Write an explicit formula for
�
�
a
n
​
, the
�
th
n
th
term of the sequence
28
,
14
,
7
,
.
.
.
28,14,7,....

The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.

Example of operation of function:

1. f(x) = x^2 + 3x - 2

When x = 3, f(3) = 3^2 + 3(3) - 2 = 14

2. g(x) = x^3 + 3

When x = 4, g(4) = 4^3 + 3 = 67

I have learned that GE4 is an introduction to mathematical proof and problem solving. We have gone through a variety of topics such as basic algebra, functions, and sets. We have also learned about the different approaches to problem solving, such as working backwards, proof by cases, and proof by PMI. I have also been introduced to the basics of logic and proof writing.

This answer explains the proof by PMI for the erie that if n is an odd number, then n^2 is an odd number. Two examples of operations of functions are also given. The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.

Learn more about sets here

https://brainly.com/question/12979762

#SPJ4

Pedro ate 3/2 of the cake that was left.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part is denominator.

Consider a fraction 1/5.

Here, numerator is 1, denominator is 5

When certain thing is divided into 5 equal parts then each part of is represented by fraction 1/5

In this situation, there is 3/4 of a large cake left over from a party.

Pedro eats 1/2 of the cake that was left.

This means, Pedro eats half of the remaning cake.

We need to find the half of fraction 3/4

We divide fraction 3/4 by 2 in order to find the amount of cake he ate.

[tex]\frac{\frac{3}{4} }{2} \\\\=2\times \frac{3}{4} \\\\=\frac{3}{2}[/tex]

Thus he ate 3/2 of cake.

Learn more about fraction here:

brainly.com/question/24638688

#SPJ4

The area of the polygon is 24 unit².

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

We have four coordinates of vertices given, K(-3,3), L(3,3), M(3,-1), N(-3,-1).

So the polygon must be a quadrilateral.

Length of KL = [tex]\sqrt{(3--3)^{2} + (3-3)^2 }[/tex] = [tex]\sqrt{6^2}[/tex] = 6

Length of LM = [tex]\sqrt{(3-3)^2+(-1-3)^2}[/tex] = [tex]\sqrt{(-4)^2}[/tex] = 4

Length of MN =[tex]\sqrt{(-3-3)^2+(-1--1)^2}[/tex] = [tex]\sqrt{(-6)^2}[/tex] = 6

Length of NK = [tex]\sqrt{(-3--3)^2+(3--1)^2}[/tex] = [tex]\sqrt{4^2}[/tex] = 4

So we get that, opposite sides are having equal length.

So the polygon must be a rectangle.

Area of the rectangle = Length × Width

                                    = 6 × 4

                                    = 24 units²

Hence the area of the polygon with the given vertices is 24 unit².

To learn more about Polygons, click on the link :

https://brainly.com/question/24464711

#SPJ1

The values of x from the given figures are 3 √29 and 24 respectively.

What is triangle ?

Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.

Given

In the figure,

The two given triangles are similar ,

So, in the first figure it is given that they are similar ,

√29 / 5  = x / 15

x  = √29 * 15  / 5

x =√29 * 3

x = 3 √29

And in the second figure , here also they gave they are similar

so we get,

12 / 13  =  x /  26

x = 12 * 26 / 13

x = 12 * 2

x = 24

Hence, The values of x from the given figures are 3 √29 and 24 respectively.

To learn more about Triangle from the given link.

https://brainly.com/question/2773823

#SPJ1

The graph and the points are added as an attachment

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

y = -x + 1 + 5

Evaluate the like terms

y = -x + 6

Set x = values from 0 to 3

So, we have

y = -0 + 6 = 6

y = -1 + 6 = 5

y = -2 + 6 = 4

y = -3 + 6 = 3

So, the points are (0, 6), (1, 5), (2, 4) and (3, 3)

Next, we plot the graph and the points

See attachment

Read more about linear functions at

https://brainly.com/question/2030026

#SPJ1

The translation or the graph must be shifted upwards by 7 units .

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph f(x)=9x

The required graph is given by g(x)=9x+7

A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.

Thus two transform the given graph into g(x) we have to translate the graph vertically or upwards by 7 units i.e f(x)=9x+7

where k=7

Hence, The translation or the graph must be shifted upwards by 7 units .

Learn more about the linear functions here:

https://brainly.com/question/28303908

#SPJ1

The minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.

