Find the largest product the positive numbers x, and y, can have if x + y2 = 16.

The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x-a). It is a faster and more efficient method than long division when dividing a polynomial by a linear factor, and is commonly used in algebra and calculus.

To use synthetic division, the coefficients of the polynomial must be written in descending order and any missing terms should be replaced by zero coefficients. The divisor must be a linear factor of the form (x-a), where 'a' is a constant.

Synthetic division can be used to find the quotient and remainder of a polynomial division by a linear factor. It is also used to simplify expressions and solve equations in algebra and calculus.

First, we need to convert the divisor to its opposite sign, so we will be dividing by x - (-0.7) = x + 0.7

The coefficients of the dividend are 0.9, 0.8, 0, 0, so we will set up our synthetic division table as follows:

-0.7 | 0.9 0.8 0 0

      | -0.63 -0.259 0.181

      |____________________

         0.9 0.17 -0.259 0.181

The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.

Therefore, 0.9x³ + 0.8x = (x + 0.7)(0.9x² + 0.17x - 0.259) + 0.181.

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The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.

A more straightforward way to divide a polynomial by a linear factor is by synthetic division. (x-a).

The polynomial's coefficients must be written in descending order and any missing terms should be substituted with zero coefficients in order to apply synthetic division. A linear factor of the type (x-a), where "a" is a constant, must be used as the divisor.

To determine the quotient and remainder of a polynomial division by a linear factor, utilise synthetic division. In algebra and calculus, it is also used to resolve equations and simplify statements.

We will divide by in order to first change the divisor to its opposite sign x - (-0.7) = x + 0.7

Since the dividend's coefficients are 0.9, 0.8, 0, 0, we will set up our artificial division table as follows:

-0.7 | 0.9 0.8 0 0

     | -0.63 -0.259 0.181

     |____________________

        0.9 0.17 -0.259 0.181

The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.

Therefore, 0.9x³ + 0.8x = (x + 0.7)(0.9x² + 0.17x - 0.259) + 0.181.

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The second difference is constant in quadratic number patterns.  The correct option is C

Quadratic number patterns are sequences of numbers that follow a quadratic or second-degree pattern or rule. This means that the sequence is generated by adding a constant difference between terms, which is itself increasing or decreasing linearly.

A quadratic sequence can be defined by a formula of the form :

an = a + bn + cn^2

Where

Therefore, the correct option is C

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The combination of goods that would maximize the consumer's Utility per dollar leads to a utility equal to 14 utils.

To determine the combination of goods that would maximize the consumer's utility per dollar, we need to use the concept of marginal utility. Assuming that the consumer has $14 to spend and chips cost $1 while soda costs $2, the consumer could purchase either 14 chips, 7 sodas or a combination of the two.

Let's say the consumer decides to buy x chips and y sodas. The total expenditure would be 1x + 2y, and the total utility would be the sum of the marginal utility of each good multiplied by the quantity purchased.

Assuming the utility function is U(x, y) = x^(1/2) * y^(1/2), the marginal utility of chips would be (1/2)x^(-1/2)*y^(1/2) and the marginal utility of soda would be (1/2)x^(1/2)*y^(-1/2).

The consumer's goal is to maximize the utility per dollar, which is calculated as the total utility divided by the total expenditure. Therefore, the utility per dollar function would be U(x, y)/(1x + 2y).

Using the Lagrange multiplier method, we can find the combination of x and y that maximizes the utility per dollar. The first-order conditions give us the following system of equations:

(1/2)x^(-1/2)*y^(1/2) = λ

(1/2)x^(1/2)*y^(-1/2) = 2λ

x^(1/2)*y^(1/2) = 14

Solving this system of equations, we get x = 4 and y = 49/4. Therefore, the consumer should buy 4 chips and 12.25 sodas, which costs $29.50.

The utility function evaluated at this point is U(4, 49/4) = (4^(1/2))*(49/4)^(1/2) = 14. The utility per dollar function evaluated at this point is U(4, 49/4)/(1(4) + 2(49/4)) = 14/29.50 = 0.4746.

Therefore, the combination of goods that would maximize the consumer's utility per dollar leads to a utility equal to 14 utils.

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Answer: Let's use the variables "r" and "c" to represent the cost of one rose and one carnation, respectively.

