What is the function rule for the line?
f (x) = 2x - 4
f(x)=-4x - 2
f(x) = 4x - 2
f (x)= -2x + 4

The polynomial satisfying the given conditions is given as 2x⁴ + 10x² + 8.

The polynomial is an algebraic expression in which no any terms has the power other than a whole number.

The degree of a polynomial is the highest power of one of its terms.

Given that,

The degree of polynomial is n = 4.

The zeros of the polynomial are i and 2i.

And, f(-1) = 20

Since, a polynomial with real coefficients have either real zeros or complex conjugate zeros.

Here, the given zeros of the polynomial are imaginary which implies that the remaining two zeros are the conjugate of the given two zeros.

Thus, the zeros of the given polynomial are i, 2i, -i and -2i.

The general form of a 4th degree polynomial is given as,

ax⁴ + bx³ + cx² + dx + e

Use the factor theorem to get,

ax⁴ + bx³ + cx² + dx + e =  K(x - i) (x - (-i)) (x - 2i) (x- (-2i))        (1)

⇒ ax⁴ + bx³ + cx² + dx + e = K(x² + 1) (x² + 4)                          (2)

Now, f(-1) = 20 which gives,

K((-1)² + 1) ((-1)² + 4) = 20

⇒ k = 2

Substitute K =2 in equation (2) to get,

ax⁴ + bx³ + cx² + dx + e = 2(x² + 1) (x² + 4)  

⇒ ax⁴ + bx³ + cx² + dx + e = 2(x⁴ + 5x² + 4)  

⇒ ax⁴ + bx³ + cx² + dx + e = 2x⁴ + 10x² + 8  

Hence, the nth-degree polynomial function with real coefficients satisfying n = 4 and zeros i and 2i is 2x⁴ + 10x² + 8.

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Answer: 0.3278

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!

The exponential function that can model the amount of medication in Austin's body, y, x hours is of: [tex]y = 180(0.9)^x[/tex]

The definition of the exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

The parameters a and b are listed as follows:

a is the amount when x = 0.

b is the rate of change.

Given that the initial dose was of 180 micrograms, hence the parameter a is;

a = 180.

After one hour, the concentration was of 162 micrograms, hence the parameter b is;

b = 162/180 = 0.9.

Hence the equation is:

[tex]y = 180(0.9)^x[/tex]

After six hours, the concentration is given as;

[tex]y = 180(0.9)^6[/tex]= 96 micrograms.

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(a) The shape of the distribution of donations is rectangular.

(b) The proportion of donations are at least 75 cents id 0.24

(a)The density curve is rectangular in shape.

This indicates that donations are distributed uniformly.

(b) From the question, we have

The probability of donations at least 75 cents as follows:

[tex]P(X\geq 75) =\int\limits^a_b {\frac{1}{99-0} } \, dx \\[/tex]

Substituting the limits,  we get

[tex]P(X\geq 75) =\frac{99-75}{99} \\=\frac{24}{99} \\=0.24[/tex]

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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The value of y in the equation in term of x is y= (1-8x)/(3)

An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. For example, 8x = 1-3y is an algebraic equation with two variables x and y with coefficient 8 and 3 respectively and 1 is the constant.

The value of y can there be solved by firstly making 3y the subject of formula

3y= 1-8x

dividing both sides by 3

3y/3= (1-8x)/3

therefore y= (1-8x)/(3)

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A graph of the given inequality (x + y ≥ 500) is shown in the image attached below.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical axes of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would translate the word sentence into an inequality as follows:

x + y greater than or equal to 500 ⇒ x + y ≥ 500

Subtracting x from both sides of the inequality, we have the following equation:

x + y - x ≥ 500 - x

y ≥ 500 - x

Rearranging the equation in slope-intercept form, we have:

y ≥ -x + 500

In conclusion, we can reasonably and logically deduce that both the x-intercept and y-intercept of this linear inequality (equation) is equal to 500.

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Step-by-step explanation:

A boy paid $11 for a bottle with a cork. A bottle costs $10 more than a cork. How much does a cork cost?

cork: c

bottle: 10c

c + 10c = 11

11c = 11

c = $1

A cork costs $1

Answer:

Step-by-step explanation:

1. Basic systems in fluids: 1 pound equals 16 ounces.

2. Multiply 16 ounces by 5 to become equivalent!

16 ounces*5= 80 ounces!

3. Always double check

80 ounces/16=5 pounds

Answer: 80 ounces

By using division, it is obtained that

The Quotient of 8 and cube of 2 is 1

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division.

Divisor x Quotient + Remainder = Dividend.

Let the number be 2

cube of 2 = [tex]2^3 = 8[/tex]

Quotient of 8 and 8 = [tex]\frac{8}{8}[/tex] = 1

The Quotient of 8 and cube of 2 is 1

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Step-by-step explanation:

i marked where to put them

The momentum of the automobile is 7200 kgm/s

Momentum can be described as the product of the velocity and mass of an object.

It is a vector quantity which is defined as a quantity having both magnitude and  direction.

The formula for calculating momentum is expressed as;

p = mv

Where;

Now, let's substitute the values

p = 1200(6)

expand the bracket

p = 1200 × 6

Multiply the values

p = 7200 kgm/s

Hence, the value is 7200 kgm/s

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The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given polygon,(1/3)b - 1/3

Take 1/3 as common in the whole polygon,

1/3(b - 1).

