The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 54 centimeters. Find the length and width of the rectangle.

Answers

Answer 1

Answer:

length = 13 cm , width = 14 cm

Step-by-step explanation:

let the length be n , then the width is n + 1

the perimeter (P) of a rectangle is calculated as

P = 2(l + w) ← l is the length and w the width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

so, length = 13 cm and width = 14 cm


Related Questions

An uber charge a flat rate of $20 plu $2 per mile. Lyft charge a flat rate of $15 plu $4 per mile. Write an equation to find the number of mile m for which uber and lyft would cot the ame amount

Answers

The required equation is 20 + 2m = 15 + 4m. The number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.

Uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. We need to find out the equation and the number of miles for which Uber and Lyft would charge the same amount for the ride.

Let the charge of Uber and Lyft be represented by the variables C1 and C2. We can write the equations given below.

C1 = 20 + 2m

C2 = 15 + 4m

We need the charge for both companies to be equal.

C1 = C2

20 + 2m = 15 + 4m

Hence, the required equation is 20 + 2m = 15 + 4m. Now we will solve this equation to find the number of miles.

2m = 5

m = 2.5

Hence, the number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.

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Determine the length of the line segment shown.

line segment from negative 5 comma 5 to 3 comma negative 1

6 units
8 units
10 units
36 units

Answers

The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.

How to find the length of a line segment?

A line segment is defined as a line bounded by two  points on a line.

The line segment from negative 5 comma 5 to 3 comma negative 1

is found by using the formula

square root of (x2-x1)² +(y2-y1)²

[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]

[tex]\sqrt{8^{2}+6^{2} }[/tex]

[tex]\sqrt{100}[/tex]

=10 units

therefore the length of the line segment is 10 units

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I need help to solve this please!!​

Answers

Answer:

Adult is 10$ and Child is 7$.

Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.

Hope this helps!

Step-by-step explanation:

2x + 4y = 48

5x + 2y = 64

2x + 4y = 48

10x + 4y = 128

( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )

8x = 80

x = 10

2 ( 10 ) + 4y = 48

20 + 4y = 48

4y = 48 - 20

4y = 28

y = 7

at the end of 12 months, the owner determined that the average weekly sales of organic fruit displayed at the front of the store were greater than the average weekly sales of organic fruit displayed at the back of the store. the difference was statistically significant. what can be concluded from the study?

Answers

The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH

Please Help!

Solve the inequality and graph it’s solution.

Answers

The answer would be x > -24, or option A.

To solve the inequality, we would multiply -6 by 4 and get rid of the 4:

x/4 < -6

= x < -24

Since we multiplied, we now switch the sign from less than (<) to greater than (>).

x > -24

On a graph, an open dot would be plotted at -24 and the line would be going to the right to resemble the “greater than” portion of the inequality.

quick help me please

Answers

Answer:

calculate the difference ere

(3-22)+5

remove unnecessary parentheses

-19+5

calculate the sum

= -14

Screams Halloween Theme Park
reduced their admission rates by 10% this
year to try and increase their attendance. If
last year’s admission price was $35 per
person, what is this year’s admission price?

Answers

Answer:

$32.50

Step-by-step explanation:

10% of 35$ is $3.50 if ur decreasing $35 by 10% it will be $3.50-$35=$32.50

HELP MEEEEE PLEASEEEE

Answers

Answer is 8.7 cm
Explanation

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Answers

The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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Which of the contexts below represents exponential growth?
An amusement park charges $3.50 to go on each of the rides.
A town's population grows at a rate of 5.3% every year.
The amount of a certain medication in a person's bloodstream decreases by 2/5
every minute.
A town's population shrinks at a rate of 9.7% every year.

Answers

Answer:

A town's population grows at a rate of 5.3% every year.

The values in the table represent a linear function. x 1 2 3 4 ​ f(x) ​ 1 4 7 10 What is the function rule? Write the rule in function notation, using the slope-intercept form of a line. Enter your answer in the box.

Answers

The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

How to express the rule in function notation using the slope-intercept form of a line?

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

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Aaliyah was given a gift card for a coffee shop. Each morning, Aaliyah uses the card to

buy one cup of coffee. The original amount of money on the gift card was $30 and

each

сир of coffee costs $2. Make a table of values and then write an equation for A,

in terms of x, representing the amount money remaining on the card after buying a

cups of coffee.

Answers

The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x  dollars.

