A Piece Of Paper Has An Area Of 80 Square Inches. A Person Cuts Off Of The Piece Ofpaper. Then A Second (2024)

Mathematics High School

Answers

Answer 1

The remaining paper after the nth person cuts off their fraction is given by:

n A(n)

0 80

1 60

2 45

3 33.75

What is an arithmetic sequence?

An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

How to calculate an arithmetic sequence?

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ = a₁ + (n - 1)d

Where:

d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.

After the first person cuts off 1/4, the piece of paper left is given by:

Fraction = 1/4 × 80

Fraction = 20

Remainder = 80 - 20 = 60 square inches.

After the second person cuts off 1/4, the piece of paper left is given by:

Fraction = 1/4 × 60

Fraction = 15

Remainder = 60 - 15 = 45 square inches.

After the second person cuts off 1/4, the piece of paper left is given by:

Fraction = 1/4 × 45

Fraction = 11.25

Remainder = 45 - 11.25 = 33.75 square inches.

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Complete Question:

A piece of paper has an area of 80 square inches. A person cuts off 1/4 of the piece of paper. Then a second person cuts off 1/4 of the remaining paper. A third person cuts off 1/4 what is left, and so on.

Complete the table where A(n) is the area, in square inches, of the remaining paper after the nth person cuts off their fraction.

A Piece Of Paper Has An Area Of 80 Square Inches. A Person Cuts Off Of The Piece Ofpaper. Then A Second (1)

Related Questions

What is the length of x

Answers

Answer:

TN/TS=NM/RS

[tex] \frac{240}{120} = \frac{x}{70 } \\ 120x = 16800 \\ x = 140[/tex]

Answer is 140 as two triangles are similar.
Hence x = base = 2 times 70

a souvenir of the eiffel tower is scaled 1/80 at inch to 1 foot. if the total height of the tower is 1,069 feet, the approximate height of the souvenir of the eiffel tower to the nearest tenth is

Answers

well, let's convert 1 foot to inches, that'd be 12 inches per foot.

so we know that the souvenir is 1/80 in, to the actual of 12 inches on the Eiffel Tower, if the Tower itself is 1069 feet high, namely (1069)(12) inches, how high is the souvenir?

[tex]\begin{array}{ccll} \stackrel{in}{souvenir}&\stackrel{in}{actual}\\ \cline{1-2} \frac{1}{80}&12\\[1em] x&(1069)(12) \end{array}\implies \cfrac{ ~~ \frac{1}{80} ~~ }{x}~~ = ~~\cfrac{12}{(1069)(12)}\implies \cfrac{ ~~ \frac{1}{80} ~~ }{\frac{x}{1}}~~ = ~~\cfrac{12}{12828} \\\\\\ \cfrac{1}{80}\cdot \cfrac{1}{x}=\cfrac{1}{1069}\implies \cfrac{1}{80x}=\cfrac{1}{1069}\implies 1069=80x\implies \cfrac{1069}{80}=x\implies 13.4\approx x[/tex]

The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1

Answers

The equations which can be solved to determine the coordinates of the other endpoints are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.

What equations can be solved to determine the other endpoint K of the line JK?

It follows from the task content that the equation which can be solved to obtain the coordinates of the other endpoint, K be identified.

Since the coordinates of the midpoint can be determined as follows;

x-coordinate of the midpoint;

x = (x1 + x2)/2; where x1 = 4 and x = -1.

Therefore, -1 = (4 + x2)/2 is the first required equation.

y-coordinate of the midpoint;

y = (y1 + y2)/2; where y1 = -15 and y = 8.

Therefore, 8 = (-15 + y2)/2 is the other required equation.

Ultimately, the required equations are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.

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What are the sides of ∠JBA ?

Answers

The sides of angle JBA is ray BJ and BA.

What is an angle ?

In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can say that the angle is the figure formed by two rays which has same initial point. These rays are also known as the sides of an angle. A angle can have two rays.

