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.

## 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!

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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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