find each value for the equations

The simplest polynomial function having integer coefficients with the given zeros is: x⁴ -2x³ + 14x² - 32x - 48

The polynomial is of degree 4

We have the values as 4i, 3 , -1

Hence we would have the following in brackets

for 4i = (x - 4i) (x + 4i)

for 3 = (x - 3)

for - 1 = (x + 1)

We would have to multiply these

(x - 4i) (x + 4i) (x - 3) (x + 1)

f(x) = x² + 4ix - 4ix (-4i)² (x² + x - 3x - 3)

f(x) = (x²  + 16)(x² - 2x - 3)

This can also be expanded to standard form if you wish

x⁴ - 2x³ - 3x² + 16x² - 32x - 48

properly arrange

x⁴ -2x³ + 14x² - 32x - 48

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where A is a real integer and A ≠ 0.

f(x) = A(x2 + 16)(x - 3)(x + 1)

The above function should be used to complete the table based on the given domain as follows;

x         0      1     2     3    4    

f(x)      -6     -5   -3     1    9

In order to use the given exponential function to complete the table, we would have to substitute each of the values of x (x-values or input values) into the exponential function and then evaluate as follows;

When the value of x is 0, the exponential function is given by;

f(x) = 2^x - 7

f(0) = 2^0 - 7

f(0) = 1 - 7

f(0) = -6.

When the value of x is 1, the exponential function is given by;

f(x) = 2^x - 7

f(1) = 2^1 - 7

f(1) = 2 - 7

f(1) = -5.

When the value of x is 2, the exponential function is given by;

f(x) = 2^x - 7

f(2) = 2^2 - 7

f(2) = 4 - 7

f(2) = -3.

When the value of x is 3, the exponential function is given by;

f(x) = 2^x - 7

f(3) = 2^3 - 7

f(3) = 8 - 7

f(3) = 1.

When the value of x is 4, the exponential function is given by;

f(x) = 2^x - 7

f(4) = 2^4 - 7

f(4) = 16 - 7

f(4) = 9.

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The possible side length of the third side is 16 inches

It is important to note that the Pythagorean theorem states that the square of the hypotenuse side is the sum of the square of the other two sides, they are the opposite and adjacent sides.

This is represented as;

a² = b² + c²

Given that;

Note: 1 feet = 12 inches

Substitute the values into the formula, we get;

20² = 12² + c²

Find the squares

400 = 144 + c²

collect like terms

c² = 256

Find the square root

c = 16 inches

Hence, the value is 16 inches

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Using the factor method, the other x-intercept for the parabola defined by the equation is; (-5, 0)

We are given the equation of the parabola as;

y = -x² - 7x - 10

We are given one of the x-intercepts as (-2, 0). Thus, let us factorize the equation of the parabola by setting it to zero to get;

-x² - 7x - 10 = 0

Let's factor it as;

-x² - 2x - 5x - 10

Factorizing it out gives;

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

Thus, we now have;

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

Thus, the other x-intercept is at;

-x - 5 = 0

x = -5

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Answer:

56 Primitive feet

Step-by-step explanation:

Are 5 ways for four people with different heights to line up single-file so that exactly two people are taller than the person immediately behind them.

Let's call the four people A, B, C, and D, and let's assume that their heights are distinct and that A is the shortest. Then, there are 3! = 6 ways for them to line up single-file without any restrictions on their heights. However, this counts the cases where A is taller than B, which is not allowed.

To correct for this overcounting, we can subtract the number of ways where A is taller than B, which is 2! = 2, since there are 2! ways to arrange B, C, and D in this case.

However, this also subtracts the case where A is taller than both B and C, which is not allowed.

So, we need to add the number of ways where A is taller than both B and C, which is 1, since there is only 1 way to arrange B, C, and D in this case. Therefore, by PIE, the number of ways for A, B, C, and D to line up single-file so that exactly two people are taller than the person immediately behind them is:

6 - 2 + 1 = 5

So, there are 5 ways for four people with different heights to line up single-file so that exactly two people are taller than the person immediately behind them.