Some common terms related to angle :

Endpoint : It is the point where the rays met to each other.

Ray : Ray is the side or line segment on which angle is formed.

Curve : It is a line but not straight i.e. a bended line.

Tangent : A line which touches the surface of curve.

In the given question, as ∠JBA is made between two lines or rays i.e. ray BJ and ray BA . Therefore sides of this angle are BJ and BA.

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The endpoints of CD are C(3,
5) and D(7, 9).
The coordinates of the
midpoint M of CD are

Answers

M = (x1 + x2)/2 , (y1 + y2)/2
M = (3+7)/2 , (5+9)/2
M = (10/2 , 14/2)
M = (5, 7)

Answer: M(5,7)

Step-by-step explanation:

[tex]\displaystyle\\C(3,5)\ \ \ \ \ D(7,9)\ \ \ \ \ M(x_M,y_M)=?\\\\M(x_M,y_M)=(\frac{3+7}{2},\frac{9+5}{2})\\\\ M(x_M,y_M)=(\frac{10}{2},\frac{14}{2} )\\\\ M(x_M,y_M)=(5,7)[/tex]

In a mathematics test of 20 questions each rightanswer is awarded 5 marks and 2 marks deducted for each wrong answer given. A certain student got 65%. How many questions did she get right?
A. 13
B. 7
C. 15
D. 5​

Answers

Answer:

C. 13

Step-by-step explanation:

65% = 65/100

divide 65 by 5= 13

why? because each answer is worth 5 marks so we divide the total by 5.

Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% of them. Zach attempted 10 more shots than Jared did and made 80% of them. Together, they made a total of 101 shots. Which equation represents this situation? Select the correct answer. 0.75x = 0.8(x + 10) 0.75(x + 10) + 0.8x = 101 0.75x + 0.8x + 10 = 101 0.75x + 0.8(x + 10) = 101

Answers

Answer:

last one 0.75x + 0.8(x + 10) = 101

Step-by-step explanation:

Jared made 75% = 0.75
let, his attempts = x

zach made 80% = 0.80
his attempts = (x+10)

total = 0.75x + 0.80(x+10) = 101

Hope it helps!
Brainly?

Brian is throwing a party. He needs 3/4 of a pound of hamburger meat for each person at the party. If 12 people are coming to the party, how many pounds of hamburger meat will Brian need to buy?

Answers

9 pounds of hamburger meat will be needed by Brian.

We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.

As per the given information, amount of hamburger meat required for one person is = 3/4 pound

Amount of hamburger meat required for 12 people = (3/4) × 12

Performing division to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 3 × 3

Performing multiplication to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 9 pounds

Therefore, Brain needs to buy 9 pounds of hamburger meat.

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Find the average rate of change of the function: f(x)=x²-3 between the values [3,5]​

Answers

Answer: 4

hope it helps

a cell phone company charges an initial price of $400 for a new phone and then $50 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function? r: ℝ r: (–[infinity], [infinity]) r: (0, 400) r: (50, 450)

Answers

The range of the average cost function of a cell phone that has an initial and monthly costs $400 and $50 is r:(50, 400)

Which method can be used to find the range of the average cost function?

Initial price for the cell phone = $400

Charges per month after purchase = $50

The rational function representing the average monthly cost = c(t)

Required; The range of the average monthly cost function, c(t)

Solution:

The total cost of owning the cell phone, C, is therefore;

C = 400 + 50•t

Where;

∆t = The number of months after purchase

The average monthly cost is therefore;

[tex]c(t) = \frac{C}{ \Delta t} [/tex]

At ∆t ≈ 0, we have;

C ≈ 400

The cost for the month at ∆t ≈ 0, is therefore, c(t) = $400

At ∆t ≈ ∞, we have;

[tex] \lim\limits_{∆t→∞} \frac{400}{ ∆t} = 0[/tex]

Therefore;

[tex] \lim\limits_{∆t→∞} c(t) = \frac{400+ 50× ∆t}{ ∆t} ≈ 50[/tex]

Which gives;

The range of c(t) is (50, 400)

The correct option is therefore;

r: (50, 400)

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Each face of a pyramid is an isosceles triangle with a 84° vertex angle. What are the measures of the base angles?