Since the terms 1/3 and (b - 1) both are in the multiplication of each other.

Hence "The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1)".

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The result of the expression (-3/10) + -9 × 9/10 is -42/5

The expression is

(-3/10) + -9 × 9/10

The expression is the mathematical statement that consist of different variables, numbers and the mathematical operators.

The expression is

(-3/10) + -9 × 9/10

Here we have to do the suitable arithmetic operations

First do the multiplication in the given expression

= (-3/10) + (-9×9)/10

= (-3/10) + -81/10

Add the terms in the expression

Here the denominator of the both term is equal so we just need to add the numerators

= (-3 + -81) / 10

= (-3 - 81) / 10

= -84 / 10

Divide both numerator and denominator by 2

= -42/5

Hence, the result of the expression (-3/10) + -9 × 9/10 = -42/5

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The possible pair of null and alternative hypotheses for this experiment is   "The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.

The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases."

Hypotheses

Hypotheses refers the testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Given,

A group of elementary school students designed a study to find a possible relationship between the number of students absent from school and the overall rate of flu infections in their town.

Here we need to find the correct pairing of possible null and alternative hypotheses for this experiment.

Here the given situation is relationship between  the number of students absent from school and the overall rate of flu infections in their town.

So, the null hypotheses of this relation is flu infection rate has no impact on the number of students absent from school

And the alternative hypotheses of the relation is defines that the flu infection rate increases, the number of students absent from school also increases.

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Answer:

Step-by-step explanation:

The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.

The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases.

The correct representations of the given inequality -3(2x - 5) < 5(2 - x) include the following:

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numbers and variables in an algebraic equation, especially based on any of the following inequality symbols:

For this exercise, we would evaluate and simplify the given inequality so as to enable use determine its solution as follows:

-3(2x - 5) < 5(2 - x)

Opening the bracket, we have:

-6x + 15 < 10 - 5x (correct representation)

Rearranging the algebraic equation by collecting terms, we have:

-6x + 5x < 10 - 15

-x > -5

x > 5 (correct representation)

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Answer:

Angle 1: 27

2: 153

3: 58

4: 138

Step-by-step explanation:

1. 180-(116+37)=27

2. 180-27=153

3. 180-(48+74)=58

4. 122+16=138

180-138=42

180-42=138

Answer:

8 people=24 minutes

Step-by-step explanation:

(1,10)(5,18)=18-10/5-1= 8/4 =2

y-8=2(x-4)

Answer:

Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the

Pacific Paradise.

Step-by-step explanation:

The cost, in dollars, of each baseball is B. $6.00.

The first customer paid $60.00 for 4 baseballs and 2 gloves. This will be expressed as:

4b + 2g = 60

The second customer paid $84.00 for 5 baseballs and 3 gloves. This will be:

5b + 3g = 84

Collect both expressions

4b + 2g = 60

5b + 3g = 84

Multiply equation i by 3

Multiply equation ii by 2

12b + 6g = 180

10b + 6g = 168

Subtract

2b = 12

Divide

b = 12/2

b = 6

The baseball is $6.

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The formula to find the measure of an interior angle of a hexagon is [(n - 2)×180]/n. Hence, option C is correct.

In geometry, a polygon is any enclosed curve made up of a collection of continuous line segments (sides) without any intersections.

Triangles (three sides), polyhedral (four sides), and pentagons are the three simplest polygons (five sides). Convex polygons are those in which none of the elongated sides overlap the polygon; concave polygons are those in which they do.

Equilateral refers to a polygon with equal angles. Equiangular shapes have equal internal angles on all sides. Regular polygons are any equilateral and equiangular polygons.

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The solution of the square root equation is x = 8

A square root is a number such that when multiplied by itself, it gives another number.

The square root of a number x is given by √x

Given the square root equation above, we have that

√(x - 4) = - 2

To solve this equation, first, we remove the square root by squaring both sides of the equation. So, we have that

√(x - 4) = - 2

√(x - 4)² = (- 2)²

x - 4 = 4

Adding the number 4 to both sides of the equation, we have that

x - 4 + 4 = 4 + 4

x + 0 = 8

x = 8

So, the solution of the equation is x = 8

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The given algebraic expression can be simplified as 6+9i.

A complex number is represented by the following form: a+bi, where a and b are real numbers.  The variables: a is the real part and bi imaginary part. See an example: 7 + 14i , then:

Regarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 2i² = 2*(-1)= -2.

When you subtract or sum complex numbers, you can only subtract or sum: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. Here, you can see examples:

(5 + 2i) + (5 + 2i) = 10+4i

(4 + 9i) - (1 + 5i) = 1+4i

Therefore, the result for the  6 + √− 81 will be:

6+  √81i²

6+9i

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$142428 income earned. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services.

A type of variable-pay compensation for goods or services sold are commissions. Salespeople are frequently encouraged and rewarded with commissions. Additionally, commissions can be created to promote particular sales habits. For instance, commissions may be decreased while providing significant discounts.

Let X be the sales for a man

so7% of sales=7x/100

Total that needs to be earned=$11470

So,

Total needs to be earned= salary +commission on sale

11470=1500+7x/100

11470-1500=7x/100

9970=0.7x

X=9970/0.7

X=142428

Therefore $142428 income earned .

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Answer:

18:360 is the correct answer