually.
Do not use negative signs with answers.
Round percentages to one decimal place (ex. 0.0345 = 3.5%).
Round all other values to the nearest whole number.
Annual Years to Coupon Issue
Yield Maturity Rate Face value Proceeds
Firm 1 8.00% 15 7.00% $300,000 $_______
Firm 2 3.00% 10 0.00% $_______ $556,853
Using the special right triangle shortcuts, what is the length of the long leg of a 30-60-90 triangle with a hypotenuse of 14?
the length of the long leg (the side opposite the 60-degree angle) is x√3, which is:
(7/2)√3 ≈ 6.06
What is the hypotenuse?
In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.
In a 30-60-90 triangle, the ratio of the side lengths is x : x√3 : 2x, where x is the length of the shorter leg, and 2x is the length of the hypotenuse.
Since the hypotenuse of this triangle is 14, we can set 2x = 14 and solve for x:
2x = 14
x = 7/2
Hence, the length of the long leg (the side opposite the 60-degree angle) is x√3, which is:
(7/2)√3 ≈ 6.06
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How do you expand and simplify a binomial?
In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms. Expanding brackets is the process by which we remove brackets. It is the reverse process of factorization.
To expand and simplify a binomial, use the distributive property. The distributive property states that for any two binomials, the product of each term in the first binomial and each term in the second binomial should be added together to get the expanded form of the expression.
For example, the binomial (2x + 3)(4x + 7) can be expanded using the distributive property by multiplying each term of the first binomial with each term in the second binomial. This gives us:
(2x × 4x) + (2x × 7) + (3 × 4x) + (3 × 7)
And simplifying this expression yields 8x² + 14x + 21.
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which fration is greater than 3\4
Answer: There are infinitely many fractions that are greater than 3/4. Any fraction whose numerator is greater than three and whose denominator is greater than four will be greater than 3/4. Here are a few examples:
4/5 is greater than 3/4
5/6 is greater than 3/4
6/8 (which simplifies to 3/4) is not greater than 3/4, but any fraction greater than 6/8 will be greater than 3/4. For example, 7/8, 8/9, 9/10, and so on.
In general, to determine whether a fraction is greater than 3/4, you can compare its numerator and denominator. If the numerator is greater than the denominator times 3/4 (which is the same as multiplying the denominator by 3/4 and comparing it to the numerator), then the fraction is greater than 3/4.
Step-by-step explanation:
What is the conversion of 38c to fahrenheit ?
The value which represents the converted value Celsius to Fahrenheit is 38 Celsius is equal to 100.4 Fahrenheit.
Units which are used to measure temperature are known by the nameCelsius and Fahrenheit .
Conversion relation between the units of the temperature is written as:
(°C × 9/5) + 32 =°F
Substitute the value 38 Celsius to convert it into Fahrenheit we get,
(38°C × 9/5) + 32
= ( 342 / 5 ) + 32
= ( 68.4 ) + 32
= 100.4°F
Therefore, the required converted value of the Celsius to Fahrenheit is given by 100.4 Fahrenheit.
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Liam is setting up folding chairs for a meeting. If he arranges the chairs in 4 rows of the same length, he has 3 chairs left over. If he arranges the chairs in 2 rows of that same length, he has 19 left over. How many chairs does Liam have?
Liam has 19 chairs.
According to given information :Let x be the number of chairs Liam has.
According to the problem, x = 4a + 3 and x = 2b + 19 for some integers a and b.
Equating these two expressions, we get:
4a + 3 = 2b + 19
4a - 2b = 16
2a - b = 8
Therefore, b = 2a - 8.
Substituting this expression for b into x = 2b + 19, we get:
x = 4a + 35
Now, since x = 4a + 3, we have:
4a + 3 = 4a + 35 - 32
Therefore, x = 4a + 35 = 2(2a + 4) + 3 = 2b + 19, where a = 4 and b = 11.
Thus, Liam has x = 4a + 3 = 4(4) + 3 = 19 chairs.
What is system of equation ?The solution to this problem involves the use of two key mathematical concepts: algebraic equations and systems of equations.
We are given two equations in terms of the same variable x, each representing a different way of arranging chairs. By setting these two equations equal to each other, we obtain an equation in terms of x that allows us to find a value of x that satisfies both of the original equations simultaneously. This process of setting two equations equal to each other is an example of solving a system of equations.
To solve the resulting equation, we use algebraic manipulation to isolate the variable x on one side of the equation. This involves a combination of simplification, substitution, and rearrangement of terms. Ultimately, we arrive at a specific value of x that satisfies both equations, which is the answer to the problem.
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10 Points ..........................................................................................
If the points lie on a straight line passing through the origin, it would support Enid's claim that the distance she jogs and the number of calories she burns are in a proportional relationship.
What is proportion ?
Proportion refers to the relationship or comparison between two or more quantities or values. It is typically expressed as a ratio or fraction that compares the part to the whole or the amount of one thing to the amount of another thing.
The two correct methods that Enid can use to test her claim are:
She could calculate the ratio change in calories burned to change in miles jogged for two data points and compare the results to the same ratio with two other data points.
This method involves calculating the ratio of the change in calories burned to the change in distance jogged for two pairs of data points, and then comparing the results to see if they are the same. If they are the same, it would support Enid's claim that the distance she jogs and the number of calories she burns are in a proportional relationship.
She could plot the data on a coordinate plane and see if a straight line starting at (0, 0) passes through all the data points.
This method involves graphing the data points on a coordinate plane and checking if they form a straight line that passes through the origin (0, 0).
Therefore, If the points lie on a straight line passing through the origin, it would support Enid's claim that the distance she jogs and the number of calories she burns are in a proportional relationship.
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A transformation is applied to a figure to create a newfigure. Which transformation does not preserve congruence?O A reflection across the x-axisO A translation 7 units downO A dilation by a scale factor of 5O A rotation of 90° clockwise
A transformation is applied to a figure to create a new figure, the transformation does not preserve congruence is option C, A dilation by a scale factor of 5.
An isometry is a transformation that retains congruence. In other words, a transformation in which the side lengths and angle measurements of the Image and Pre-Image are the same. Isometries include translations, reflections, and rotations. A translation is a "direct isometry" since it not only maintains congruence but also, unlike reflections and rotations, maintains orientation.
A dilation, on the other hand, is not an isometry since its Image is not consistent with its Pre-Image.
A transformation composition indicates that two or more transformations will be executed on the same item. On the same point, for example, we may do a reflection and then a translation.
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