Need asappp!

Answers

Answer is base angles will both be 48 degrees.

Step by step

The base angles are the 2 congruent angles in an isosceles triangle.

Sum of the interior angles =180 degrees.

The vertex is 84, so we know one angle.

180 - 84 = 96

Since the base angles will be equal, we divide 96 by 2 = 48.

The base angles will each be 48 degrees.

You add a mixture of salt, sugar, and cooking oil to a glass of water. You stir everything together and wait a few minutes. What will you see in the glass? (2 points)

a
All of the parts of the mixture will disappear because they are all soluble in water.

b
The salt and sugar will seem to disappear, and the oil will float on the surface of the water.

c
The salt and sugar will settle to the bottom of the glass, and the oil will float on top of the water.

d
The salt will settle to the bottom of the glass, and the sugar and oil will disappear in the glass.

Answers

Answer:b. the salt and sugar will disappear and the oil will float on the surface of water

Step-by-step explanation: If you stir salt and sugar it will dissapear but oil in thick and if you know it will float to the surface

Answer number 6 pleaseeeee

Answers

Answer:

Step-by-step explanation: The answer is B

What is the equation of the line that is parallel to the line y =
Oy=-x+3
O y=-x+7
Oy= 3x - 13
Oy= 3x +5
-x+4 and passes through the point (6, 5)?

Answers

Answer:

Step-by-step explanation:

x=4 is a vertical line.

horizontal line through (-6,5): y=5

y=6 is a horizontal line.

vertical line through (-6,5): x=-6

The equation of line parallel to y = -( 1/3 )x + 4 and passing through the point P ( 6 , 5 ) is y = -( 1/3 )x + 7

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -( 1/3 )x + 4

Let the first point be P ( 6 , 5 )

Slope m = -1/3

The parallel lines have the same slope , so the point-slope form of the equation of a line to find the equation of the line passing through P(6,5) with slope -1/3 is

y - 5 = ( -1/3 ) ( x - 6 )

Adding 5 on both sides , we get

y = ( -1/3 )x + 2 + 5

y = -( 1/3 )x + 7

Hence , the equation of line is y = -( 1/3 )x + 7

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The complete question is attached below :

What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?

A) y = -1/3x + 3

B) y= -1/3x + 7

C) y= 3x - 13

D) y= 3x + 5

The circle graph shows the most important problems for
the 14,054,077 high school teenagers in a country..
Without using a calculator, estimate the number of high
school teenagers for whom doing well in school is the
most important problem.
Most Important Problems for High School Teenagers
Doing Wel in School, 12%
Social Pressures and Fitting in, 22%
Drugs, 22%
Others, 29%
Getting along with Parents. 2%
Geting into College, 2%
Sexual Issues, 2%
Crime and Violence in School, 9%
Doing well in school is the most important problem for approximately how many of the high school teenagers?
OA. 4,200,000
OB. 1,400,000
LOC. 2,800,000
OD. 5,600,000

Answers

According to the circle graph, doing well in school is a problem that affects B. 1,400,000 high school teenagers.

Which high school students are affected?

The circle graph shows that 12% of high school students have the problem of doing well in school.

In actual numbers, this is:

= 12% x number of high school teenagers

Solving gives:
= 12% x 14,054,077

= 1,686,489 students

= 1,400,000 approximate

In conclusion, option B is correct.