Domain of Y = -x³ + 2: A = {-2, -1, 0, 1, 2}. The equation is defined for all x in the set A.

Range of Y = -x³ + 2: To find the range, we need to find the minimum and maximum values of Y for x in the set A. Using the formula Y = -x³ + 2, we can substitute the values of x from the set A and find the corresponding values of Y:

x = -2, Y = -(-8) + 2 = 10

x = -1, Y = -(-1) + 2 = 3

x = 0, Y = -(0) + 2 = 2

x = 1, Y = -(1) + 2 = 1

x = 2, Y = -(8) + 2 = -6

Thus, the minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.

Relation Y = -x³ + 2 is a function: A relation is a function if every input x in the domain corresponds to only one output Y in the range. To check if the relation is a function, we need to ensure that no two different inputs in the domain result in the same output.

For this relation, every input x in the domain results in only one unique output Y, so the relation is a function.

Function Notation: If the relation is a function, we can write it in function notation as: f(x) = -x³ + 2, where f is the function name and x is the input.

Evaluating f(-5), f(0) and f(1):

f(-5) = -(-125) + 2 = 127

f(0) = -(0) + 2 = 2

f(1) = -(1) + 2 = 1

Thus, f(-5) = 127, f(0) = 2 and f(1) = 1.

To know more about domain, visit:

https://brainly.com/question/28135761

#SPJ1

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

To learn more about probability:

https://brainly.com/question/24756209

https://brainly.com/question/13604758

#SPJ4

To represents JKLM is a parallelogram the required value of x is equal to 7.

In the parallelogram JKLM,

Let us consider the measure of each side in form of 'x' is represented by :

JK = 4x + 13

KL = 4x - 1

LM = 3x + 20

MJ = 5x - 8

Opposite side of the parallelogram JKLM are congruent to each other.

JK = LM

⇒ 4x + 13 = 3x + 20

⇒ 4x - 3x = 20 - 13

⇒ x = 7

When

KL = MJ

⇒ 4x - 1 = 5x - 8

⇒ 5x - 4x = 8 - 1

⇒ x = 7

JK = 4(7) + 13

    = 41

LM = 3(7) + 20

     = 41

KL = 4(7) -1

    = 27

MJ = 5(7) - 8

     = 27

Therefore, the value of x  which represents that JKLM is a parallelogram is equal to 7.

Learn more about parallelogram here

brainly.com/question/29147156

#SPJ4

I apologize for misunderstanding your question.

Regarding your new question, it depends on the specific expressions provided in column A and column B. Without knowing the exact expressions, I am unable to determine if they are equivalent or not. Additionally, if they are not equivalent, then to make them equivalent, you can use algebraic properties such as the commutative property, associative property, distributive property and simplification techniques to change one of the expressions so that it has the same value as the other expression for every input in their domain.

Please let me know the specific expressions you are working with and I will be happy to help you determine their equivalence and/or how to change one of the expressions to make them equivalent.

Answer:

SO bassically its is equivalent bc i seethat the dgene is really good

Step-by-step explanation:

1 + 1 =2w + 2x +2y = 3x and equiavelnt number

84 inches times as long as a Thimble jellyfish is a Lion's Mane jellyfish.

Now, According to the question:

"Information available from the question"

A Thimble jellyfish is a Lion's Mane jellyfish.

Thimble jellyfish = 1 inch,

Lion's mane jellyfish = 7 feet

Convert feet into inches.

To calculate a value in feet to the corresponding value in inches, just multiply the quantity in feet by 12 (the conversion factor).

Here is the formula:

Value in inches = value in feet × 12

Formula: multiply the value in feet by the conversion factor '12'.

So, 7 feet = 7 × 12 = 84 inches.

Learn more about Conversion of unit at:

https://brainly.com/question/18761654

#SPJ4

The object has both kinetic energy and potential energy.

The values of each type of energy the object has are KE = 67.5 J

GPE = 367.5 J

Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.

If a 15-kg child is tossed up into the air by her parent and the child is 2.5 meters off the ground traveling 3 m/s.

Then boy has kinetic energy due to his motion and also has potential energy due to his height.

Thus, M = 15-kg, h = 2.5 meters and V = 3 m/s

KE = 1/2(M)(V)² = 1/2 × 15 × 3² = 67.5 J

GPE = mgh = 15 × 9.8 × 2.5 = 367.5 J

KE + PE = 67.5 + 367.5 = 435 J

Learn more about energy on:

brainly.com/question/25959744

#SPJ1

Answer: lol no it won't

Step-by-step explanation:

In order to determine if the circular tabletop with a diameter of 88 inches will fit through the door, we must compare the dimensions of the tabletop to the dimensions of the door.

