The ordered pairs (1, 6), (2, 36), (3, 216), (4, 1296), and (5, 7776) represent a function. What is a rule that represents this function?

Answers

Answer 1
From what I gathered the x-values are going up by plus 1(+1) and the y-value are going up by times 6(×6). Now that you have this find the formula/rule.
The Ordered Pairs (1, 6), (2, 36), (3, 216), (4, 1296), And (5, 7776) Represent A Function. What Is A
Answer 2

Answer:

The rule is [tex]\\ f(x) = 6^{x}[/tex]

Step-by-step explanation:

The resulting values are powers of 6:

[tex]\\ 6^{1} = 1[/tex]

[tex]\\ 6^{2} = 36[/tex]

[tex]\\ 6^{3} = 216[/tex]

[tex]\\ 6^{4} = 1296[/tex]

[tex]\\ 6^{5} = 7776[/tex]

One factor that is not defined in the question is whether the domain (the set of values for which a function is defined [WolframAlpha, 2019]) of the function [tex]\\ f(x) = 6^{x}[/tex]  is only for x = {1, 2, 3, 4, 5} or defined for all possible values this function can take, that is, x = (-∞;∞) or all real numbers.

As you can see from the graph attached:

Theoretically, this function could take all values for x = (-∞;∞). If this were the case, the function is a continuous line with resulting values (that is, the range of the function) for f(x)>0 (0;∞). The graph below shows only positive values (x > 0) and values for x ≤ 5.For values x = {1, 2, 3, 4, 5}, the function is discrete (not a continuous line) and only defined for these values. In this case, the function would be represented only by the points in the graph, and the values it could take would be only f(x) = {6, 36, 216, 1296, 7776}, which would represent the range for this function.

In the last case, we have to redefine the function as:

[tex]\\ f(x) = 6^{x}[/tex] for [tex] x = \{1, 2, 3, 4, 5\}[/tex].

The Ordered Pairs (1, 6), (2, 36), (3, 216), (4, 1296), And (5, 7776) Represent A Function. What Is A

Related Questions

A1+a2+a3=180 solve for a1

Answers

Answer: a1=180-a2-a3....
A1 = 180 - (a2 + a3) ;
_______________________
or: 
_______________________
A1 = 180 - a2 - a3.
_______________________.
Since there are no values given, we solve for "A1" by isolating "A1" and solving in terms of the remaining values.

In the formula A=\pi r^{2}, if the radius is 6 centimeters, what is the correct unit for the area of the circle?
A)\pi cm
B)cm^2
C)cm
D)cm^3

Answers

I hope this helps you



Area=pi.6^2



Area=36pi cm^2

Watermelons cost $0.35 per pound. Joseph’s watermelon costs between $4.20 and $5.25. Which compound inequality correctly represents the possible weights of his watermelon?

Answers

The answer is 12 < x < 15

x - the weight of Joseph's watermelon 

Watermelons cost $0.35 per pound:
0.35x

Joseph’s watermelon costs between $4.20 and $5.25:
4.20 < 0.35x < 5.25

Divide all by 0.35:
4.20/0.35 < 0.35x/0.35 < 5.25/0.35
12 < x < 15

Answer: 12 < x < 15

Step-by-step explanation:

how to find a whole number in this question 4% of ... is 56?

Answers

[tex] \frac{4}{100} * x=56[/tex]
[tex] \frac{1}{25} * x=56[/tex]
[tex]1400[/tex]

The product of 9 and a number is 12 less than three times that number.

What is the number?

Answers

So let me give you the answer with procedure so that you can understand it better:
Let x = Number 

Product of 9 and Number:
9x 
is 12 less than 3 times that number. So: 
3x - 12 
Set them equal and solve for x like this:
9x = 3x - 12 
6x = -12 
x = -2
I hope this is very useful for you

At the beginning of April, Owl Corporation has a balance of $12,000 in the Retained Earnings account. During the month of April, Owl had the following external transactions.


