The perimeter of a rectangle is 84 cm. the length is 3 cm shorter than the width. find the length and width of the rectangle.

Answers

Answer 1

Taking into account the definition of a system of linear equations, the length and width of the rectangle is 22.5 cm and 19.5 cm respectively.

System of linear equations

Systems of linear equations are groupings of first degree equations with the same unknowns, of which a common solution must be found.

In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

Number of sodas and hot dogs sold

In this case, a system of linear equations must be proposed taking into account that:

"x" is the length of the rectangle."y" is the width of the rectangle.

You know:

The perimeter of a rectangle is 84 cm. The perimeter of a flat geometric figure is called the length of its contour. It is obtained as a result of the sum of the sides of a flat geometric figureThe length is 3 cm shorter than the width.

The system of equations to be solved is

2x + 2y= 84

x= y + 3

The substitution method is a way to solve systems of equations. To use the substitution method, you choose an equation and find an expression for one of the variables in terms of the other variable. Then substitute that expression for the variable in the other equation.

In this case, substituting the second equation in the first one you get:

2×(y+3) + 2y= 84

Solving:

2y+ 2×3 + 2y= 84

2y+ 6 + 2y= 84

2y + 2y= 84 - 6

4y= 78

y= 78÷4

y= 19.5

Replacing this value in the second equation, you get:

x= 19.5 + 3

x= 22.5

Finally, the length of the rectangle is 22.5 cm and the width of the rectangle is 19.5 cm.

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Related Questions

Please help

Dean collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:

Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.17 0.24 0.05 0.46
Grade 9 0.14 0.18 0.22 0.54
Column totals 0.31 0.42 0.27 1

Based on the data, which statement is most likely correct?
In Grade 8, 17 students liked swimming.
In Grade 9, 27% of students liked volleyball.
In Grade 9, 14 students liked running.
In Grade 9, 18% of students liked running.

Answers

Based on the data, the statement that is most likely correct is D. In Grade 9, 18% of students liked running.

How to illustrate the information?

The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.

From the information, the Dean collected data on the favorite sports of the students of two grades.

Here, the table shows the relative frequencies of rows for the data collected:

Swimming Running Volleyball Row totals

Grade 8 0.17 0.24 0.05 0.46

Grade 9 0.14 0.18 0.22 0.54

Column totals 0.31 0.42 0.27 1

In the table, Grade 9, 18% of students liked running. This is Illustrated above. The correct option is D.

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the diagram shows 2 mathematically similar vases. vase A has height 20cm and volume 1500^3. vase B has volume 2592cm^3. calculate h, the height of vase b.

Answers

The height of vase b is 34.56 cm.

What is volume?

In mathematics, volume is the space taken by an object.

V=pi*r²*h

Here, given that,

vase A has height 20cm =H

and volume 1500^3. =V

And, A & B similar vases.

Again, vase B has volume 2592cm^3 =v

let, h, the height of vase b.

both radius are equal

so, we get, V/pi*H = v/pi*h

i.e. 1500/20=2592/h

so, h= 34.56 cm

Hence, the height of vase b is 34.56 cm.

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A. What must the side length of each square represent for the rectangle to correctly represent (0. 3). (0. 5)?

Answers

The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.

A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.

Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).

Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).

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Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. In how many week will he have enough money to the bike?Use the bar diagram to solve arithmetically. Then use an equatuio to slove algebraically.

Answers

Answer:

It will take him 9 weeks to be able to buy the bike.

Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. The correct answer is 9 weeks.

What were the steps to lead us to this answer?

So, we have:

- Cost of the bike = $189

- Money saved = $99

- Money saving each week = $10

We are trying to find how many weeks will he have enough money to the bike.

So, we are going to multiply and add the numbers to find are answer:

→ (n × $ 10) + $ 99 = $ 189

→ n × $ 10 = $ 90 n = $ 90 $ 10 n=9 weeks.

Therefore, Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. The correct answer is 9 weeks.

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Is a 45 45 triangle isosceles?

Answers

Yes, a 45 45 triangle is an isosceles triangle, meaning that two of its sides are equal in length.

A 45 45 triangle is a triangle in which two of its angles are 45 degrees. This type of triangle is also known as an isosceles triangle because it has two sides of equal length. To determine whether a triangle is isosceles, we need to measure the lengths of its sides. In a 45 45 triangle, both sides are equal in length as the angles are equal. Therefore, a 45 45 triangle is an isosceles triangle. The triangle also has two acute angles (less than 90 degrees) and one obtuse angle (greater than 90 degrees). This type of triangle is a special type of triangle and is often used in geometry and trigonometry.

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Triangle J K L. Side J K is 5 inches and side J L is 10 inches.
Which could be the length of Side K L?
4 in.
9 in.
16 in.
19 in.

Answers

Answer:

9 in.

Step-by-step explanation:

the sum of two sides in a triangle is always longer than the 3rd side. so 9 is the only answer that fits this condition.

To divide 572 4, Stanley estimated to
place the first digit of the quotient. In which
place is the first digit of the quotient?