The width of the door is 36 inches and the height of the door is 84 inches. The diameter of the tabletop is 88 inches. To fit through the door, the tabletop's diameter must be less than or equal to both the width and the height of the door.

88 inches > 36 inches and 88 inches > 84 inches

In this case, the tabletop will not fit through the door because its diameter is larger than both the width and the height of the door.

The end behavior of the function f(x) = −x³ + 2x² +1 is:

as  x → ∞, f(x) → -∞

as  x → -∞, f(x) → ∞

Here we want to find the end behavior of the function below:

f(x) = −x³ + 2x² +1

Notice that the degree is odd, this means that the end behaviors are opposite in opposite values of x.

Because we have a negative sign on the term with the highest exponent, then as x tends to infinity, the function will tend to negative infinity.

And thus, because the degree is odd, the value of f(x) as x tends to negative infinity tends to positive infinity.

Thus we can write:

as  x → ∞, f(x) → -∞

as  x → -∞, f(x) → ∞

Learn more about end behavior at:

https://brainly.com/question/1365136

#SPJ1

The scientific notation of the given result is 8 x 10³

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

We are given that Maddie performed a calculation on her calculator and received a result of 8E3.

WE know that "E" means the power of ten

Therefore,

8E3 = 8 x 10³

This is the scientific notation.

For the standard form it should be 8,000.

Learn more about scientific notation here:

https://brainly.com/question/3112062

#SPJ1

To find out how many cans of white paint Emma will need to mix with 12 cans of pink paint, we can use the proportion of white paint to pink paint that she is currently using: 6 cans of white paint to every 4 cans of pink paint.

We can set up an equation using the proportion:

white paint/pink paint = 6/4 =3/2

We know that Emma wants to use 12 cans of pink paint, so we can use this information to solve for the number of cans of white paint she needs:

white paint/pink paint = 3/2

white paint = (3/2) * pink paint

white paint = (3/2) * 12 cans

white paint = 18 cans

So Emma will need 18 cans of white paint to mix with 12 cans of pink paint to get the desired color.

The amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.

To calculate how much paint Mr.Todd needs to buy to cover the outside of the entire birdhouse, we must first know the dimensions of the birdhouse. Let's assume the birdhouse has the dimensions of 10 inches long, 8 inches wide and 6 inches tall, and each side requires 1 coat of paint. The total surface area of the birdhouse is then 10 x 8 + 10 x 6 + 8 x 6 = 176 inches squared. Next, we need to know the coverage of the paint, which we will assume is 250 square feet per gallon. Since 1 square foot is equal to 144 square inches, the coverage of the paint is 36000 square inches per gallon. To find out how many gallons of paint are needed to cover the birdhouse, we need to divide the total surface area of the birdhouse (176 square inches) by the coverage of the paint (36000 square inches per gallon). Therefore, the amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.

Learn more about total surface area here:

https://brainly.com/question/8419462

#SPJ4

Answer: 16

Step-by-step explanation:

8 * (6/3)

= 8 * 2

= 16

Answer:

0

Step-by-step explanation:

First, you do 17 - 8, which is 9 and then you do 13 - 4, which is 9. Then, you subtract 9 from 9, which gives you 0.

The amount of salt in the tank is decreasing exponentially with time.

At time t, the amount of salt in a tank containing oz of salt dissolved in gallons of water can be calculated using the following formula:

Salt in tank (oz) = 200 - 140e^(-t/25)

For example, at time t = 10 min, the amount of salt in the tank is 200 - 140e^(-10/25) = 200 - 140(0.7787) = 124.42 oz.

This calculation assumes that brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. Thus, the amount of salt in the tank is decreasing exponentially with time.

Learn more about Total amount here:

https://brainly.com/question/29066172

#SPJ4

Answer: (-45 , -25)

Step-by-step explanation:

Please mark brainliest!!

An inequality which shows the constraint on the amount of apple John has to make pies and cobblers is: D. 4x + 2y ≤ 16.

