when do we say that a real number, say r, is a root of a given polynomial equation in x?

Answers

Answer 1

check picture below.

When Do We Say That A Real Number, Say R, Is A Root Of A Given Polynomial Equation In X?

Related Questions

The base of a pyramid covers an area of 13.3 acres (1 acre = 43,560 ft2) and has a height of 473 ft. if the volume of a pyramid is given by the expression v = bh/3, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.

Answers

V = 43560 * 473 / 3 = 6867960 cu feet

1 cubic meter = 35.315 cu ft

Volume of the pyramid = 6867960 / 35.315 = 194,477.13 cubic meters

Why is the mean greater than the median in right skewed?

Answers

Right skewed makes a bar graph table have a right tail, meaning the left-side of the data is higher than that of the left-side. The median does not change based on the size of the data but the mean does because the left-side of the data has grown, when you add them all together and divide by the number of data sets, it will be larger by a certain amount.

When BA = 10 ft, find the area of the region that is NOT shaded. Round to the nearest whole number.

A) 52 ft^2

B) 262 ft^2

C) 43 ft^2

D) 305 ft^2

Answers

(1) Area of the whole circle:
A = πr²
Substitute the value of BA to r,
A = (π)(10 ft)² = 314.16 ft²

(2) Area of the sector is calculated through the equation,
As = πr²(x/360°)
where x is the intercepted angle. Substituting the values,
As = π(10 ft)²(60°/360°) = 52.36 ft²

(3) Area of the equilateral triangle BAJ,
At = (√3)(a2²/4
where a is also equal to r or BA. Substituting,
At = (√3)(10 ft)²/4 = 43.30 ft²

The area of the region not shaded is equal to,
= (A) - (As - At)

Substituting,
= (314.16 ft²) - (52.36 ft² - 43.30 ft²)
Area = 305.10 ft²

Therefore, the answer to this answer is letter D.

(05.02)
Two quantities are related, as shown in the table:

x

y

2 3
4 4
6 5
8 6

Which equation best represents the relationship?
y = 1 over 2 x + 2
y = 1 over 2 x + 1
y = x + 2 y = 2x + 1

Answers

first equation y=1/2x +2

x=2 = 1/2(2) +2 =1+2 =3

x=4 = 1/2(4)+2 = 2+2 =4

first equation is the answer

Answer:

[tex]y=\dfrac{1}{2}x+2[/tex]

A is correct

Step-by-step explanation:

Given: Table of x and y

x : 2 4 6 8

y : 3 4 5 6

Using two point find the slope:

(2,3) and (4,4)

[tex]Slope=\dfrac{4-3}{4-2}[/tex]

[tex]\text{Slope }=\dfrac{1}{2}[/tex]

Now we find slope using last two point

(6,5) and (8,6)

[tex]\text{Slope }=\dfrac{6-5}{8-6}[/tex]

[tex]\text{Slope }=\dfrac{1}{2}[/tex]

Slope is equal. Thus, The given relation is linear.

[tex]y-3=\dfrac{1}{2}(x-2)[/tex]

[tex]y=\dfrac{1}{2}x+2[/tex]

Hence, The relation represents a linear equation [tex]y=\dfrac{1}{2}x+2[/tex]

STVU is an isosceles trapezoid. If SV = 3x + 1 and TU = x + 21, find the value of x.

Answers

Definition of isos trapezoid=> A trapezoid with congruent legs.
Theorem=> Diagonals in a isosceles triangle are congreunt.
Answer=> SV is a diagonal and so is TU therefore they are equal.
Set aside=> 3x+1=x+21
Solve=> 2x=20
x=10

Answer:

The value of x is 10.

Step-by-step explanation:

Given information: STVU is an isosceles trapezoid, SV = 3x + 1 and TU = x + 21.

According to the properties of isosceles trapezoid, then diagonals of an isosceles trapezoid are equal.

SV and TU are diagonals of the isosceles trapezoid, so

[tex]SV=TU[/tex]

[tex]3x+1=x+21[/tex]

Separate like terms.

[tex]3x-x=21-1[/tex]

[tex]2x=20[/tex]

Divide both sides by 2.

[tex]x=10[/tex]

Therefore the value of x is 10.

Evaluate the function f(x) = 4x -1 when x= -1 ..... f(-1) =___

Answers

4x-1 when x=-1
4(-1)= -4 *bam* That's your answer.

Final answer:

To evaluate the function f(x) = 4x - 1 for x=-1, you first substitute -1 into the equation, then perform multiplication before subtraction as per the order of operations resulting in f(-1) = -5.