Answers

Answer:

The hundreds place

Step-by-step explanation:

143, first digit is , 1 is in the hundreds place

Which direction is XYZ?

Answers

The directions of XYZ in graph are left and right, top and bottom and outward from the screen respectively.

The term graph is known as a pictorial representation or a diagram that represents data or values in an organized manner.

Here we have to find the directions of XYZ on the graph.

Here we have know that X-Y-Z matrix is a three-dimensional structure whereby the x-axis and y-axis denote the first two dimensions and the z-axis is the third dimension.

And then in a graphic image, then the x denotes width, y denotes height and the z represents depth.

The directions of the x axis is in the plane of the screen and is positive toward the right and negative toward the left. Where as the directions of the y axis is in the plane of the screen and is positive toward the top and negative toward the bottom.

Finally the directions of the z axis is perpendicular to the screen or keyboard, and is positive extending outward from the screen.

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b.94 inches?
2. At a hardware store, a tool set normally costs $80. During a sale this week, the toc
set costs $12 less than usual. What percentage of the usual price is the savings?
Explain or show your reasoning.

Answers

Answer:

12%

Step-by-step explanation:

15%

80-12=68

68/80= .85 so you’re paying 85% of the original which means you are saving 15%.

80*.15=12 which is the amount that was taken off

If $3x 7\equiv 2\pmod{16}$, then $2x 11$ is congruent $\pmod{16}$ to what integer between $0$ and $15$, inclusive

Answers

2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.

If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.

To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.

First, we can solve for x in the given equation:

3x 7 is congruent to 2 mod 16

3x is congruent to 2 mod 16

x is congruent to 6 mod 16

Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:

2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16

So the solution is that 2x 11 is congruent to 13 mod 16.

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The nth term of a sequence is 3n squared -1. The nth term of a different sequence is 30 - n squared. Find the only number that is in both of these sequences

Answers

The number that belongs to both sequences is 26.

The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."

By changing the term number's value, we can create a series that uses the nth term (n).

To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.

We have two sequences, let's call one as A and the other as B.

The n-th term of sequence A is written as:

aₙ = 3*n^2 - 1

the nth term of sequence B is written as:

bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

Then we will heave:

3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

3*n^2 = 31 - x^2

n^2 = (31 - x^2)/3

n = √( (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √( (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √( (31 - 2^2)/3) = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

Therefore, The number that belongs to both sequences is 26.

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nter (A,B,C,D)in order below if $A$, $B$, $C$, and $D$ are the coefficients of the partial fractions expansion of $$12\cdot\frac{x^3 4}{(x^2-1)(x^2 3x 2)}

Answers

The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.

A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.

The denominator is

(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)

(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)

So by partial fraction expansion

(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))

(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²

A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4

(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4

Thus from coefficients of x³, x², x and 1,

A + B + C = 1

2A + 4B + C + D = 0

-A + 5B - C + D = 0

-2A + 2B - C - 2D = 4

Solving

A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2

--The question is not clear, the question is given below--

"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of

[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex] "

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What is the standard from of the equation for the line of y=1/4x+4. (Please help meeee)

Answers

Answer: - x + 4y = 16

1. Move your ax term to the other side by subtracting it on both sides.
y - 1/4x = 4

2. Now multiply everything by 4 to get rid of the fraction.
4y - x = 16

3. Reorder the terms into standard form
- x + 4y = 16

Find the length of the third side. If necessary round to the nearest tenth

Answers

The side lengths of a right-angle triangle can be calculated using the Pythagorean Theorem. Which states that the square of the hypotenuse is equal to the sum of squares of the other sides in the triangle.

[tex]a^2+b^2=c^2[/tex]

the hypotenuse is always the longest side of a triangle and is always the opposite side length to the right angle

rearranging the equation can help calculate the third side:

[tex]c^2-a^2=b^2[/tex]

[tex](5)^2-(4)^2=b^2[/tex]

[tex]25-16=b^2[/tex]

[tex]9=b^2[/tex]

[tex]\sqrt{9}=\sqrt{b^2}[/tex]

[tex]{ {{b_1=+3} \atop {b_2=-3}} \right.[/tex]

note: a length can never be negative so never take into account a negative answer

b = 3

A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the
base of the pole how long is the wire? Give your answer to two decimals.

Answers

A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the base of the pole 7.81 m long is the wire. This can be solved by using the concept of Pythagoras theorem.

What is Pythagoras theorem?

The widely accepted geometric principle known as the Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle).

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three designated sides.

Let, assume ΔABC is a right-angled triangle

where, AC = 6m be the pole.

AB = 5m is the length of a guy wire and is attached to stake B

By Pythagoras theorem,

BC² = AB² + AC²

or, BC² = (5)² + (6)²

or, BC² = 36 + 25

or, BC = √61 m

or, BC = 7.81 m

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Select all the correct answers.
Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.

60, 58, 64, 64, 68, 50, 57

On the eighth day, she drinks 82 ounces of water. Select all the true statements about the effect of the eighth day's amount on Joanna's daily amount distribution.