From the first sentence, we know that 8 roses and 5 carnations cost $31.75. So we can write the equation:

8r + 5c = 31.75

From the second sentence, we know that 1 rose and 3 carnations cost $5.75. So we can write the equation:

r + 3c = 5.75

Now we have two equations with two variables. We can use substitution or elimination to solve for "c". Let's use substitution:

r = 5.75 - 3c (from the second equation)

Substitute this expression for "r" into the first equation:

8(5.75 - 3c) + 5c = 31.75

Simplify and solve for "c":

46 - 24c + 5c = 31.75

-19c = -14.25

c = 0.75

Therefore, the cost for a carnation is $0.75.

Step-by-step explanation:

The graph that shows the solution set of 7 ≤ n + 5 include the following: A. graph A.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

In this exercise, we would determine the solution set by evaluating the given equation 7 ≤ n + 5 as follows;

7 ≤ n + 5

7 - 5 ≤ n + 5 - 5

2 ≤ n

n ≥ 2

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Answer:

[tex]\frac{61}{66}[/tex]

Step-by-step explanation:

Freshmen:

1200 + 20 = 1220

Sophomores:

12(15) = 180  60/5 = 12

1500 - 180 = 1320

[tex]\frac{1220}{1320}[/tex] = [tex]\frac{61}{66}[/tex]  (to simplify divide the numerator and denominator by 20)

Helping in the name of Jesus.

Answer:18 cents.

Step-by-step explanation: I did the math.

Hope this helps <3

She will save $0.18

To find the answer, you use the amount of what it usually costs and subtract the sale price to get the amount she saves.

$0.34 - $0.16 = $0.18

Answer:

4√3

Step-by-step explanation:

length > width

If width = y

length =4y

Length × width = area

y × 4y = 192

4 y^2 = 192

y^2 = 48

y = 4 √3

Pedro earns $5.1 per hour than Oliver according to the given graph.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. That will be regarded as a phrase.

Given that, Pedro earned $521.40 in 22 hours.

The per hour rate is thus,

521.40 / 22 = 23.7 per hour.

For Olive we have:

372 - 186 / 20- 10 = 186 / 10 = 18.6

The difference between their earnings is:

23.7 - 18.6 = 5.1

Hence, Pedro earns $5.1 per hour than Oliver.

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The complete question is:

To determine if the ratio of female players to male players is the same in both countries, we need to calculate the ratios and compare them.

For the first country,

let female players be f1,male players be m1

the ratio of female players to male players is:f1:m1 (i.e f1/m1)

11,200 / 14,000 = 0.8

For the second country,

let female players be f2,male players be m2

the ratio of female players to male players is:f2:m2 (i.e f2/m2)

10,400 / 13,000 = 0.8

As we can see, both ratios are the same, which means that the ratio of female players to male players is the same in both countries. Therefore, we can conclude that there is no significant difference in the gender ratio of soccer players between these two countries.

Answer:

The female-to-male ratios for both countries are the same (0.8), indicating that the ratio of female players to male players is the same for both countries.

Explanation:

To determine whether the ratio of female players to male players is the same for both countries, we need to calculate the ratio of female players to male players for each country and compare them.

Country 1: Female-to-male ratio

= 11,200 / 14,000

= 0.8

Country 2: Female-to-male ratio

= 10,400 / 13,000

= 0.8

a) The amount of the insurance or the sum assured by Julia Carson on his brick home is $80,000.

b) The annual premium is $5,148.00.

The sum assured represents the fixed amount that the insurance company pays to Julio Carson (the policyholder) if the unpredictable event, such as fire, occurs and damages his brick home.

The purpose of the payment is to reimburse Julio not for the costs incurred but according to the risks undertaken and it is a fixed sum of money unlike the sum insured, which reimburses to cover the costs incurred.

Replacement value of the brick home = $100,000

Sum insured = 80%

= $80,000 ($100,000 x 80%)

Monthly premium = $429

Number of insured years = 10 years

Annual premium = $5,148 ($429 x 12)

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Thus, the simplification of the given function using difference quotient formula is found as 4.

The difference quotient is the product of the difference between the function values, f(x + h) - f(x), and indeed the difference between the input values, (x + h) - x, given a function f(x) and two input values, x as well as x + h (where h is indeed the distance between x and x + h).

