What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

Answer:

Step-by-step explanation:

600 minus 399 is 201

The trip will take at least two days given the car's mileage limit per tank and the daily driving limit.

To determine how long a journey will take with the given constraints, we first need to understand the limitations. The car can run for 399 miles on one tank of gas, and the maximum you can drive in one day is fixed at 600 miles. Since the daily maximum driving distance is greater than the mileage per tank, the limiting factor is the gas tank range.

Assuming you start with a full tank, you would need to refill once you've driven 399 miles. If there is no wait time for refilling and the efficiency of the car does not change, you could potentially drive for another 399 miles after refilling. However, due to the 600 miles per day limit, you would need to stop before exhausting your second tank. To find out the total driving time, divide the total distance by the daily driving limit (if the total distance is larger than what can be covered in one day).

For example, if the total trip is 700 miles, it would take at least two days because you can cover 600 miles on the first day and the remaining 100 miles on the second day. However, this does not account for any potential stops, breaks, or other delays.

Answer:

64 in2

hope it helps (:

Answer:

A

Step-by-step explanation:

it is what it is; you either know it or you don't.

What the object adds up to

21x is 21x im glad that I can help you

This problem can be solved using probability, the equation of the probability of an event A is P(A)= favorable outcomes/possible outcomes. The interception of two probable events is P(A∩B)= P(A)P(B).

There are 12 black marbels, 10 red marbles, and 18 white marbels, all the same size. If two marbles are drawn from the jar without being replaced.

The total of the marbles is 40.

If two marbles are drawn from the jar without being replaced, what would the probability be:

1. of drawing two black marbles?

The probability of drawing one black marble is (12/40). Then, the probability of drawing another black marble after that is (11/39) due we drawing one marble before.

P(Black∩Black) = (12/40)(11/39) = 132/1560, simplifying the fraction:

P(Black∩Black) = 11/130

2. of drawing a white, then a black marble?

The probability of drawing one white marble is (18/40). Then, the probability of drawing then a black marble after that is (12/39) due we drawed one marble before.

P(White∩Black) = (18/40)(12/39) = 216/1560, simplifying the fraction:

P(White∩Black) = 9/65

3. of drawing two white marbles?

The probability of drawing one white marble is (18/40). Then, the probability of drawing another white marble after that is (17/39) due we drawed one marble before.

P(White∩White) = (18/40)(17/39) = 306/1560, simplifying the fraction:

P(White∩White) = 51/260

4. of drawing a black marble, then a red marble?

The probability of drawing one black marble is (12/40). Then, the probability of drawing then a red marble after that is (10/39) due we drawed one marble before.

P(Black∩Red) = (12/40)(10/39) = 120/1560, simplifying the fraction:

P(Black∩Red) = 1/13

Answer:

D. [tex]A\subset \mathbb{R}\times\mathbb{R}.[/tex]

Step-by-step explanation:

Consider the set

[tex]A=\left\{(2,3),\ (5,1),\ (-3,-2),\ (0,3)\right\}[/tex]

This set consists of four ordered pairs.

The first numbers in these pairs are [tex]2,\ 5,\ -3,\ 0.[/tex] These numbers are integer numbers (not natural, because -3 is negative).

The second numbers in these pairs are [tex]3,\ 1,\ -2,\ 3.[/tex] These numbers are integer numbers too (not natural, because -2 is negative).

Options contain only natural and real sets, so, the first and the second numbers are real numbers and

[tex]A\subset \mathbb{R}\times\mathbb{R}.[/tex]

Answer:

D. R X R

Step-by-step explanation:

The answer is choice D because, the set of the actual numbers of R has a 0 so A is a subset of R X R

Let's call the first unknown integer x and the second one y.

"Four times an unknown integer"

"Multiplied by three times the unknown integer plus a different unknown integer"

"Equals 100."

And so the answer is C: 12x²+4xy-100=0

12x²+4xy-100=0. The equation that represents the statement of the problem is 12x²+4xy-100=0.

The equation is represents by  "Four times an unknown integer, multiplied by three times the unknown integer plus a different unknown integer, equals 100."

First, we have the statement "four times an unknown integer", this is:

4x

Then, multiplied by three times the unknown integer plus a different unknown integer, that is:

4x(3x+y)

And finally, the equation above is equals to 100.

4x(3x+y)=100

Operating

(4x)(3x)+(4x)(y)=100

12x²+4xy=100

Then,  subtracting 100 on both sides of the equation.