Define the term equation?A single mathematical phrase is referred to as a term. It could be a single number (negatively or positively), a single variable (a letter), or a combination of variables multiplied but still never added or eliminated. Variables with such a number ahead of them are used in some words. A coefficient is the number that appears ahead of a phrase.

The original value of the gift card was $30.

Coffee costs $2 per cup.

Let 'x' be the number of cup of coffee purchased by Aaliyah.

Total cost be 'A' be paid by her.

Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;

A = 30 - 2x  dollars.

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The equation of line s is y=3/5x2/5 Line t, which is parallel to line s, includes the point
(2, 1). What is the equation of line t?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
8

Answers

The equation of line t in slope intercept form is 5y - 3x = -1

The equation of line s is y=3/5x + 2/5

This is in the slope intercept form

y = mx + c

where m represents the slope of the line

The slope of the line  y=3/5x + 2/5 is 3/5

The slope of two parallel line is same

The slope of line t is 3/5, it passes through the points (2, 1)

The equation of the line is

y - y₁ = m(x - x₁)

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

5y - 5 = 3x - 6

5y - 3x = -6 + 5

5y = 3x  -1

y = 3/5 x - 1/5

Therefore, the equation of line t in slope intercept form is 5y - 3x = -1

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the length of time for one individual to get to a construction site is a random variable having an exponential distribution with a mean of 4 minutes. what is the probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days?

Answers

The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.

Define probability.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Given,

Mean = 4 minutes

= 1/4

= 0.25

The probability that someone will be attended to in less than three minutes on any given day is:

P( X ≤3)

= 1- e⁻⁰²⁵⁽³⁾

= 0.5267

The probability is:

P( X ≥ 4)

= P( X = 4) +P( X = 5 ) + ( X = 6)

= 0.2594 + 0.1159 + 0.216

= 0.3969

The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.

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Tony is decorating a ballroom ceiling with garland. If the rectangular ceiling is 5 meters by 12 meters, how much garland will Tony need to reach from one corner of the ceiling to the opposite corner?

Answers

Answer: 13

Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.

Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.

The ceiling of the ballroom is rectangular in structure.

The dimensions of the rectangle are 12 by 5 meters.

So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.

We will use Pythagoras theorem to calculate the length of the diagonal.

12² +5 ² = D²

or, D² = 144 + 25

or, D =√169

or, D = 13

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.

Hence Tony will need 13 meters of garland.

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Which inequality correctly compares One-half, Three-fourths, and Two-thirds?

One-half < Three-fourths < Two-thirds
One-half < Two-thirds < Three-fourths
Two-thirds < One-half < Three-fourths
Three-fourths < One-half < Two-thirds

Answers

An inequality correctly compares One-half, Three-fourths, and Two-thirds is: One-half < Two-thirds < Three-fourths.

What is an inequality?

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values (numbers) and variables in an algebraic equation, especially based on any of the following inequality symbols:

Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).

Translating the numbers in word to numerical values, we have:

One-half = 1/2 or 0.5

Three-fourths = 3/4 or 0.75

Two-thirds = 2/3 or 0.67

Next, we would compare the above numerical values by using the less than (<) inequality symbol as follows:

0.5 < 0.67 < 0.75

One-half < Two-thirds < Three-fourths.

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a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion is called

Answers

The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .

A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.

Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.

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an old-model machine can stamp 1000 parts in four hours. a newmodel machine can stamp 1000 parts in just two hours. how long will it take one old-model and one new-model machine to stamp 1000 parts working together?

Answers

It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

Given that;

Finding the hourly cost of stamping parts for each machine is one way to approach this issue.

In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).

If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.

By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;

250t + 500t = 1000

750t = 1000

t = 1000/750

t = 1.333

It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

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can someone please help me solve this paper

Answers

the given expressions solved by using factorization.

What is factorization of the expression ?

  To factorize an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse.