1. Issue common stock for cash, $8,000.
2. Provide services to customers on account, $6,100.
3. Provide services to customers in exchange for cash, $2,400.
4. Purchase equipment and pay cash, $5,600.
5. Pay rent for April, $1,000.
6. Pay workers' salaries for April, $2,500.
7. Pay dividends to stockholders, $1,100.

Using the external transactions above, compute the balance of Retained Earnings at April 30 ...?

Answers

common stock: 8000 cash: 8000 5600 2400 1000 2500 1100 ----------- 10400 10200 +200 equip: 5600 notes recv: 6100 revenue: 6100 2400 ------- 8500 rent: 1000 wages: 2500 dividends: 1100 ------- 4600 ------------------------------- 8500 -4600 ------ 3900 - gross profits

Name the property of 11xn=1

Answers

Is it 11x or 11 time n = 1?

Does antibiotics help kill the common cold??

Answers

Antibiotics don't work on the common cold. They fight bacteria-related illnesses. Colds are caused by viruses, so antibiotics won't do you any good. They can, however, do you harm.Mar 29, 2016
No it doesn't because colds are made up of viruses. So the antibiotics won't help.

graph the line y=3/4x-2

Answers

c. Intersecting lines

Step-by-step explanation: First, notice that this line is in slope intercept or more commonly known as y = mx + b form because y is by itself on one side of the equation.

Our slope or m therefore is the coefficient of the x-term which in this case is 3/4. Our b or y-intercept is the constant term which in this case is -2.

To graph a line given the slope and y-intercept, we will first start with its y-intercept. The y-intercept of a line is the point where the line crosses the y-axis. Since our y-intercept is -2, we start by plotting the point that is down 2 units on the y-axis and we call that point A.

From there we take our slope of 3/4 so our rise is 3 and our run is 4 and we end up at point B. Now we can connect the two points and we have our line.

I attached the image of the line in the image provided.

explai n how a number and its reciprocal are related

Answers

A non-zero number times its reciprocal is always equal to 1.

[tex]a * \frac{1}{a} = 1[/tex]

Write 16 1/2 as an improper fraction

Answers

the improper fraction of 16 1/2 would be 33/2
To write 16 1/2 as an improper fraction, multiply the whole number by the denominator and then add the product to the numerator.

Then place the final answer the denominator.

16 1/2 becomes 33/2.

The des moines register recently reported the ratings of high school sportsmanship as complied by the iowo high school athletic association. For each school, the participants and coaches were rated by referees, where 1= superior, and 5= unsatisfactory. A regression analysis of the averages scores given to football players and coaches is shown below.

interpret the value of the correlation between the ratings of coaches and participants.

Answers

The correlation coefficient "r" is square root of of the "R^2" .... square root (.45) which yields 0.67

the circular blade on a saw has a diameter of 7.5 inches and rotates at 2400 revolutions per minute.
A) find the angular speed in radians per sec
B) Find the linear speed of the saw teeth ( in feet per sec) as the contact the wood being cut.

Formulas--> Linear speed= arc length/time= s/t
Angular speed= central angle/time ...?

Answers

For a:
    
       (2400*2*PI)/60(seconds) = 80 PI RAD/Sec

For b: 
   
        arc length s= radius r * central angle(in radians) 

                          = ((80*pi*7.5)/(2*pi)
                          =25


                          



The angular speed of the saw is 80π radians per second and the linear speed of the saw teeth is 25π feet per second.Explanation:To solve these tasks, we need to convert the rotation speed to radians per second for part A, and we use the formula for the circumference of a circle to find the linear speed for part B.A) Angular speed is normally measured in radians per second. To convert the revolutions per minute to radians per second, we need to know that one full revolution equals 2π radians. After this, convert the minutes to seconds. Hence:2400 revolutions per minute * 2π radians per revolution = 4800π radians per minuteTo convert to seconds: 4800π radians per minute / 60 seconds = 80π radians per secondB) The linear speed of the saw teeth as they contact the wood being cut can be determined by calculating the circumference of the saw's circular blade (which will be the distance travelled in one revolution), and then multiplying that by the rotational speed. The formula for the circumference of a circle is 2πr. Here the diameter is given, so the radius would be half the diameter, that is 7.5/2= 3.75 inches.Circumference = 2*π*3.75 inches = 7.5π inchesLinear speed = 7.5π inches per revolution * 2400 revolutions per minute = 18000π inches per minuteTo convert to feet per sec, we know 1 foot = 12 inches and 1 minute = 60 seconds, thus: 18000π inches per minute / 12 inches per foot / 60 seconds per minute = 25π feet per second

