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The polynomial function of least degree with only real coefficients is y = x³ - 8 · x² + 22 · x - 20.

The statement indicates that the polynomial has a leading coefficient of 1 and zeros of 2 and 3 + i. By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then, all the roots of the polynomial function of least degree are 2, 3 + i and 3 - i. The complete expression is shown below:

y = 1 · (x - 2) · (x - 3 - i) · (x - 3 + i)

y = (x - 2) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 2) · (x² - 6 · x + 9 - i²)

y = (x - 2) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer: J(2,2) K(1,-1) thats all I got

Step-by-step explanation:

Using a proportional relationship, it is found that:

The graph for this relationship is given at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For this problem, we have that the variables are:

Hence the proportional relationship between these two variables is given by:

y = 2x.

Then:

The linear graph of the relationship, considering the given points, is given at the end of the answer.

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Answer:

I. 1) 32124, 32456, 32532, 32934, 32983

 2) 62279, 62312, 62345, 62387, 62398

 3) 89123, 90246, 89345, 89534, 89923

 4) 19087, 19216, 19312, 19432, 19910

 5) 31821, 31839, 31861, 31876, 31890

II. 1) 58240, 58204, 58042, 58024

  2) 10908, 10809, 10098, 10089

  3) 85703, 85370, 85307, 85073

  4) 98705, 98570, 98507, 98057

  5) 41810, 41108, 41081, 41018

Step-by-step explanation:

Step-by-step explanation:

it is always the same. the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.

the direction itself does not matter, but it is important to use the same direction for the x and the y comparison.

I prefer to go from left to right, so let's go from

(-3, 4) to (2, -4).

x changes by +5 (from -3 to 2).

y changes by -8 (from 4 to -4).

the slope is

-8/+5 = -8/5

Answer:

0.08

Step-by-step explanation:

[tex]\frac{10}{45+10+64}[/tex]  The numerator is the number of times a customer used a debit card.  The denominator is the total of all the ways that customers have paid.

[tex]\frac{10}{19}[/tex] = 0.08403361344

This rounded to the nearest hundredths is

0.08

Answer:

0.08

Step-by-step explanation:

45 cash, 10 debit card, and 64 credit card.

= 45+10+64=119

There were a total of 119 customers. 10 paid with a debit card.

Probability the next customer will pay with a debit card:

10/119

=0.084033...

≈0.08

18 units is the distance between points F and G.

Assume a line with points marked on it.

Center is 0.

Left to the point 0 indicates negative numbers.

Right to the point 0 indicates positive numbers.

Given,

A number line is marked with negative 10 to positive 14.

Point F is placed at negative 6.

Point G is placed at positive 12.

We have to determine the distance between points F and G.

We can consider the number line.

From 0 to negative 10 there were 10 units.

From 0 to positive 14 there were 14 units.

Now points F and G,

From 0 to negative 6 there were 6 units.

From 0 to positive 12 there were 12 units.

We can add this together:

That is,

6 units + 12 units = 18 units.

Therefore, the distance between points F and G is 18 units.

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The  the savings, expressed in percent if you order the combo is 18.75%, if the combo is bought at $6.50

What is the amount saved when combo is ordered?

The amount saved when ordering for combo instead of ordering hamburger and French fries is the difference between the total cost cost when for individual orders and the cost of the combo

total cost for individual orders=$5.00+$3.00

total cost for individual orders=$8.00

combo cost=$6.50

savings on combo=total cost for individual orders-combo cost

savings on combo=$8.00-$6.50

savings on combo=$1.50

% savings on combo=$1.50/$8.00

% savings on combo=18.75%

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According to the given statement the following car seats are adequate for a 32-pound child:

Interval notation tells which part of the number line, from left to right, is included in the solution (i.e., which part of the number line is shaded). Parentheses are written next to endpoints which are NOT included in the solution while brackets are written next to included endpoints.

The Inequality car seat is intended for children weighing up to 30 pounds.

let the child's weight = x

x ≤ 30

Inequality for a car seat built for a child weighing between 15 and 40 pounds;

15 < x < 40

Inequality for a car built for a youngster weighing between 30 and 85 pounds;

30 < x < 85

According to the given statement the following car seats are adequate for a 32-pound child:

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The given question is not complete.

A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?

Answer:

26

Step-by-step explanation:

[tex]FH=7+19=26[/tex]

Answer:

FH = 26

Step-by-step explanation:

The equation will be,

→ FH = FG + GH

Then the value of FH will be,

→ FH = 19 + 7

→ [ FH = 26 ]

Hence, the value of FH is 26.