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Ella bought 12 mini cakes. The solution has been obtained using the unitary method.

What is a unitary method?

In the unitary technique, the value of a single unit is determined first, and then the value of the required number of units is determined. Simply expressed, the unitary approach is used to determine the value of a single unit from a specified multiple.

We are given that the bakery charges $35 for 7 mini cakes

So, the charge for 1 mini cake is

⇒$35/7 = $5

Now, Ella has bought mini cakes for $60.

So, the number of mini cakes bought by her are

⇒$60/$5 = 12

Hence, Ella bought 12 mini cakes.

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The inequality equations is

a) The point ( -9 , 4 ) lies on the inequality relation

b) The point ( 6 , -2 ) lies on the inequality relation

c) The point ( 0 , -4 ) does not lie on the relation

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

a)

Now , let the first point be represented as P ( -9 , 4 )

The shaded region is below 4 in the y axis and less than -4 in the x axis

So , the point ( -9 , 4 ) does lies on the inequality equation graph

b)

Now , let the first point be represented as Q ( 6 , -2 )

The shaded region is below -8 in the y axis and less than 8 and more than 4  in the x axis

So , the point ( 6 , -2 ) does lies on the inequality equation graph

c)

Now , let the first point be represented as R ( 0 , -4 )

The shaded region is above -8 in the y axis and more than -4 in the x axis and less than -1

So , the point ( 0 , -4 ) does not lie on the inequality equation graph

Hence , the inequality equations is solved

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The number of ways to load the cars onto the truck is  [tex]^{25}C_3[/tex] i.e. 2300 ways.

To find the number of ways to load the cars on the truck we can use the formula for combination, which is given by -

C(n,k) = n! / (k! (n-k)!)

where n is the total number of cars (25), k is the number of cars we want to choose (3)

Using this formula, we can calculate the number of ways to load the cars as follows -

C(25,3) = 25! / (3! (25-3)!) = 252423 / (321) = 2300

Hence, there are 2300 ways to load 3 cars out of 25 onto the truck for transport.

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It is not a triangle.

Does given feet is a triangle or not?

The Triangle Inequality theorem states that in a triangle, , where  and  are shorter side lengths and  is the longest side length.

Given that  5+9<15, the given side lengths do not compose a valid triangle.

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Answer:

You can find the unit rate for each cereal an see which one is a better deal.  You divide and quantity of cereal by the price.

72 words per minute

Step-by-step explanation:

Say one box of cereal has 100 ounces and it cost $4.50 and another box of cereal has 150 ounces for $5.25

4.50/100 = .045 cents per ounce the other box would be

5.25/150 = .035 cents per ounce.

1800/25 = 72

If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3  and number of 6 cent stamps used is 12 .

Let number of 41 cents stamps used be = x ;

and let number of 6 cents stamps used be = y ;

converting amount 41-cents in dollars is = $0.41  ;

and converting amount 6-cents in dollars is = $0.06  ;

the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;

this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 195  ;

⇒ y = (195 - 41x)/6 ;

We will test this equations for values of x and y , the number of stamps must be whole numbers .

If x = 1 , then value of y is = 25.66

If x = 2 , then value of y is = 18.833

If x = 3 , then value of y is = 12

If x = 4 , then value of y is = 5.166 .

the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .

Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .

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Denominator can be defined as the bottom number in a fraction that shows the number of equal parts an item is divided into. It is the divisor of a fraction

The given problem is

13x^6

51 x^4

From here, we must exclude all values that make the denominator equal to zero.

This is defined if and only if

x ≠ 0

Even the given expression can be simplified to obtain:

13x^6

51 x^4

The exclusion is

x ≠ 0

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Answer:

x = 0

Step-by-step explanation:

I got it correct on Odyssey. Feel free to let me know if you need any help in the future  : )

The cost of each raffle ticket is thus $14.50, and the cost of 90 tickets is $1305.

In multiplication, the numbers being multiplied are referred to as factors, and the end result is referred to as the product. In division, the dividend is the number being divided, the divisor is the number dividing it, and the quotient is the outcome of the division.