The interquartile range of the data increases when the eighth day's amount is included in the data.
The median amount of water is higher when the eighth day's amount is included in the data.
The interquartile range of the data decreases when the eighth day's amount is included in the data.
The median amount of water is the same with or without the inclusion of the eighth day's amount.
The average daily amount of water is the same with or without the inclusion of the eighth day's amount.

Answers

The interquartile range of the data decreases when the eighth day's amount is included in the data is true.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Joanna set a goal to drink more water daily.

The number of ounces of water she drank each of the last seven days is

60, 58, 64, 64, 68, 50, 57

On the eighth day, she drinks 82 ounces of water.

Raw data: [60,58,64,64,68,50,57,82],

Sorted data: [50,57,58,60,64,64,68,82]

Sample size = 8 (even)

mean = 62.875

median = (60+64)/2 = 62

1st quartile = (57+58)/2 = 57.5

3rd quartile = (64+68)/2 = 66

IQR = 66 - 57.5 = 8.5

Data without the eight day's measurement.

Raw data: [60,58,64,64,68,50,57]

Sorted data: [50,57,58,60,64,64,68]

Sample size = 7 (odd)

mean = 60.143

median = 60

1st quartile = 57

3rd quartile = 64

IQR = 64 -57 = 7

Hence, the interquartile range of the data decreases when the eighth day's amount is included in the data is true.

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Answer: It's just

The interquartile range of the data decreases when the eighth day's amount is included in the data.

Step-by-step explanation: The question asks you to select ALL correct answers, but there is only one correct answer.

BROO PLS SOMEONE HELP IM SO CONFUSED

The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31

Answers

The 30th term of the arithmetic sequence is 265

What is an arithmetic sequence in math?

Arithmetic sequences are those in which each term is increased by the addition or subtraction of a constant k. In contrast to a geometric sequence, where each term rises by being multiplied by or divided by a constant k,A series of numbers is considered to be an arithmetic progression or sequence if there is a constant difference between the terms. Consider the mathematical progression with a common difference of 2 in the numbers 5, 7, 9, 11, 13, and so on.An is equal to a1 + d(n - 1), where d is the common difference across terms in the series, and a1 is the first term in the sequence.

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words, [tex]a_{n}[/tex]= [tex]a_{1}[/tex]+ d ( n - 1 )

Arithmetic Sequence: d = 9

This is the formula of an arithmetic sequence.

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )

Substitute in the values of [tex]a_{1}[/tex] = 4 and d = 9

[tex]a_{n}[/tex]= 4 + 9 ( n - 1 )

[tex]a_{n}[/tex]= 4 + 9n - 9

[tex]a_{n}[/tex] = 9n - 5

.30th term = [tex]a_{n}[/tex] = [tex]a_{1}[/tex]+ d ( n - 1 )

= [tex]a_{30}[/tex]= 4 + 9 ( 30 -1 )

[tex]a_{30}[/tex]= 4 + 9 x 29

[tex]a_{30}[/tex]= 265

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Find the total surface area of this cuboid.
5 cm
4 cm
6 cm

Answers

Answer: 15cm2

Step-by-step explanation:

5cm+4cm+6cm=15cm2

I don’t know this question
help me

Answers

The number of groups of like terms is 3

What is an algebraic expression?

An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.

These algebraic expressions are also composed of mathematical operations, such as;

AdditionSubtractionDivisionBracketParenthesesMultiplication, etc

A term can be described a single variable, number or numbers and variables that are multiplied together.

From the information given, we have the terms;

3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰

The similar terms are;

3x¹³, 3x¹⁰, 3¹³

Hence, the number is 3

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Camille thinks that -(-4) has a positive value and Laura thinks -(-4) has a negative value. Who is correct?

Answers

camille, negative times a negative is a positive.

3x+2y=2 in slope intercept form!!!

Answers

Answer:

[tex] \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]

Step-by-step explanation:

Slope-intercept is in form of y = mx + b where m is slope and b is y-intercept. We simply solve for y in term of x and then we will obtain the slope-intercept form.

Given the linear equation:

[tex] \displaystyle{3x + 2y = 2}[/tex]

First, subtract both sides by 3x:

[tex] \displaystyle{3x + 2y - 3x= - 3x + 2} \\ \\ \displaystyle{2y = - 3x + 2}[/tex]

Then divide both sides by 2:

[tex] \displaystyle{ \dfrac{2y}{2} = \dfrac{ - 3x + 2}{2}} \\ \\ \displaystyle{ y = \dfrac{ - 3x + 2}{2}}[/tex]

Separate fractions (Simplify):

[tex] \displaystyle{ y= \dfrac{ - 3x}{2} + \dfrac{2}{2}} \\ \\ \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]

And we have finally converted the equation to slope-intercept form.

Before sending track and field athletes to the Olympics, the U. S. Holds a qualifying meet. The upper box plot shows the top 12 men's long jumpers at the U. S. Qualifying meet. The lower box plot shows the distances (in meters) achieved in the men's long jump at the 2012 Olympic games. Which pieces of information can be gathered from these box plots?

Answers

We require median, interquartile range, outliers, minimum and maximum value.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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We require median, interquartile range, outliers, and minimum and maximum values.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.