12x²+4xy-100=100-100

Obtaining

12x²+4xy-100=0

Answer: A) movies for less cost $5 more

Step-by-step explanation:

10 × 3 =30

15 × 2= 30+10=40 movie plus

15 × 3= 45 movies for less

Answer:

A)Movies For Less costs $5 more.

Step-by-step explanation:

Movies Plus charges its customers a $10 monthly service fee plus $2 for each movie the customer rents.

So, 15 movies from this provider will cost = [tex]10+2(15)[/tex]

=> [tex]10+30=40[/tex] dollars.

Movies For Less charges $3 for each movie but does not have a monthly service fee.

So, 15 movies from this provider will cost = [tex]15\times3=45[/tex] dollars.

Comparing both providers, we can see that Movies For Less charges $5 more than Movies Plus.

Therefore, option A is correct.

Answer:

Infinitely many solutions.

Step-by-step explanation:

In the equation −2y + 2y + 3 = 3  we see only one variable, and that variable is of the first power.  Ordinarily, we'd say that this equation will have 1 solution.  However, if we combine like terms, we get 0 + 3 = 3, or 0 = 0, which is true for any and all y values.  Infinitely many solutions.

Answer:

Infinitely

Step-by-step explanation:

we have

[tex]-2y+2y+3=3[/tex]

Group terms that contain the same variable

[tex]-2y+2y=3-3[/tex]

Combine like terms

[tex]0=0[/tex] ----> the equation is true for any value of y

therefore

The equation has infinite solutions

Answer:

D) GE = 10 and GI = 12

Step-by-step explanation:

Given: KI = 4 and GH = 5

K is the centroid of EFG

So

KI = 1/3 (GI)

GI = 3 (KI) = 3(4) = 12

Because K is the centroid of EFG so GH = HE = 5

GE = GH + HE

GE = 5 + 5

GE = 10

Answer

GE = 10 and GI = 12

Answer:

D. GE = 10; GI = 12

Step-by-step explanation:

Given that K is the centroid of EFG, then GH = HE = 5, so GE = GH + HE = 5 + 5 = 10

The 2/3 rule states that the centroid is 2/3 of the way from the vertex to the opposite midpoint. This means that GK is doubled than KI, then GK = 2*4 = 8, and GI = GK + KI = 8 + 4 = 12

Answer:

The slope of a line is the change in y divided by the change in x.

( y1 - y2 ) / ( x1 - x2 )

It does not matter which point you choose as (x1, y1) and (x2,y2)

( 7 - 1 ) / ( 1 - 10 )

( 6 ) / ( -9 ) This will simplify to -2/3.

Answer:

hey user!

your answer is here...

laws ( rules ) of reflection are :-

• angle of incidence is equal to angle of reflection.

• the incident ray, Normal ray and reflected ray all lie in same plane.

cheers!!

Step-by-step explanation:

Answer:

6/6

Step-by-step explanation:

If a standard number cube has six sides and all the numbers are larger than 0 you have a 6/6 chance

Answer:

Yellow of course but it depends on how you look in the colors

Step-by-step explanation:

Answer:

If your day is not feeling good then I would recommend a yellow to brighten it up. If your day is already good but feeling not good where a purple to stand out. Good Luck I hope your day is doing well!!

Step-by-step explanation:

Answer:

it has both line and rotational symmetry

Answer:

youre answer is it has both line and rotational symmetry

Step-by-step explanation:

Answer:

1/6 (1 gallon of orange juice for every 6 gallons of apple juice)

Step-by-step explanation:

4/24=24/4x1/36

This is because you reverse the division (or fraction) into a easier to solve equation, and the 1/36 is there to balance out that change.

Answer:

The range of the function is [0 , ∞) ⇒ answer B

Step-by-step explanation:

* lets revise the meaning of the domain and the range

- The domain is the values of x

- The domain is all the values of x which make the function is defined

- If there are some values of x make the function undefined, we

 exclude these values from the domain

- The range is the values of f(x) which corresponding to the value of x

* Now lets look to the figure

∵ f(x) = √x

- We can not use the negative values for x because there is no

 square root for negative numbers

∴ All real negative numbers make the function undefined

- We must exclude them from the domain

∴ The domain is all real numbers greater than or equal zero

∴ x ≥ 0

- To find the range use the first value of the domain

∵ the first value of x = 0

∴ f(0) = √0 = 0

∵ x can not be negative

∵ f(x) = √x

∴ f(x) can not be negative

∴ the range is all real numbers greater than or equal zero

∴ f(x) ≥ 0

OR

f(x) = [0 , ∞)

* The range of the function is [0 , ∞)

so parallel is just numbers with the same slope but different x value

and perdicular is the One with different signs and oppisite reciprocals

a) perpendicular because -2 is the oppisite sign and reciprocal of 1/2

b)neither

c) niether

and B)

a) 3x-2

b)y=5/2 +4

i think

Answer:

x^7

Step-by-step explanation:

The expression is written as a single exponent in x⁷

Index forms are forms used to represent numbers or variables that are too large or small in more convenient forms.