The given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determined by using Pythagorean theorem which is the correct option (C).

Pythagoras theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

The given triangle whose sides are 6cm, 10cm, and 12cm

Now, applying Pythagorean's theorem:

⇒ 6² + 10² = 12²

⇒ 36 +100 = 144

⇒ 136 = 144

Here, it is clearly observed that 136 <  144 therefore, the triangle is obtuse.

Therefore, the given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle

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

Work below!

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

Simply multiply the inches by 20 (the scale per inch), and you have your answer!

3.5 x 20 = 70

The height is 70 inches.

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

Good luck! :)

(Consider leaving a Brainliest if this helped!)

~pinetreee

Answer:

70

Step-by-step explanation:

If you multiply 3.5 times 20 you get 70

Answer:

see below

Step-by-step explanation:

RATE is  560 mi / 8hr = 70 mi/hr

Rate * time = distance

         then

time = distance / Rate = 200 mi /  70 mi/hr = 2.857 hr   ( or 2 hr 51 min)

Answer:

given

Step-by-step explanation:

When doing a two-column proof, you usually begin with what you are given.

The ticket price of

A Senior citizen = $14

A Child               = $4

First day of ticket sales :

Senior citizen tickets (s) = 14

Child tickets (c)             = 14

Total price of both tickets = $252

14s + 14c = 252   eq. (1)

Second day of ticket sales :

Senior citizen tickets (s) = 9

Child tickets (c)              = 7

Total price of both tickets = $154

9s + 7c = 154   eq. (2)

Multiplying equation 2 with 2, we get

18s + 14c = 308    eq. (3)

Now, we will subtract eq. (1) from eq. (3)

18s + 14c = 308    eq. (3)

-14s - 14c = -252    eq. (1)

____________________

          4s = 56

            s = 56/4

            s = 14

We get the ticket price of one senior citizen which is 14 Dollars.  

Now, we will put s = 14 in eq. 2,

So,  9s + 7c = 154

 (9×14) + 7c = 154

              7c = 154  - 126

                c = 28 / 7

               c = 4

Ticket price of one child is 4 Dollars.

Hence, the ticket price of a senior citizen and a child is $14 and $4, respectively.

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Answer:

Vertex: (-1, 4)

Domain: All Real Numbers

Range: y < or equal to 4

Step-by-step explanation:

Vertex: Using my calculator, i determined the vertex. The vertex is the most bottom/top point of the parabola, depending on if it opens down or up.

Domain: All the answers have all real numbers so its obvious.

Range: the parabola opens down at (-1, 4), so all the numbers on the y axis below 4 fit in with the line

Using equations, the solutions for the problems are given as follows:

1. She played 5 games.

2. Gary had 7 rebounds.

3. The width of the rectangle is of 38 inches.

4. Mark had 21 rebounds.

5. Tony spent 45 minutes studying for his Biology test.

6. The length of the rectangle is of 72 inches.

7. He rented the limousine for 6 hours.

8. The two numbers are 11 and 26.

9. Pamela is 8 years old.

10. Debra is 1 year old now.

The situation is modeled by the following linear function:

P(n) = 2.75 + 4.25n.

We have that P(n) = 24, hence we have to solve for n.

24 = 2.75 + 4.25n.

n = (24 - 2.75)/4.25

n = 5.

She played 5 games.

The situation is modeled by the following system of equations:

Hence:

3y + y = 28

4y = 28

y = 7.

Gary had 7 rebounds.

Considering the equations for the perimeter of the triangle, and the situation described, we have that:

Hence:

2(2w - 4 + w) = 220

2(3w - 4) = 220

3w - 4 = 110

3w = 114

w = 114/3

w = 38.

The width of the rectangle is of 38 inches.

Solution x for item 2, hence:

x = 3y = 3 x 7 = 21.

Mark had 21 rebounds.

This situation is modeled by the following equation:

3x + 5 = 140

3x = 135

x = 135/3

x = 45.

Tony spent 45 minutes studying for his Biology test.

This is the solution for l of item 3, hence:

l = 2w - 4 = 2 x 38 - 4 = 72.

The length of the rectangle is of 72 inches.

The situation is modeled by the following equation:

P(x) = 125 + 50x.

We have that P(x) = 425, hence we solve for x as follows:

425 = 125 + 50x

50x = 300

x = 300/50

x = 6.

He rented the limousine for 6 hours.

The situation is modeled by the following system:

Hence:

15 + y + y = 37

2y = 22

y = 11.

x = 15 + 11 = 26.