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(2x−6)(x−2) multiply

Answers

Step-by-step explanation:

Solving steps

(2x-6)×(x-2)

Multiply

2x×x-2x×2-6x-6x 2

Calculate Multiply

2x²-4x-6x+12

Collect like terms

Solution

2x²- 10x + 12

The answer will be 2x^2 - 10x + 12

PLEASE PLEASE PLEASE ANSWER !!!

What is the equation of the given line?

x = 0

y = -2

x = -2

y = -1

Answers

Answer:

y = -1

Step-by-step explanation:

→ First determine which axis the line passes through

y

→ Find which point the line passes through

-1

→ Equate both variables

y = -1

The length of a rectangular sign is 3 feet longer than the
width. If the sign's area is 54 square feet, find its length and
width.

(Anyone else taking Algebra 2?)

Answers

Answer:

length is 9 and width is 6

Step-by-step explanation:

List the factors of 54 and choose the numbers that only have a difference of 3. In this case it is 6 and 9, then put them in the order they go based on the instructions.

Make a mapping diagram for the relation.
{(-3, 4), (1, 1), (3, -6), (4, -1)}

Answers

Check the picture below.

can someone answer 2 1/8 x 1 7/9 =

Answers

Answer:

Exact Form: 34/9

Mixed-Number Form: 3 7/9

Step-by-step explanation:

Hope this helps.

Answer:

3 7/9

Step-by-step explanation:

2 1/8

convert mixed numbers to improper fractions

2x8+1/8 = 17/8

1 7/9

1x7+9/9 =16/9

17/8 x 16/9

Factor the number 16=8x2

17x8x2/8x9

cancel the common factor =8

=17x2/9

=34/9

convert improper fractions to mixed numbers

34/9 =3 remainder of 7

34/9 = 3 7/9

Which of the following is the equation of a line in slope-intercept form for a
line with slope = 2/3 and y-intercept at (0,-2)

Answers

The equation of the line with slope 2/3 and y-intercept at ( 0, - 2) is y = ( 2/3 )x - 2.

The slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible.

We have the slope 2/3 of a line and the y-intercept at ( 0, - 2 ).

Now, we know that

The slope-intercept form of the equation of a line with slope m and y-intercept at the point (0, c) is given by:

y = mx + c

The slope of the line is :

m = 2/3

And, the y-intercept is (0, c) = ( 0, -2)

Hence, the equation of the line in the slope-intercept form will be:

y = mx + c

y = ( 2/3 )x + ( - 2)

y = ( 2/3 )x - 2

Therefore, the slope-intercept form of the equation of the line is y = ( 2/3 )x - 2.

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How can u determine whether a relation represented as an equation is a function

Answers

It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.

which also signifies that for each value of x , there is a value of y which exists and is real.

A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.

Or in simple words if there is no corresponding value of y for any x, then that is not a function.

For example,

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

when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.

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The price of a sofa was £880. It was reduced in a sale by 35%. What is the cost of the sofa in the sale?

Answers

£880 x 0.65 = £572 :)

Answer: 308

Step-by-step explanation:

SOLUTION STEPS

880×35%

Reduce the fraction

[tex]\frac{35}{100}[/tex]

to lowest terms by extracting and canceling out 5.

[tex]880*(\frac{7}{20} )[/tex]

Express [tex]880*(\frac{7}{20} )[/tex]

as a single fraction.

[tex]\frac{880*7}{20}[/tex]

Multiply 880 and 7 to get 6160.

[tex]\frac{6160}{20}[/tex]

Divide 6160 by 20 to get 308.

308

In a​ week, a man received a paycheck for ​$826.60. The withholding for taxes was ​$91.40. If he worked 34 hours in that​ week, what is his hourly pay​ rate?

Answers

The hourly rate will be $21.6

Percentages and taxes

Taxes are money charged from the good bought or sold. Given the following parameters

Amount received = $826.60

Tax paid = $91.40

Balance = 826 - $91.40

Balance = $734.6

This shows that the man collected $734.6 for a 34 hours work. The hourly rate will be;

Hourly rate= $734.6/34

Hourly rate= $21.6

Hence the hourly rate will be $21.6

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choose the first set in the list of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers that describes the following number.