From the information given, we have that the expression is;

x to the ninth over x squared

This is represented as;

x⁹/x²

Since the forms are of like bases, subtract the exponents, we get;

x⁹⁻²

Subtract the exponents, we get;

x⁷

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Answer:

31

Step-by-step explanation:

Do the subtraction: 37 - 6 = 31

for the first part:

Let's solve for x.

−x+3y=14

Step 1: Add -3y to both sides.

−x+3y+−3y=14+−3y

−x=−3y+14

Step 2: Divide both sides by -1.

−x/−1  =  −3y+14/−1

x=3y−14

Answer:

x=3y−14

Second part:Let's solve for x.

3x−3y=−6

Step 1: Add 3y to both sides.

3x−3y+3y=−6+3y

3x=3y−6

Step 2: Divide both sides by 3.

3x/3= 3y−6/3x=y−2

Answer:

x=y−2

The constant p is determined by the half-life of 1600 years, and since after one half-life, the amount of the element is half of its initial value, we find that x=1/2 and y=1/1600, as e^p can be expressed as (1/2)^(1/1600). Therefore, option (a) is the correct answer.

The equation Q(t) = Q(0)e^pt describes an exponential decay process, such as the decay of a chemical element over time. Given that the half-life of the chemical element is 1600 years, after this period the quantity of the element will be half of its original amount. According to the properties of exponential decay, we know that after one half-life, Q(t) = Q(0)/2.

Substituting t = 1600 into the equation and knowing that Q(1600) = Q(0)/2, we get Q(0)/2 = Q(0)e^(1600p). Simplify by dividing both sides by Q(0), resulting in 1/2 = e^(1600p). To find p, take the natural logarithm of both sides, yielding ln(1/2) = 1600p ln(e), and since ln(e) = 1, we have p = ln(1/2)/1600.

Now, to express e^p as x^y, with both x and y being rational numbers, we look for a rational base x that can represent e^ln(1/2), which simplifies to (1/2). So, x would be 1/2, and because the half-life is 1600 years, y will be proportional to the fraction of that time. Hence, y = t/1600, where t is time in years. From this, you can infer that the base x equals 1/2 and y is 1/1600 for each year surpassing the half-life. Therefore, the correct answer is (a) x = sqrt(1/2), y = 1/1600.

Answer: a) x=37,

              b)no solutions

              c)x=0

Step-by-step explanation:

In then the problem, you will need to isolate the x, use the inverse operation, and solve. For example, if I had the problem x-6=64, i would have to use the inverse operation  of  6 to isolate the x. You would add 6 on both sides.(addition is the inverse of subtraction). THat would be x=58.

Answer:

A. 12 edges. 6 vertices, and 8 faces.

Step-by-step explanation:

The edges are the places where the faces meet. They can be easily identified as the lines that form the shape. There are 12 edges.

The vertices are the places where the edges meet. They are more commonly known as the corners of the figure. There are 6 vertices.

The faces are the flat sides/surfaces of the figure. In this case, the faces are the triangles. There are 8 faces.

Hope this helps!

The given figure has 12 edges, 6 vertices, and 8 faces. This can be obtained by understanding what edges, vertices and faces are and counting them.

In the given figure we can count  the edges, vertices and faces.

It is observed that there are 12 edges, 6 vertices, and 8 faces.

Hence the given figure has 12 edges, 6 vertices, and 8 faces. The correct answer is A.

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Answer:

it would be 3 because if you list words then just divide 12 by 4 and you get 3

The number of the 4 letter words that can be made from a list of 12 letters will be 495.

Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Then the number of the 4 letter words can be made from a list of 12 letters will be

¹²C₄ = 12! / [(12 - 4)! x 4!]