Explanation:

To evaluate the function f(x) = 4x - 1 when x is -1, we simply replace the variable x in the equation with -1. The equation becomes f(-1) = 4(-1) - 1.

Now to perform the operations indicated in the equation, we should start with multiplication before subtraction according to the order of operations.

The multiplication of 4 and -1 gives -4 so the equation becomes f(-1) = -4 - 1.

Finally subtracting 1 from -4 gives -5. Therefore, f(-1) = -5.

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An elevator descends into a mine shaft at the rate of 6 m/min. If the descendstarts from 20 meter above the ground level, how long will it take to reach - 340m?

Answers

it has to travel 20 meters before it gets to ground level, then another 340 meters till it reaches -340.....so it has to travel a total of 360 meters

and if it descends at a rate of 6 meters per minute...
360/6 = 60 minutes....or 1 hr to reach -340 <==

juanita and lauren are painting a circular mural on one wall of the community center the area of the mural is 88 square meters what is the radius.

Answers

To set up this equation, you would enter 88=pi times radius^2. Then, you would divide 88 by pi and set it up equal to radius^2. Therefore the radius^2 equals approximately 28.0112. To find the radius, you need to square root that number. 28.0112 square rooted is approximately 5.293. Therefore, 5.293 is the radius length.

Answer:

Radius of circular mural = 5.29 m

Step-by-step explanation:

Area of circle is given by πr².

Juanita and Lauren are painting a circular mural on one wall of the community center the area of the mural is 88 square meters

Area of circle = 88 square meters

That is

πr² = 88

[tex]r^2=\frac{88}{\pi}=28.01\\\\r=5.29m[/tex]

Radius of circular mural = 5.29 m

The two-way table shows the number of students in a school who have hamsters and/or dogs as pets.

Have Hamsters

Do Not Have Hampsters

Total

Have Dogs

16

24

40

Do Not Have Dogs

25

35

60

Total

41

59

100

How many more students have hamsters than dogs?
1
5
8
9

Answers

Answer:

Step-by-step explanation:

There are a total of 16+25 = 41 students that own hamsters.

There are a total of 16+24 = 40 students that own dogs.

This is a difference of 41-40 = 1.

Answer: 1

Step-by-step explanation:

Total number of students that own hamsters 16+25 = 41.

Total of students that own dogs 16+24 = 40.

To get how many more students own hamsters than dogs, we find the difference;

That is 41-40 = 1.

Good luck

Does any one know how to solve this -4n^2-2n=-6-7n-5n^2

Answers

[tex]-4n^2-2n=-6-7n-5n^2 \\ -4n^2-2n+6+7n+5n^2=0\\n^2+5n+6=0 \\ n^2+2n+3n+6=0 \\ n(n+2)+3(n+2)=0 \\ (n+2)(n+3)=0 \\ n+2=0 \ \ \ \ or \ \ \ \ n+3=0\\n=-2 \ \ \ \ \ \ \ \ \ \ \ \ \ n=-3[/tex]

Answer: n=-2, n=-3

-4n^2-2n=-6-7n-5n^2

Add 5n^2 to both sides
n^2-2n=-6-7n

Add 7n to both sides
n^2+5n=-6

Add 6 to both sides to put the equation into quadratic standard form
n^2+5n+6=0

Factor the equation
(n+2)(n+3)=0

3+2=5, 3*2=6

To solve a quadratic equation, find roots using Zero Product Property.
(n+2)=0
n=-2

(n+3)=0
n=-3

Final answers: n=-3, n=-2

Estimate 12.56+12.69 using front-end estimation.

A. about $25.30

B. about $26.30

C. about $26.80

D. about $23.80

Answers

12.56+12.69 = 12.60 + 12.70 = 25.30

answer

A. about $25.30

The function F(x) = 6x-2/5 is an example of a rational function.
A. True
B. False

Answers

Final answer:

The function F(x) = (6x-2)/5 is an example of a rational function.

Explanation:

The function F(x) = (6x-2)/5 is an example of a rational function. A rational function is a function that can be expressed as the quotient of two polynomial functions, where the denominator is not equal to zero.

In this case, the function F(x) has a numerator of 6x-2 and a denominator of 5. Both the numerator and denominator are polynomial functions since they involve multiplication, addition, and subtraction of terms with x.

Therefore, the function F(x) = (6x-2)/5 is indeed a rational function, so the correct answer is True.

The function F(x) = (6x-2)/5 is an example of a rational function because it can be expressed as a ratio of two polynomials.