Answers

The given number is a real number.

What are real numbers?

A real number is a value of a continuous quantity that can be used to indicate a distance along a line in mathematics.

We are given the following in the question:

{natural​ numbers, whole​ numbers, integers, rational​ numbers, real numbers}

π / 108

We have to tell the type of number that describes the given fraction.

Evaluating the value, we have,

0.0290888208666...........

This is not a natural number or a whole number. This is not a rational number.

Since is an irrational number, thus quotient of an irrational number and a rational number is an irrational number.

Thus, it is a real number.

The complete question is given below:-

Choose the first set in the list of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers that describes the following number. StartFraction pi Over 108 EndFraction.

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2. Why does this
equation have no
solutions?
3(4x12) = 2(6x + 8)

Answers

The equation 3(4x + 12) = 2(6x + 8) has no solution because the variable x was neglected as it equals 0.

How to calculate the value?

It should be noted that the equation given is illustrated as:

3(4x + 12) = 2(6x + 8)

Open the parentheses

12x + 36 = 12x + 16

Collect like terms

12x - 12x = 16 - 36

0 = -20

Therefore, it has no solution.

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send help guys thanks ​

Answers

The solutions associated with each case are listed below:

3 · x + 22 - x2 · x² + 4 · x1 / 2 + 1 / x2 · x + 22 · x + 4x + 44 · x- 82How to use operations between functions and evaluate resulting expressions

According to the statement, we find that the two functions are f(x) = x + 2 and g(x) = 2 · x and we are asked to perform on the functions to obtain all resulting expressions and, if possible, to evaluate on each case:

Case 1

(f + g) (x) = f (x) + g (x) = (x + 2) + 2 · x = 3 · x + 2

Case 2

(f - g) (x) = f (x) - g (x) = (x + 2) - 2 · x = 2 - x

Case 3

(f · g) (x) = f (x) · g (x) = (x + 2) · (2 · x) = 2 · x² + 4 · x

Case 4

(f / g) (x) = f (x) / g (x) = (x + 2) / (2 · x) = 1 / 2 + 1 / x

Case 5

(f ° g) (x) = f [g (x)] = 2 · x + 2

Case 6

(g ° f) (x) = g [f (x)] = 2 · (x + 2) = 2 · x + 4

Case 7

(f ° f) (x) = f [f (x)] = (x + 2) + 2 = x + 4

Case 8

(g ° g) (x) = g [g (x)] = 2 · (2 · x) = 4 · x

Case 9

(g ° g) (- 2) = 4 · (- 2) = - 8

Case 10

(f ° f) (- 2) = - 2 + 4 = 2

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HELP ME PLEASE I AM SO CONFUSED

Answers

Answer:

19,,

Step-by-step explanation:

Determine if the expression - s5 +8s5t² is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.​

Answers

Step-by-step explanation:

Its a polynomial because it is

Tanner's parents give him x dollars per month for his allowance. however, since his birthday is in february, he gets an extra 20% bonus that month. pick all the expressions that represent how much tanner's allowance is in february. 120x x+0.2x x+1.2x 1.2x

Answers

it is given in question that Tanners parent give him x dollars per month plus 20% extra in February therefore the amount become 0.2x

What do you mean percentage?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Tanner's parents give him x dollars per month for his allowance.

however, since his birthday is in february

he gets an extra 20% bonus that month.

pick all the expressions that represent how much tanner's allowance is in february month

20% = 20/100

= 2/10

=1/5

= 0.2

since it is given in question that Tanners parent give him x dollars per month plus 20% extra in February

therefore the amount become 0.2x

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A Piece Of Paper Has An Area Of 80 Square Inches. A Person Cuts Off Of The Piece Ofpaper. Then A Second (2024)

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