¹²C₄ = 12 x 11 x 10 x 9 x 8! / 8! x 4 x 3 x 2 x 1

¹²C₄ = 11 x 5 x 9

¹²C₄ = 495

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Answer:

see below

Step-by-step explanation:

4(-3 +15) = 48

4(4 + 2 + 5) = 44

4(7 + 2 + 3) = 48

4(8 + 6-2) = 48

4(-2-4 + 16) = 40

We are required to select all expressions equivalent to 48

All expressions are equivalent to 48 except 4(4 + 2 + 5) and 4(-2-4 + 16)

Check all options:

= 4(12)

= 48

= 4(11)

= 44

= 4(12)

= 48

= 4(12)

= 48

= 4(10)

= 40

Therefore, all expressions are equivalent to 48 except 4(4 + 2 + 5) and 4(-2-4 + 16)

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Answer:

2nd statement is true

Step-by-step explanation:

Please use " ^ " to denote exponentation:   f(x) = 4x^2 + 20x + 25.

Take a look at the second statement.  If you'll substitute -2.5 for x, to find f(-2.5), you'll find that the result is 0;  Thus, this second statement is true.

Answer:

The graph touches the x-axis at (–2.5, 0).

Step-by-step explanation:

Given  : f(x) = 4x² + 20x + 25.

To find : Which statement describes the graph .

Solution : We have given

f(x) = 4x² + 20x + 25.

On factoring

4x² + 10x + 10x+ 25 = 0

On taking  common 2x from first two terms and 5 from last two terms.

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

On grouping

(2x +5) (2x +5)  = 0

For 2x +5 = 0

On subtracting 5 both side

2x = -5

On dividing by 2

x = [tex]\frac{-5}{2}[/tex] = - 2.5

x = - 2.5 .

Points (-2.5 , 0)

Therefore, The graph touches the x-axis at (–2.5, 0).

Answer:

D. [tex]y=3\cos \left(\dfrac{4}{3}x-2\pi\right)+2[/tex]

Step-by-step explanation:

The period of the functions [tex]y=\cos x,\ y=\sin x[/tex] is [tex]2\pi.[/tex]

The period of the function [tex]y=a\cos (kx+b),\ y=a\sin(kx+b)[/tex] is ALWAYS [tex]\dfrac{2\pi}{k}[/tex]

In your case, you have function [tex]y=-3\sin \left(\dfrac{2}{3}x-2\pi \right)+2[/tex] and this function has the period

[tex]\dfrac{2\pi}{\dfrac{2}{3}}=3\pi.[/tex]

You need to find the function that will have the period that is half of [tex]3\pi,[/tex] so

[tex]\dfrac{3\pi}{2}=\dfrac{2\pi}{k}\\ \\3k=4\\ \\k=\dfrac{4}{3}.[/tex]

So, correct choice is

[tex]y=3\cos \left(\dfrac{4}{3}x-2\pi\right)+2[/tex]

Answer:

The answer is y = 3 cos(4/3 x - 2π) + 2 ⇒ last answer

Step-by-step explanation:

* Lets revise the sine function

- If we have a sine function of the form f(x) = Asin(Bx + C) + D, where

 A, B , C and D are constant, then

# Amplitude is A

- The Amplitude is the height from the center line to the peak .

 Or we can measure the height from highest to lowest points and

 divide that by 2

# Period is 2π/B

- The period goes from one peak to the next

# phase shift is C (positive is to the left)

- The Phase Shift is how far the function is shifted horizontally  

 from the usual position.

# vertical shift is D

- The Vertical Shift is how far the function is shifted vertically from

 the usual position.

* Now lets solve the problem

∵ y = -3sin(2/3 x - 2π) + 2

- the period is 2π ÷ 2/3 = 2π × 3/2 = 3π

∴ The period of the function is 3π

- We look for a function has one-half (3π), means 3π/2

* Lets look to the answer to find the right one

- All of them have the same value of B except the last one, lets

 check it

∵ y = 3cos(4/3 x - 2π) + 2

∵ B = 4/3

∴ The period = 2π ÷ 4/3 = 2π × 3/4 = 6π/4 = 3π/2

∵ 3π/2 is half 3π

∴ The last answer is right

The correct answer is B.

Distance = speed + 90

The equation relates the distance she traveled to her speed is Speed x 90 = distance.

The speed a person travels is the total distance driven per the total time it took to travel.

Speed = total distance / total time

The time it took to drive is 90 minutes:  Speed = distance / 90

In order to determine the equation that relates distance to speed, make distance the subject of the formula. In order to do this, multiply both sides of the equation by 90: Speed x 90 = distance.

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Answer:

6

Step-by-step explanation:

the square root is basically exponents 6*6 is 6^2 which is 36.