Here

4) [tex]x^4-36[/tex]

=> [tex](x^2)^2 -6^2[/tex]

=> [tex](x^2-6)(x^2+6)[/tex]

5)64[tex]c^3+1[/tex]

=> [tex](4c)^3+1^3[/tex]

=> (4c+1)([tex](16c^2+4c+1)[/tex]

6)[tex]k^3-27[/tex]

=> [tex]k^3-3^3[/tex]

=>(k-3)([tex]k^2+3k+9[/tex])

7)[tex]54x^3+250y^3[/tex]

=> 2([tex]27x^3+125y^3[/tex])

=> 2([tex](3x)^3+(5y)^3[/tex])

=> 2 ( 3x+5y)([tex]9x^2+15xy+25y^2[/tex])

8)[tex]3m^4-48n^2[/tex]

=> 3([tex](m^2)^2-(4n)^2[/tex])

=> 3[tex](m^2-4n)(m^2+4n)[/tex]

9)[tex]a^7b^2-ab^2[/tex]

=> [tex]ab^2(a^6-1)\\[/tex]

=>[tex]ab^2(a^3-1)(a^3+1)[/tex]

=> [tex]ab^2(a+1)(a-1)(a^2-a+1)(a^2+a+1)[/tex]

10)[tex]x^3y^2-343y^5[/tex]

=> [tex]y^2(x^3-(7y)^3)[/tex]

=>[tex]y^2(x-7y)(x^2-7xy+49y^2)[/tex]

11)[tex]9y^7-144y[/tex]

[tex]= > 9y(y^6-16)\\= > 9y((y^3)^2-4^2)\\= > 9y(y^3+4)(y^3-4)[/tex]

Hence we can solve by using factorization formula.

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tim and angel are working on promoting an event for a club they are in on campus. in one afternoon tim can make 4 flyers or 5 posters, and angel can make 3 flyers or 6 posters. if you were to graph angel's ppc with posters on the horizontal axis, what would be the slope of her ppc

Answers

If we graph the angel's ppc then the slope of angel's ppc will be -1.

Given, Tim and Angel are working on promoting an event for a club they are in on campus.

In one afternoon, Tim can make 4 flyers or 5 posters, and Angel can make 3 flyers or 6 posters.

we have to find the slope of the angel's ppc if we graph the angel's ppc.

As, the graph of the angel's ppc will pass through the point (3 , 6).

so, the slope = (6 - 5)/(3 - 4)

slope = 1/-1

slope = -1

Hence, if we graph the angel's ppc then the slope of angel's ppc will be -1.

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Deshaun works as a busboy making $9 per hour and as a theater usher making $10 per hour. Let b be the number of hours he works as a busboy this
month, and let u be the number of hours he works as an usher.
His goal this month is to earn more than $1400 total

Answers

Answer:

[tex]9b + 10u > 1400[/tex]

Need help lol for this

Answers

In the given rectangle, the values of f and g are the same that is 2√6cm.

What are rectangles?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.Therefore, a particular case of a square is a rectangle. To put it another way, a rectangle can also be a square (when all sides to are equal).

So, the values of f and g are:

We know that APQD is a square and its area is 24 cm².

Now, calculate the sides as follows:

Formula: A = s²

24 = s²s = √24s = √2×2×2×3s = 2√6

So, each side of APQD measures  2√6cm.

So, DQ (g) = 2√6cmNow,  we know that ABCD is a rectangle and we know that AD || CB and AD  = CD.

Then,

AD = CB = 2√6cmSo, CB (f) = 2√6cm

Therefore, in the given rectangle, the values of f and g are the same that is 2√6cm.

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PLEASE ANSWER
What are the coordinates of the point that is one half the distance between A(−1, −2) and B(6, 12)?


( , )

Answers

This is called the midpoint = ((-1 + 6)/2 , (-2 + 12)/2) = (5/2 , 10/2) = (2.5 , 5)
Find the average of the x and y coordinates separately

How was the Greeks and mathematics related

Answers

Greek mathematicians, who were first influenced by the Egyptians, would go on to produce innovations like Pythagoras' theory of right-angled triangles and, by concentrating on the abstract, bring accuracy and clarity to venerable mathematical conundrums.

How related Greeks and mathematics?Modern mathematics was created as a result of the contributions made by the ancient Greeks to the subject. The Greeks generally concentrated on geometry in an effort to describe shapes using numbers. This emphasis produced a number of quite important discoveries, many of which are still applicable to the mathematics we practice today.Miletus, a city of Ionia in Asia Minor and the cradle of Greek philosophy, mathematics, and science, was the location of the greatest Egyptian and Babylonian influence.Modern mathematics was created as a result of the contributions made by the ancient Greeks to the subject. The Greeks generally concentrated on geometry in an effort to describe shapes using numbers.