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Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 5(x + 8)2(x - 8)3
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3

B. -8, multiplicity 2; 8, multiplicity 3

C. -8, multiplicity 3; 8, multiplicity 2

D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

Answers

f(x) = 5(x + 8)2(x - 8)3

the true answer is B. -8, multiplicity 2; 8, multiplicity 3
because 
e.g: (x + 8)2= (x-  (-8))²,  -8 is the zero and 2 is the multiplicity

The given polynomial has roots -8 with multiplicity 2 and 8 with multiplicity 3. Hence option  B is correct.

Use the concept of polynomial defined as:

An expression that contains exponents, variables, and constants that is combined using mathematical operations such as addition, subtraction, multiplication, and division is known as a polynomial.

The given polynomial is:

f(x) = 5(x + 8)²(x - 8)³

To find its root equate this polynomial to 0.

Then,

5(x + 8)²(x - 8)³ = 0

(x + 8)²(x - 8)³ = 0

(x + 8)(x + 8)(x - 8)(x - 8)(x - 8) = 0

Therefore,

x = -8, -8, 8, 8, 8

Hence,

It has root -8 with multiplicity 2 and 8 with multiplicity 3 which is option B.

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The complete question is:

Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 5(x + 8)²(x - 8)³

A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3

B. -8, multiplicity 2; 8, multiplicity 3

C. -8, multiplicity 3; 8, multiplicity 2

D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

The sensory somatic nervous system controls all _________ responses of the body.

unconscious
voluntary
sequenced
repeated

Answers

Answer:

The sensory somatic nervous system controls all voluntary responses of the body.

Step-by-step explanation:

The sensory somatic nervous system controls all voluntary responses of the body.

The movements includes muscles and organs movements and reflex movements. Here the sensory neurons carry impulses to the brain and the spinal cord.

The ratio of sues age to her fathers age is 2:7 in three years their ages will total 60, how old is sue and her dad right now

Answers

Sue is 12 and her father is 42
Sue is 12, her father is 42.

I HATE MATH (and im lazy)

Oliver borrowed $215 from his friend John. He used this money to advertise his tutoring services. Oliver earned 8 times the amount he borrowed in his first month of tutoring. Approximately how much did Oliver earn in his first month of tutoring?

Answers

The answer is $1720
215×8=1720

Answer:

then f the teacher

Step-by-step explanation:

A sequence in which each term is found by adding the same number

Answers

that would be an arithmetic sequence

XY is the perpendicular bisector of JK. which of the following statements must be true? check all that apply?

A. XY and JK form four right angles
B. P is the midpoint of XY
C. m D. XP=YP
E.JP=KP
F. XY perpendicualr to JK

Answers

Final answer:

According to the properties of a perpendicular bisector, XY will form four right angles with JK, XY is perpendicular to JK, and it must bisect JK into two equal parts, making statements A, D, E, and F true.

Explanation:

The question tells us that XY is the perpendicular bisector of JK. This tells us a few things about the relationship between the two lines and the points on them:

XY and JK form four right angles: Because XY is a perpendicular bisector, it intersects line JK at a 90° angle.XY perpendicular to JK: This simply restates that the angle formed by the intersection of XY and JK is a right angle.JP=KP: Perpendicular bisectors not only intersect the other line at a right angle, but they also bisect it, which means they cut it into two equal parts. Thus, point J is as far from the point of intersection as point K, making JP equal to KP.XP=YP: This is also a property of the perpendicular bisector. It means that the point of intersection P is the midpoint of XY, making segment XP equal to segment YP.

The options regarding P being the midpoint of XY and the statement that includes an undefined variable 'm' were ignored due to lack of context.