Function F(x) = (6x-2)/5 is an example of a rational function because it is a ratio of two polynomials. The numerator, 6x-2, is a linear polynomial, and the denominator, 5, is a constant polynomial.

To determine if a function is rational, we check if the function can be expressed as a quotient of two polynomials. In this case, F(x) is a ratio of a linear polynomial, 6x-2, and a constant polynomial, 5.

Therefore, the statement is True.

Determine algebraically whether the function is even, odd, or neither even nor odd.
f as a function of x is equal to 2 divided by x squared.

Neither
Even
Odd

Answers

I think
The answer probably is "EVEN"
I hope it's right and it's helps you!

Answer:

Even

Step-by-step explanation:

A function is said to be even function if we put -x instead of x and we get the same result of both function. i.e. f(-x) = f(x)

A function is said to be odd function if we put -x instead of x and we get the result as negative of that function. i.e. f(-x) = -f(x)

Now we have function, f(x) = [tex]f(x) = \frac{2}{x^{2}}[/tex]

Now putting -x in place of x

[tex]f(-x) = \frac{2}{(-x)^{2}}\\ = \frac{2}{x^{2}} = f(x)[/tex]

Hence, given function is an Even function.

Find the constant sum for an ellipse with foci F1 (0, -12), F2 (0, 12) and the point on the ellipse (9, 0).

Answers

sqrt((0-9)^2+(-12-0)^2)+sqrt((0-9)^2+(12-0)^2) using the distance formula equals sqrt(81+144)+sqrt(225)=15+15=30

A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each month and select the correct answer below.

Answers

well, the house is increasing by 10% each year, so whatever the current price is, the new price is THAT plus 10%, well, since THAT is 100%, shouldn't that be 100% + 10%, or 110%?

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &120,000\\ r=rate\to 10\%\to \frac{10}{100}\to &0.10\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=120000(1+0.10)^t\implies \begin{array}{lclll} A=120000(&1.1&)^t\\ &\uparrow \\ &rate\\ &of\\ &growth \end{array}[/tex]

1.1 is the decimal format, but you can simply multiply it by 100 to get the percentage, 1.1 * 100 = 110%

Use graphs and tables to find the limit and identify any vertical asymptotes of the function

lim x->4^- x/x-4

Answers

You want to do exactly what this says, use the graph. If you were to just plug the 4 into the equation, you would end up with an undefined fraction. However, if you graph it in your calculator, take a look at what is going on with the graph as the x approaches 4 to easily find your limit. Remember to put parenthesis around the denominator when putting it into the calculator so it will graph correctly. Also, remember to write your asymptote as a linear equation, not just a number.

Solve for w. 3w – 10 = -w – 8 + 3w

Answers

Combine like terms
3w-10=2w-8

Add 10 to both sides
3w= 2w+2

Subtract 2w from both sides
w=2

Final answer: w=2

Find the distance between the points with coordinates (5, 7) and (-3, 1)

Answers

You would use the function root(Xsub2-Xsub1)^2+(Ysub2-Ysub1)^2.

Now plug in your numbers.

This gives you root(7-1)^2+(5-(-3))^2.

Simplify to root(6)^2+(8)^2. Simplify again to root36+64.

Simplify one more time to root 100. now solve.

Your answer is 10.

A cylinder has a radius of 1 inch and height of 1 inch.

What is the approximate volume of a cylinder?

Answers

volume = PI * radius^2* height

3.14 x 1^2 x 1

v=3.14 cubic inches

The answer is 3.14 or C. I just took the test.

Graph the line y = -1/4x+2.

a. Sketch the line that is perpendicular to y = -1/4x+2 that passes through the point (5,5)

b. Write the equation of the perpendicular line.

c. Where do the lines intersect?

Answers

a- in image
b- 4x-15
c- (4,1)

A number is *K* units to the left of 0 on the number line. Describe the location of its opposite

Answers

K units is to the right of 0

Syreeta wants to buy some cds, each costing $14, and a dvd that costs $23. she has $65 to spend. write an equation to find how many cds she can buy

Answers

Answer:

14x+23y=65

Step-by-step explanation:

let cds=x and dvds=y

14x+23y=65

what is the answer to this equation 2(3-X)=-16

Answers

2(3 - x) = -16
3 - x = -16/2
3 - x = -8
-x = -8 - 3
-x = - 11
x = 11

[tex]Hello, again \\ 2(3)-x - (-16) \\ -2(x) - 11 \\ x - 11 = 0 ; x +11 = 11x ; 11 + 0 = 11 \\ One SolutionWasFoundInHere [/tex]
[tex]x = 11 [/tex]

[tex]Good \\ Luck \\ On \\ Your \\Assignment [/tex]

simplify the expression. 7m^2+6.5n-4n+2.5m^2-n
A.) 1.5m^2+4.2n
B.)4.2m^2+1.5n
C.)1.5m^2-4.2n
D.)4.2m^2-1.5n

Answers

B.) 4.2^2+1.5n is the answer

What is the perimeter of a square with a side length of 5x -8 and a bottom length of 3x of a square?