In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:

Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:

4x + 2y ≤ 16

Read more on equation here: brainly.com/question/18912929

#SPJ1

Answer:

equiangular triangle

Step-by-step explanation:

The final resultant expressions are  3.9 - 0.8 x , 1.5 + t+0.66 x ,

77/5 k - 3m.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expressions,

-2.5x+3.9 + 1.7x

3.9 + 1.7x-2.5x

3.9 - 0.8 x

1  1/2 + t + 2/3 s

= (2+1) / 2 + t+ 2/3  s

= 3/2 + t + 2/3 s

= 1.5 + t+0.66 x

15k+2/5 k -3m

k(15+2/5 ) - 3m

k (75 + 2 / 5 )  - 3m

77/5 k - 3m

Hence, The final resultant expressions 3.9 - 0.8 x , 1.5 + t+0.66 x ,

77/5 k - 3m

To learn more about Algebraic expression from the given link.

brainly.com/question/953809

#SPJ1

The equation of the line is 6x-5y = 25.

What is equation of line?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept equation.

Here in the given graph the points are [tex](x_1,y_1)=(0,-5)[/tex] and [tex](x_2,y_2)=(5,1)[/tex]

Now using slope formula  m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{1-(-5)}{5-0}[/tex]

=> m =  [tex]\frac{1+5}{5} = \frac{6}{5}[/tex]

Now using equation formula [tex]y-y_1 = m(x-x_1)[/tex] then

=> [tex]y - (-5) = \frac{6}{5}(x-0)[/tex]

=> y+5 = [tex]\frac{6}{5}[/tex]x

=> 5y+25 = 6x

=> 6x-5y = 25.

Hence the equation of line is 6x-5y = 25.

To learn more about equation of line refer the below link

https://brainly.com/question/25262302

#SPJ1

As per the formula of compound interest the amount in his account after 6 year 3 months is $40,085.307

In math the term called compound interest is defined as when you earn interest on both the money you've saved and the interest you earn.

Here we know that Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years and 2. 3% thereafter.

Here we need to find the amount in his account after 6 years and 3 months.

Then it can be calculated as,

FV = PV(1 + i)ⁿ

Here we know that PV = 34000 and i = 3.4% for two years,

Then the FV is value is calculated as,

=> FV = 34000(1 + 3.4/100)²

=> FV = 34000 ( 1 + 0.034)²

=> FV = 36351.304

Similarly, the FV value of 4 years 3 months is calculated as,

=>  FV = 36351.304(1 + 2.3/100)⁴°³

=> FV = 36351.304(1 + 0.023)⁴°³

=> FV = 40085.307

To know more about compound interest here

https://brainly.com/question/29335425

#SPJ4

The ball travel horizontally 37 feet before it hits the ground.

What is Distance ?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

we have;

A(x) = -0.02x2 + 0.6x + 5

where

The horizontal distance, x, is given in feet.

The ball's height is indicated by the symbol A ---> in feet.

The fact that

The ball's altitude was zero when it landed on the earth.

so,

For A(x)=0

-0.02x^2 + 6x +5 = 0

'

the quadratic equation to be solved

The equation solving formula for a quadratic equation of the type;

ax^2 + bx + c = 0

this equation is equal to ;

[tex]x = \frac{-b\pm \sqrt{b^{2}- 4ac } }{2a}[/tex]

we have ;

-0.02x^2 + 0.6x +5 = 0

So,

a = -0.02

b = 0.6

c = 5

Subsititue this values in the formula;

[tex]x = \frac{-0.6\pm \sqrt{0.6^{2} -4 *(-0.02)(5) } }{2*(-0.02)}[/tex]

[tex]x = \frac{-0.6\pm \sqrt{0.76 } }{-0.04}[/tex]

[tex]x = \frac{-0.6\pm \ 0.87 }{-0.04}[/tex]

[tex]x = \frac{-0.6\ + \ 0.87 }{-0.04}= -6.75[/tex]

[tex]x = \frac{-0.6\ - \ 0.87 }{-0.04}= 36.75[/tex]

therefore

The ball travel horizontally 37 feet before it hits the ground.

Learn more about Distance click here:

https://brainly.com/question/26046491

#SPJ1

Answer: 12

Step-by-step explanation:

Say that your friends number is x

She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27, so:

(x/4 + 6) * -3 = -27

We can solve the equation by first dividing by -3 on both sides:

x/4 + 6 = 9

Multiply both sides by 4:

x + 24 = 36

Subtract 24 from both sides:

x = 12

Double checking...

(12/4 + 6) * -3

= (3+6) * -3

= 9 * -3

= -27

Correct :>

So your friend chose the number 12