Given that the equation to find the cost of a single ticket is:

1218 ÷ 84 = x

x = 14.5

The cost of each raffle ticket is thus $14.50.

The cost of 90 tickets is given by:

90 × 14.50 = y

y = 1305.

Hence, the cost of 90 tickets is $1305.

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A 250ml tin of paint costs £3.35  tin is better value for money.

The best balance of price, quality, and sustainability to satisfy consumer needs is referred to as best value for money. Cost in this sense refers to taking into account total cost of ownership.

Value for money is seen as an effective framework for evaluating performance in not-for-profit organisations since it takes into account both the costs and benefits of delivering a service.

A 345ml tin of paint costs £4.80

345 / 4.80 = 71.87

A 250ml tin of paint costs £3.35

250 / 3.35 = 74.62

so

A 250ml tin of paint costs £3.35 is 74.62,

A 250ml tin of paint costs £3.35  tin is better value for money.

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If you had only 5 and 11 cent stamps, it would be impossible to make a postage stamp for any amount less than 16 cents.

This is because 16 cents is the smallest amount that can be made with those two denominations of stamps.

To prove this, let's start by looking at the possible combinations of 5 and 11 cent stamps that can be used to make a postage stamp:

5 cent stamps x 11 cent stamps

1 x 0 = 0

1 x 1 = 11

2 x 0 = 10

2 x 1 = 16

As you can see, the smallest possible combination of 5 and 11 cent stamps is 2 five cent stamps and 1 eleven cent stamp, which totals 16 cents. Therefore, it is impossible to make a postage stamp for any amount less than 16 cents using only 5 and 11 cent stamps.

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The shape of the banana curve is a parabola, the number of zeros is 1, the zeros of the polynomial are (-3, 4), and the quadratic polynomial is a(x² - 16).

(i) The shape of the banana curve from the figure is a parabolic shape.

(ii) The number of zeros of the polynomial for the shape of the banana is 1.

(iii) To find the zeroes of f(x) = x² - x - 12, we need to solve the equation x² - x - 12 = 0 using the quadratic formula.

x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = -1, c = -12

x = (1 ± √(1 + 48)) / 2

x = (1 ± √49) / 2

So, the zeroes are (1 + 7) / 2 = 4 and (1 - 7) / 2 = -3.

(iv) If the representation of the banana curve whose one zero is 4 and the sum of the zeroes is 0, then the equation is x = -4 and x = 4.

The quadratic polynomial is f(x) = a(x - 4)(x + 4) = a(x² - 16).

Since the coefficient a is not given, we cannot determine the exact polynomial, but we know it must be of form f(x) = a(x² - 16).

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--The given question is incomplete; the complete question is

"The below quadratic function can model the natural shape of a banana. Now, we know that a parabolic shape must have a quadratic function, therefore an equation in standard form of f(x) = ax² + bx + c. To find an equation for the parabolic shape of the banana, we need to find the values of a, b, and c. From the banana picture above, we can see that a quadratic function is able to model the banana quite accurately, with a=0.1, b=0, and c=0. Therefore, the equation is f(x) = 0.1x²

(i) Name the shape of the banana curve from the above figure.

(ii) Find the number of the zeroes of the polynomial for the shape of the banana.

(iii) If the curve of banana represented by f(x) = x² - x - 12. Find its zeroes.

(iv) If the representation of banana curves whose one zero is 4 and the sum of the zeroes is 0, then find the quadratic polynomial.​"--

A statement which is false include the following: D. In the ordered pair (9, 7), 7 is the x-coordinate.

In Mathematics, an ordered pair is a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate and the y-coordinate on the coordinate plane of any graph such as the following:

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(6 - 3)² + (7 - 7)²]

Distance = √[3² + 0²]

Distance = √9

Distance = 3 units.

In conclusion, in the ordered pair (9, 7), 9 is the x-coordinate while 7 is the y-coordinate.  

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A total of 31 child tickets were sold that day.