Answers

5x-8=3x (This is because all sides are equal in a square)
-5x -5x
-8=-2x
x=4

4(3)=20-8
12=12

12+12+12+12
48

The required perimeter of the square is 48 units as of the given condition.

Given that,
The perimeter of a square with a side length of 5x -8 and a bottom length of 3x of a square is to be determined.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The length of all sides of the square is always remains equal,
5x - 8 = 3x
2x = 8
x = 4
Side length,
3x = 3(4) = 12
Now,
The perimeter of the square is 4-time sides,
Perimeter = 4 (12)

Perimeter = 48 units.

Thus, the required perimeter of the square is 48 units as of the given condition.

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Ken wants to build a table and put a border around it. The table and border must have an area of 3,276 square inches. The table is 36 inches wide and 72 inches long without the border. Which quadratic equation can be used to determine the thickness of the border, x?

4x^2 + 216x + 2,592 = 0
4x^2 + 216x − 684 = 0
2x^2 + 216x − 3,276 = 0
x^2 + 108x + 3,276 = 0

Answers

The quadratic equation that can be used to determine the thickness of the border, x is 4x² + 216x - 684 = 0

Which quadratic equation can be used to determine the thickness of the border, x?

From the question, we have the following parameters that can be used in our computation:

Length = 72

Width = 36

Border = x

Area = 3276

The area can be represented as

Area = (Width + 2x) * (Length + 2x)

Substitute the known values into the equation

(36 + 2x) * (72 + 2x) = 3276

Expand

4x² + 216x + 2592 = 3276

So, we have

4x² + 216x + 2592 - 3276 = 0

4x² + 216x - 684 = 0

Hence the quadratic equation is 4x² + 216x - 684 = 0

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 6 vans and 8 buses with 202 students. High School B rented and filled 12 vans and 10 buses with 284 students. Each van and each bus carried the same number of students. How many students can a van carry?How many students can a bus carry? please show work thank you.

Answers

Class A: 6v + 8b = 202

Class B: 12v + 16b = 284

Solve using the elimination method:
since 6v and 12v are perfect for elimination, multiply the class A equation by 2 so that the van variable cancels out:

12v + 16b = 404
12v + 10b = 284

Then subtract the bottom equation from the top:

6b = 120
b = 20

Now you know that each bus can hold 20 students.
Just plug this into one of the original equations to solve for vans:

6v + 8(20) = 202
6v + 160 = 202
6v = 42
v=7

So then you know that each van can hold 7 students.

Check:
12 (7) + 10 (20) = 284

What are the rules for adding and subtracting negative numbers?

Answers

a negative sign and a negative sign next to each other is a positive sign ex..

-14 - -3
= -14 + 3
= -11

a negative sign and a positive sign next to each other is a positive sign ex..

-14 + -3
= -14 - 3
= -17

the bigger a negative number the smaller it is
the bigger a positive number the larger it is
which supports the rule if you are subtracting the
number will become smaller and if you are adding
the number will become larger

Work the following pricing problems for services rendered. (For all calculations use hundredths.)

Labor time = 8 hours
Overhead rate = 65%
Retail price of parts = $98.70
Total cost of job = $242.58
What is hourly rate for labor?
a=27.67
b=13.32
c=10.90
d=117.08

Answers

8(1.65)R + 98.70 = 242.58
Solve for R
13.2R=242.58-98.7
13.2R=142.88
R=143.88÷13.2
R=10.9....answer

Answer:

10.90

Step-by-step explanation:

The graph represents this piecewise function

Answers

top one is x+3, bottom one is 5

Answer:

Step-by-step explanation:

Given is a piecewise graph.

From the graph we find that the domain is [-3,1]

From [-3,-1) the line is slant passing through (-3,0)(-2,1)

Slope =change in y/change in x = 1

Equation is y = x+3

Thus the function is x+3 for -3≤x<-1

and 5, -1≤x≤1

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