Final answer:

The statements that must be true when XY is the perpendicular bisector of JK are: XY and JK form four right angles, P is the midpoint of XY, XP = YP, and XY is perpendicular to JK.

Explanation:

To determine which of the statements must be true, we need to understand the properties of a perpendicular bisector. A perpendicular bisector of a line segment is a line that divides the line segment into two equal parts and forms a right angle with the line segment.

From this definition, we can conclude that the following statements must be true:

A. XY and JK form four right angles - Since XY is the perpendicular bisector of JK, it forms a right angle with JK at each point of intersection.

B. P is the midpoint of XY - The perpendicular bisector passes through the midpoint of the line segment it bisects.

C. XP = YP - Since P is the midpoint of XY, XP and YP have equal lengths.

F. XY is perpendicular to JK - This is the definition of a perpendicular bisector.

Why is a plane a undefined term

Answers

In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness.

hope this helps

Determine c so that f(x) is continuous on the entire real line if f(x)= x^2 when x<=3 and c/x when x>3 ...?

Answers

f(x) = x^2  .... if x ≤ 3

f(x) = c /x    ... if x > 3

Contidition of continuity => Lim f(x) when x approaches 3 from the right side equals f(3).

f(3) = x^2 = 9

Lim c/ x when x -> 3+  = c/3

Then c / 3  = 9 => c = 3*9 = 27

Answer: c = 27.

Katie wants to buy 6 pencils from the school store.Each pencil costs 15¢.How much money will she get back if she pays with a five dollar bill?

Answers

Answer: The amount she will get is $4.10

Step-by-step explanation:

My reason is because .15 times 6 since she is buying 6 pencils, it is .90. The you subtract the decimal 5.00-0.90 and you get 4.10. Hope this helps. PLease mark brainliest!!!!!

how to write four hundred thousand in numbers?

Answers

400,000 is how to write four hundred thousand in numbers
400,000
:) :) :) :) :) :) :) :) :)

Sam is flying a kite. the length of the kite string is 80 meters, and it makes an angle of 75° with the ground. the height of the kite from the ground is meters.

Answers

height equals 80 meters times sin(angle of 75 degrees)

h = 80 (0.966) = 77.27 meters height of kite from the ground

Answer:

Height of the kite from ground is 77 m.

Step-by-step explanation:

Given: Length of the kite string = 80 m

           Angle of elevation = 75°

To find: Height of the kite from the ground.

Figure is attached.

In ΔABC

using trigonometric ratio,

[tex]sin\,75^{\circ}=\frac{AB}{AC}[/tex]

[tex]0.97=\frac{AB}{80}[/tex]

[tex]AB=0.97\times80[/tex]

AB = 77.27 m

AB = 77 m (approx.)

Therefore, Height of the kite from ground is 77 m.

Which answer shows these decimals written in order from greatest to least?   46.95
48.1
46.581

Answers

48,1 > 46.95 >46.581            

Solve log base(x − 1) 16 = 4.

Answers

i hope this helps you


x=3

Answer:

x = 3

Step-by-step explanation:

  Given:[tex]\log _{x-1}\left(16\right)=4[/tex]

We have to solve for x.

Consider the given expression [tex]\log _{x-1}\left(16\right)=4[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(b\right)=\frac{\ln \left(b\right)}{\ln \left(a\right)}[/tex]

[tex]\log _{x-1}\left(16\right)=\frac{\ln \left(16\right)}{\ln \left(x-1\right)}[/tex]

Thus, the expression becomes,

[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}=4[/tex]

Multiply both side by [tex]\ln \left(x-1\right)[/tex]

[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}\ln \left(x-1\right)=4\ln \left(x-1\right)[/tex]

Simplify, we get,

[tex]\ln \left(16\right)=4\ln \left(x-1\right)[/tex]

Divide both side by 4, we have,

[tex]\frac{4\ln \left(x-1\right)}{4}=\frac{\ln \left(16\right)}{4}[/tex]