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Guys, what is the answer to 5-x=12? ​

Answers

Answer:

x= -7

Step-by-step explanation:

here you go.....

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A box is put on a table. The face of the box in contact with the table is in the shape of a rectangle, 2 m by 1.25m. The pressure on the table due to the box is 42 newtons/m² Work out the force exerted by the box on the table.​

Answers

Answer:

  105 N

Step-by-step explanation:

You want the force exerted on an area 2 m by 1.25 m by a pressure of 42 N/m².

Area

The area is ...

  A = LW

  A = (2 m)(1.25 m) = 2.50 m²

Force

The force is the product of the pressure and the area:

  F = PA

  F = (42 N/m²)(2.5 m²) = 105 N

The box exerts a force of 105 N on the table.

Describe the end behavior of each fund f(x) = x4 - x2 - x

Answers

Answer:

[tex]\lim_{x \to -\infty} f(x) = \infty[/tex] and [tex]\lim_{x \to \infty} f(x) = \infty[/tex]

Hope this helps!

Step-by-step explanation:

PLEASE HELP!!!!!!! A warehouse store sells 5.5​-ounce cans of tuna in packages of 5. A package of 5 cans costs ​$10.45. The store also sells ​4.5-ounce cans of the same tuna in packages of 8. A package of 8 cans costs ​$12.96. The store sells 3.5​-ounce cans in packages of 4 cans for ​$4.76. Which package is the best​ buy? find the one with the smallest unit rate!!!

Answers

Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.

What is the average rate change?

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

A discount store sells 5.5 - ounce jars of fish in bundles of 5. A bundle of 5 jars costs $10.45. Then the unit rate is given as,

⇒ ($10.45 x 5) / (5.5 x 5 x 5)

⇒ $0.38 per ounce

The store likewise sells 4.5-ounce jars of similar fish in bundles of 8. A bundle of 8 jars costs $12.96. Then the unit rate is given as,

⇒ ($12.96 x 8) / (4.5 x 8 x 8)

⇒ $0.36 per ounce

The store sells 3.5 - ounce jars in bundles of 4 jars for $4.76. Then the unit rate is given as,

⇒ ($4.76) / (3.5 x 4)

⇒ $0.34 per ounce

Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.

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a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 15 ft from the base of the pole?

Answers

The speed of the tip of her shadow would be 5.714 ft/sec.  ft/sec.

let H, be the height of the pole = 20 ft.

h, be the height of the woman = 6 ft.

x, be the length of the woman's shadow,

and s, be the distance from the pole to the woman = 15

by using the equation of similar triangles,

[tex]\frac{H}{h} = \frac{(s+x)}{x}[/tex] or Hx = h(x+s)

differentiating, [tex]H\frac{dx}{dt} = h (\frac{ds}{dt} + \frac{dx}{dt} )[/tex]

[tex]20\frac{dx}{dt} = 6(4 + \frac{dx}{dt} ) = 24 + 6 \frac{dx}{dt}[/tex]

[tex]14\frac{dx}{dt} = 24[/tex],

[tex]\frac{dx}{dt} = \frac{24}{14}[/tex] ≈ 1.714 ft/sec, is how fast her shadow is lengthening.

the speed of the tip of her shadow would be the speed of shadow lengthening + speed of her traveling = 1.714 + 4 = 5.714 ft/sec.

thus, a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. the speed of the tip of her shadow would be 5.714 ft/sec.

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The school art club at a large high school is in charge of designing school T-shirts and getting them printed this year. A local business charges $35 to set up their T-shirt printing machine with the design and $4.25 in materials per T-shirt to print.
1). Create an equation to represent the average cost C(x), in dollars, per T-shirt if x T-shirts are printed by this business.
2). what is the average cost per shirt to print 25 shirts? 100 shirts?
3). what is the cheapest the average cost per T-shirt will get? Explain or show your reasoning.

Answers

Total cost includes initial charge for printer set up and material cost.

C(x) = 4.25x + 35 represents the total cost, where C(x) is the cost of x T- shirts.

Part 1

Average cost per T-shirt is

C(x)/ x = (4.25x + 35)/x = 4.25 + 35/x

Part 2

Average cost to print 25 T-shirts

4.25 + 35/25 = $5.65

Average cost to print 100 T-shirts

4.25 + 35/100 = $4.60

Part 3

The average cost 4.25 + 35/x depends on the number of T-shirts printed.

The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.

Other Questions
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