For the given question:

function F(x) = -4x+8

difference quotient formula:

[f(x + h) -f(x)] / h

Put x = x + h

F(x+ h) = -4(x + h) + 8

F(x+h) = -4x  -4h + 8

F(x) = -4x+8

Now,

[f(x + h) -f(x) ]/ h = [-4(x + h) + 8  + 4x - 8]/ h

On simplifying:

[f(x + h) -f(x) ]/ h = 4h/h = 4

Thus, the simplification of the given function using difference quotient formula is found as 4.

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Answer:

C

Step-by-step explanation:

For the given functions f(x) and g(x), the inverse functions of f and g are:

a. f(g(x)) = x; g(f(x))  = x

ƒ and g are inverses of each other.

b. (g(x)) = x; g(f(x))  = x

ƒ and g are inverses of each other

The inverse functions of the functions f(x) and g(x),are determined as follows;

a. f(x) = 2x, g(x) = x/2

f(g(x)) = f(x/2)

f(g(x)) = 2(x/2)

f(g(x)) = x

g(f(x)) = g(2x)

g(f(x))  = (2x)/2

g(f(x))  = x

Since f(g(x)) = g(f(x)) = x, ƒ and g are inverses of each other.

b. f(x) = 2x + 1, g(x) = (x -1)/2

f(g(x)) = f((x-1)/2)

f(g(x)) = 2((x-1)/2) + 1

f(g(x)) = x - 1 + 1

f(g(x)) = x

g(f(x)) = g(2x + 1)

g(f(x)) = ((2x + 1) - 1)/2

g(f(x)) = 2x/2

g(f(x)) = x

Since f(g(x)) = g(f(x)) = x, ƒ and g are inverses of each other.

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Answer:

Step-by-step explanation:

Answer:

-12.6

Step-by-step explanation:

-4.5 - 8.1

= -4.5 + -8.1

= -12.6

The equation for the volume of the rectangular prism is V = x³ + 2x² - 8x.

A three-dimensional solid structure called a rectangular prism contains six rectangular faces, each of which is perpendicular to the faces around it. The term "rectangular parallelepiped" is another name for it. Rectangular prisms are frequently employed in geometry because they may be used to represent a variety of real-world objects, including boxes, buildings, and rooms. A rectangular prism's surface area is equal to the total of the areas of its six faces, whereas its volume is determined by the product of its length, breadth, and height.

The volume V of a rectangular prism is given by the formula:

V = lwh

Substituting the values:

V = (x + 4)(x - 2)(x)

= (x² + 2x - 8)(x)

= x³ + 2x² - 8x

Hence, the equation for the volume of the rectangular prism is V = x³ + 2x² - 8x.

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Any expression that involves only integers and basic Arithmetic operations can simplify to a rational answer, while expressions involving irrational numbers cannot.

There are several expressions that simplify to a rational answer. In mathematics, a rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. Therefore, any expression that involves only integers, addition, subtraction, multiplication, and division can simplify to a rational answer.

For example, if you have an expression like (3 + 2)/(4 - 1), this can be simplified to 5/3, which is a rational number. Similarly, expressions like 6/3 or 7 - 2 also simplify to rational answers.

However, expressions that involve irrational numbers such as pi or the square root of 2 cannot simplify to rational answers. For example, the expression sqrt(2) + 3 cannot be simplified to a rational number.

In summary, any expression that involves only integers and basic arithmetic operations can simplify to a rational answer, while expressions involving irrational numbers cannot.

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yes. use u substitution to get the answer

[tex]U(\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad N(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{2 +2}{-3} \implies \cfrac{ 4 }{ -3 } \implies - \cfrac{4 }{ 3 }[/tex]

Answer:

n(EnS)= 10

Step-by-step explanation:

n(U)= 55

n(EnS)= x

n"(EuS)"= 2x

n(EuS)= 35

We have,

n"(EuS)"= n(U) - n(EuS)

=55-35

=20

n(EnS) /n"(EuS)" = 1/2

x/20 = 1/2

2x=20

x=20/2

x=10

Therefore, n(EnS) = 10

To solve this expression, we need to apply the order of operations (also known as PEMDAS): 8 15/22 - 3/4 x 2 divided by 12 = 351/44.

What is PEMDAS?

1.  First, we need to simplify any expressions inside parentheses, but there are no parentheses in this expression.

2. Next, we need to perform any multiplication or division, working from left to right. So, we need to calculate 3/4 x 2 = 3/2.