System of Equations:

Problems with two unknown values require a system of equations containing two variables.

A unique solution is obtained only when the lines formed by the equations intersect at only one point.

Let C be the number of child tickets and A be the number of Adult tickets

Now, like most coin, cost, or earnings problems, you can make a number balance and a money balance and get two equations for the two unknowns defined above:

4C=adults, because four times as many tickets were sold

6.50C+9.80(4C)=1436.80

6.50C+39.2C=652.50

45.7C=1436.80

C=31

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Answer:

0.51

Step-by-step explanation:

45 / (45 + 6 + 37) = 0.51

Answer:

A function is concave downward if its second derivative is negative. To find the values of x for which the graph of y = x^4 - 6x^2 + x is concave downward, we need to find the values of x for which the second derivative of y is negative.

The second derivative of y = x^4 - 6x^2 + x is y'' = 12x^2 - 12x

To find the values of x for which y'' is negative, we need to find the roots of the equation 12x^2 - 12x = 0.

We can factor the equation as: 12x(x-1) = 0

which gives us x = 0 and x = 1 as the roots.

Now, we need to test the sign of the second derivative in the intervals between the roots.

In the interval (0,1)

y'' = 12x^2 - 12x is positive, therefore the function is not concave downward in this interval.

In the interval (-infinity,0)

y'' = 12x^2 - 12x is negative, therefore the function is concave downward in this interval.

In the interval (1,infinity)

y'' = 12x^2 - 12x is negative, therefore the function is concave downward in this interval.

Therefore, the values of x for which the graph of y = x^4 - 6x^2 + x is concave downward are all values of x less than 0 or greater than 1.

When it comes to baking bread, Jennifer has an absolute advantage. But when it comes to making cookies, Janet has an absolute advantage.

Absolute advantage is used when there is efficient production.  It is used to describe the ability of a person, place, business, or nation to produce a lot of goods or services with the same amount of inputs in a given amount of time.

Here, a loaf of bread baked by Jennifer takes about 2 hours but it takes about 3 hours for Janet to bake a loaf of bread. So, Jennifer has an absolute advantage in baking a loaf of bread.

Also, Jennifer takes about 1 hour to bake 12 cookies but it only takes 3/4 hours or 45 minutes for Janet to bake cookies 12 cookies. So, Janet has an absolute advantage in baking a dozen cookies.

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Laverne said the number 222 before Shirley flees

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

To solve this exercise we are going to apply the formula of the arithmetic sequence:

S = (n/2)[a1 + a1 + d(n - 1)]

Where;

Information about the problem:

Clearing the (n) variable we get:

S = (n/2)[ 7 +  7 + 5(n-1) ] > 5000

(n/2) [ 9 + 5n ]  > 5000

n[ 9 + 5n  ] > 10000

5n^2 + 9n - 10000 > 0

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 9 ± √ [9² - (4* 5*-10000)]} / (2 * 5)

x= {- 9 ± √ (81+ 200000)} / 10

x= {- 9 ± √200081} / 10

x= (- 9 ± 447.30) / 10

x = 43.83

n > 43 then n = 44

Calculating the 44th term, we get:

aₙ= a + d*(n-1)

a44 = [ 7 +5(44 - 1) ]

a44 =  [ 7 +5(43) ]

a44 = 222

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As per the perimeter of rectangle, the  the amount area of fence does she need to buy to build around her new garden is 40 feet.

In math the term called perimeter is defined as the length of the outline of a shape. And the general form to calculate the perimeter of the rectangle is written as,

=> P = 2(l + b)

here l refers the length of rectangle and b refers the breadth of rectangle.

Here we know that the gardens old measurements is written as,

=> length = 14 feet

=> breadth = 16 feet.

Then the perimeter of garden is calculated as,

=> P1 = 2(14 + 16)

=> P1 = 2(30)

=> P1 = 60

Then the new measurement is given that,

length = 28 feet

width = 12 feet.