[tex]\frac{\ln \left(16\right)}{4}:\quad \ln \left(2\right)[/tex]

Thus, [tex]\ln \left(x-1\right)=\ln(2)[/tex]

[tex]\mathrm{When\:the\:logs\:have\:the\:same\:base:\:\:}\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]

thus, x - 1 = 2

simplify for x, we have,

x = 3

Tim is setting up the course for a 9 mile walk.he places a sign every 0.15 mile along the path. how many signs will tim place

Answers

Divide the values

9/0.15 = 60

so he will place 60 signs

Please solve the eqution
Cos4x + cos2x - 2 =0

Answers

cos4x = cos2x

We know that:

cos2x = 1-2cos^2 x

==> cos4x = 1-2cos^2 (2x)

Now substitute:

==> 1-2cos^2 (2x) = cos2x

==> 2cos^2 (2x) + cos2x - 1 = 0

Now factor:

==> (2cos2x -1)(cos2x + 1) = 0

==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3

==> x1= pi/6 , 7pi/6

==> x1= pi/6 + 2npi

==> x2= 7pi/6 + 2npi

==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.

==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}

The solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.

Here, we have to solve the equation cos(4x) + cos(2x) - 2 = 0, we can use trigonometric identities to simplify it.

We know the following trigonometric identities:

[tex]cos(2x) = 2cos^2(x) - 1\\cos(4x) = 2cos^2(2x) - 1[/tex]

Now, let's rewrite the equation using these identities:

[tex]2cos^2(2x) - 1 + 2cos^2(x) - 1 - 2 = 0[/tex]

Combine like terms:

[tex]2cos^2(2x) + 2cos^2(x) - 4 = 0[/tex]

Divide the entire equation by 2:

[tex]cos^2(2x) + cos^2(x) - 2 = 0[/tex]

Now, let's simplify further:

We can rewrite [tex]cos^2(2x)[/tex] as [tex](1 - sin^2(2x))[/tex]using the Pythagorean identity: [tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]

So, the equation becomes:

[tex](1 - sin^2(2x)) + cos^2(x) - 2 = 0[/tex]

Rearrange the terms:

[tex]cos^2(x) - sin^2(2x) - 1 = 0[/tex]

Now, use the double-angle identity: [tex]sin^2(2x) = 2sin(x)cos(x)[/tex]

[tex]cos^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]

Now, we can rewrite [tex]cos^2(x) as (1 - sin^2(x))[/tex] using the Pythagorean identity:

[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]

[tex](1 - sin^2(x)) - 2sin(x)cos(x) - 1 = 0[/tex]

Now, simplify further:

[tex]1 - sin^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]

We can see that [tex](1 - sin^2(x))[/tex] cancels out:

-2sin(x)cos(x) = 0

Divide both sides by -2:

sin(x)cos(x) = 0

Now, there are two possible solutions for this equation:

sin(x) = 0

cos(x) = 0

Let's solve each case:

sin(x) = 0

This occurs when x is an integer multiple of π (π, 2π, 3π, ...). So the solutions are x = nπ, where n is an integer.

cos(x) = 0

This occurs when x is an odd multiple of π/2 (π/2, 3π/2, 5π/2, ...). So the solutions are x = (2n + 1)π/2, where n is an integer.

Therefore, the solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.

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who good at the math

Answers

Im pretty good at Math depending on what type of math it is?

AB=21; AD=28. What is the value of AC+BD?

Answers

The length of AC and BC is 35 by Pythagoras theorem, so that the sum of both gives 70

The value of AC + BD will be 70.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangle ABCD,

AB = 21

AD = 28

Now,

Since, ABCD is a rectangle.

Hence, We get;

⇒ AC = BD

Here, In rectangle ABCD,

AB = 21

AD = 28

So, By using definition of Pythagoras theorem, we get;

⇒ BD² = AB² + AD²

⇒ BD² = 21² + 28²

⇒ BD² = 441 + 784

⇒ BD² = 1225

⇒ BD = 35

Thus, The value of BD + AC is find as;

⇒ AC + BD = 35 + 35

                 = 70

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