The two numbers are 11 and 26.

The situation is modeled by the following system:

Hence:

x + 6 = 2(x - 7 + 6)

x + 6 = 2(x - 1)

x + 6 = 2x - 2

x = 8.

Pamela is 8 years old.

This is the solution for y of the previous item, hence:

y = x - 7 = 8 - 7 = 1.

Debra is 1 year old now.

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[tex](6d+5)-(2-3d)[/tex]

We subtract algebraic expressions exactly as we would integers, or as we would in a 'normal' subtraction sentence. First, we must open up the brackets:

[tex]= 6d+5-2+3d[/tex]

Now, combine like terms:

[tex]= 9d+5-2\\= 9d+3[/tex]

9d+3

Answer: $5.49

Step-by-step explanation:

Unit price = 21.96/4 = 5.49

Answer:

x = -0.27 or 3.77

Step-by-step explanation:

explanation in pic

Answer:

This simplifies to 7x^2 - x.

Step-by-step explanation:

(x + 1)3 − x (x − 2)2 − 1

= x^3 + 3x^2 + 3x + 1 - x(x^2 - 4x + 4) - 1

= x^3 + 3x^2 + 3x + 1 - x^3 + 4x^2 -4x - 1

= 7x^2 - x

Using translation concepts, function g(x) is given as follows:

C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is given by:

[tex]f(x) = \sqrt[3]{x}[/tex]

The translations for g(x) are as follows:

Thus the rule is:

C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]

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Using it's concept, the average rate of change is given as follows for the intervals:

a) -6 millions of dollars per year.

b) -18 millions of dollars per year.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, we have that:

Hence:

r = (366 - 372)/1 = -6 millions of dollars per year.

For item b, we have that:

Hence:

r = (318 - 372)/3 = -18 millions of dollars per year.

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The amount of fiber asked by the doctor to be consumed is 30 grams .

Method to calculate percentages :

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .

Let the amount of fiber asked by the doctor to be consumed be x .

According to question ,

40 % of x = 12

Solving the equation ,

( 40 / 100 ) * x = 12

x = 1200 / 40

x = 30

Hence ,  the amount of fiber asked by the doctor to be consumed is 30 grams .

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Answer:

30

Step-by-step explanation:

Answer:

100 cards?

Step-by-step explanation:

Answer:

f(0) = 0

f(-2) = 0

f(5) = 15

f(-10) = 16

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases} \begin{aligned}-2x-4 & \;\;\textsf {if }\;x < 0\\3x & \;\;\textsf {if }\;x\geq 0\\\end{aligned}\end{cases}[/tex]

Therefore, the function has two definitions:

When graphing piecewise functions:

First piece of the function

Substitute zero into the first function:

[tex]\implies f(0)=-2(0)-4=-4[/tex]

Place an open circle at point (0, -4).

To help graph the line, find another point on the line by inputting another value of x that is less than zero into the same function:

[tex]\implies f(-2)=-2(-2)-4=0[/tex]

Place point (-2, 0) and draw a straight line from the open circle at (0, -4) through (-2, 0).  Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of the function

Substitute zero into the second function:

[tex]\implies f(0)=3(0)=0[/tex]

Place an closed circle at point (0, 0).

Again, to help graph the line, find another point on the line by inputting another value of x that is more than zero into the same function:

[tex]\implies f(2)=3(2)=6[/tex]

Place point (2, 6) and draw a straight line from the closed circle at (0, 0) through (2, 6).  Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

To find the given functions, decide which function to use based on the given value of x, then solve.

f(0) means to find the value of the function when x = 0.

Therefore, input x = 0 into the second function as x ≥ 0.

[tex]\implies f(0)=3(0)=0[/tex]

f(-2) means to find the value of the function when x = -2.

Therefore, input x = -2 into the first function as x < 0.

[tex]\implies f(-2)=-2(-2)-4=0[/tex]

f(5) means to find the value of the function when x = 5.

Therefore, input x = 5 into the second function as x ≥ 0.

[tex]\implies f(5)=3(5)=15[/tex]

f(-10) means to find the value of the function when x = -10.

Therefore, input x = -10 into the first function as x < 0.

[tex]\implies f(-10)=-2(-10)-4=16[/tex]

========================================================

Explanation:

t = number of t-shirts

t = 100 shirts are in the box

Plug this into the equation and simplify to find W

W = 250+132.5t

W = 250+132.5(100)

W = 250+13250

W = 13500

The box weighs 13500 grams

This is equivalent to 13500/1000 = 13.5 kg