Then the new measurement is calculated as,

=> P2 = 2(28 + 12)

=> P2 = 2(40)

=> P2 = 80

Then additional fence does she need to buy to build around her new garden is

=> P = P2 - P1 = 80 - 40

=> P = 40 feet.

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Answer: Your GCF would be 1!

Step-by-step explanation:

First you need to:

Factor 10x² as shown - 2 · 5 · x · x

Factor 21x as shown - 3 · 7 · x

Factor 49 as shown: 7 · 7

GCF = 1

I hope this helps!

Answer:

12

Step-by-step explanation:

Assuming that $300 and $50 are the respective cost(s) of the premium and discount tickets, if we didn't buy any premium tickets, we could afford to buy 12 discount tickets at $50 because 12($50) = $600 

The ratio of the volume of the figure is 3:1.

The term called volume in math is defined as the space occupied within the boundaries of any three-dimensional solid

Here we know that the cylinder and a cone are having equal radii of their bases and heights.

Then let us consider that radius of the cone is equal to radius of the cylinder is defined as r and Height of the cone and height of the cylinder is defined as h.

Then their volume is written as,

=> Volume of cylinder /volume of cone

=> πr²h/ (1/3)πr²h

When we simplified this on, then we get the fraction as,

=> 3/1

Then the resulting ratio is 3:1.

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Answer:

To factor the equation y = x^2 + 6x + 8, we can use the method of finding the factors of the constant term (8) that add up to the coefficient of the x term (6).

In this case, the factors of 8 are 1 and 8, and -1 and -8. But only -1 and -8 add up to 6, so we can factor the equation as:

(x + 8)(x + 1) = 0

So the solutions are x = -8 and x = -1.

The trigonometric function that accurately fits the data is as follows:       y = 1.87sin(–0.29x + 4.79) + 6.13. So the option D is correct.

The following is the trigonometric function that best represents the data:

y = 1.87sin(-0.29x + 4.79) + 6.13

Check the values in the table using the aforementioned equation;

At x = 1

y = 1.87sin(-0.29 x 1  + 4.79) + 6.13

y = 1.87sin(4.5 rad) + 6.13

y = 4.3

At x = 2

y = 1.87sin(-0.29 x 2  + 4.79) + 6.13

y = 1.87sin(4.21 rad) + 6.13

y = 4.49

At x = 4

y = 1.87sin(-0.29 x 4  + 4.79) + 6.13

y = 1.87sin(3.63 rad) + 6.13

y = 5.2

At x = 7

y = 1.87sin(-0.29 x 7  + 4.79) + 6.13

y = 1.87sin(2.76 rad) + 6.13

y = 6.8

At x = 9

y = 1.87sin(-0.29 x 9  + 4.79) + 6.13

y = 1.87sin(2.18 rad) + 6.13

y =7.7

At x = 10

y = 1.87sin(-0.29 x 10  + 4.79) + 6.13

y = 1.87sin(1.89 rad) + 6.13

y = 7.9

At x = 13

y = 1.87sin(-0.29 x 13  + 4.79) + 6.13

y = 1.87sin(1.02 rad) + 6.13

y = 7.72

At x = 17

y = 1.87sin(-0.29 x 17  + 4.79) + 6.13

y = 1.87sin(-0.14 rad) + 6.13

y = 5.9

At x = 20

y = 1.87sin(-0.29 x 20  + 4.79) + 6.13

y = 1.87sin(-1.01 rad) + 6.13

y = 4.6

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The complete question is:

Review the table showing wind speed, y, in miles per hour, measured x hours after midnight. Which trigonometric function best models this data?

Hours after Midnight                          Wind Speed (mph)

              1                                                      4.3

              2                                                     4.2

              4                                                      5

              7                                                      6.8

              9                                                      8

              10                                                     8.1

              13                                                     7.2

              17                                                     6

              20                                                    5.1

y = 1.87sin(0.29x + 6.13) + 4.79

y = 1.87sin(0.29x + 4.79) + 6.13

y = 1.87sin(–0.29x + 6.13) + 4.79

y = 1.87sin(–0.29x + 4.79) + 6.13