3. Then, we can rewrite the expression with the new result: 8 15/22 - 3/2 divided by 12.

4. Next, we need to perform the division, which means we need to divide 3/2 by 12. To do this, we can rewrite 12 as a fraction with a denominator of 2: 12/1 x 1/2 = 6/1. Then, we can simplify 3/2 divided by 6/1 by multiplying by the reciprocal of 6/1: (3/2) x (1/6) = 1/4.

5. Now we can substitute this value back into the expression: 8 15/22 - 1/4.

6. Finally, we need to convert the mixed number 8 15/22 to an improper fraction: 8 x 22/22 + 15/22 = 181/22.

7. Now we can combine like terms: 181/22 - 1/4 = (181 x 4)/(22 x 4) - 1/4 = 724/88 - 22/88 = 702/88.

8. We can simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF), which is 2: 702/88 = 351/44.

Therefore, 8 15/22 - 3/4 x 2 divided by 12 is equal to 351/44.

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Answer:

Step-by-step explanation:

50$ (Sorry for the mistake, it’s a little hard for me to give such assignments, if the translator would translate correctly, then there would be no mistake, sorry again)

Answer:

Step-by-step explanation:

A tire is sold at a discount of 10%. It is sold for $45. Find the usual price of the tire.

from the question you understand that $45 is 90% of the original price (100%-10%=90%), so we divide 45 by 90 and multiply by 100 and we  find the original price

45 : 90 x 100 =

0.5 x 100 =

50$

----------------------------

50$ - 10% = 45

The probability that a randomly selected student from the set has a height less than 115 cm is approximately 0.04, or 4%

A z-score (or standard score) is a measure of how many standard deviations a data point is from the mean of its distribution. It is a way to standardize data and compare observations from different distributions.

To find the probability that a randomly selected student from the set has a height less than 115 cm, we need to standardize the value using the standard normal distribution.

First, we calculate the z-score:

z = (115 - 150) / 20

  = -1.75

Then, we look up the area under the standard normal distribution curve to the left of z = -1.75 using a table or a calculator. The table or calculator gives us the value 0.0401.

Therefore, the probability that a randomly selected student from the set has a height less than 115 cm is approximately 0.04, or 4%, rounded to two decimal places:

P(X < 115) = 0.04

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A set of middle school student heights are normally distributed with a mean of 150150150 centimeters and a standard deviation of 202020 centimeters. Let XXX represent the height of a randomly selected student from this set. Find P(X<115)P(X<115)P, left parenthesis, X, is less than, 115, right parenthesis. You may round your answer to two decimal places.

Answer:

pi/6

Step-by-step explanation:

the full arc of the circle is the circumference = 2pi×r.

since r = 1, we get circumference = 2pi.

the full arc of 2pi is for 360° or 2pi radians (hence the definition).

an angle given in radians for the norm circle with radius = 1 IS therefore already the arc length for that angle.

for 2pi the arc length is 2pi.

for pi/6 the arc length is ... pi/6.

Dilation is a transformation that changes the size of an object while keeping its shape the same.

In this case, the scale factor of 3 tells us that the triangle will be three times larger than the original triangle.

To perform the dilation, you would take each vertex of the triangle and multiply the x-coordinate and y-coordinate by 3. For example, if one vertex of the original triangle had coordinates (x, y), the coordinates of that same vertex in the dilated triangle would be (3x, 3y).

It's also worth noting that the dilation is done with respect to a fixed point called the center of dilation. You can think of this point as the "pivot" around which the dilation occurs.

The center of dilation is typically represented by the letter "O".

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Answer:

To find ƒ⁻¹(x), we need to solve for x in terms of ƒ⁻¹(x).

So, we start with the equation:

x = 2 (ƒ⁻¹(x) - 1)

We isolate ƒ⁻¹(x) by dividing both sides by 2 and adding 1 to both sides:

ƒ⁻¹(x) = (x/2) + 1

Therefore, the inverse of the given function f(x) is:

ƒ⁻¹(x) = (x/2) + 1

Answer:

24 students turned in there homework assignments.

Step-by-step explanation:

80% = .8

30 x .8 = 24

Step-by-step explanation:

All you would need to do is to use the circumference of a circle equation, C = 2pi(r) or C=pi(d). Since we are given the radius we will use C= 2pi(r).
C=2pi(4.4)

C=8.8pi inches