The perimeter of a rectangle is 66cm.
Its longest side has a length of 17cm.
State the length of the shortest side.

Answers

Answer 1

[tex]{ \red{\boxed{ \tt{Step-by-step-explaination}}}}[/tex]

Perimeter of a rectangle : [tex]{ \purple{ \tt{2(l+b)}}}[/tex]

length = [tex]{ \red{ \tt{17cm}}}[/tex]

breadth= [tex]{ \red{ \tt{?}}}[/tex]

now,

according to the rule.

perimeter = 2(l+b)

66 = 2(17+b)

66 = 34 + 2b

66 - 34 = 2b

32 = 2b

32/2 = b

16 cm = b

hence b = [tex]{ \pink{ \sf{16cm}}}[/tex]


Related Questions

Algebraic fractions which option is correct

Answers

Answer:

A

Step-by-step explanation:

because to solve this question the division would change into multiplication and the second fraction would be converted upside down

Which equation represents how to determine the speed of an object?

Answers

The equation that the speed of an object is speed = distance/time

How to determine the equation of an object

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

Parameter = Object

Argument = Speed

By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object

Mathematically, this can be represented as

Speed = Distance : Time

Express as fraction

Speed = Distance/Time

Hence, the equation is Speed = Distance/Time

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there are 5 children on your guest list and 40 people in total. what percentage of the people are children?

Answers

Answer: 12.5%

Step-by-step explanation:

5/40

0.125 x 100

12.5%

Answer:

2 children I believe so

Step-by-step explanation:

because you take 40%×5 and u will get 2

What is the y-intercept of this line?​

Answers

Answer: b=13

Step-by-step explanation:

This equation is in point-intercept form:  y = mx + b

slope = m = 4/3

y-intercept = b = 13

A large pizza at palanzio pizzeria cot $6. 80 plu $. 90 for each topping. The cot of a large pizza at guido' pizza i $7. 30 plu $. 65 for eachtopping. How many topping need ti be added ti a large pizza from palanziod pizzeria and guido' pizza in order for the pizza to cot the ane not including tax

Answers

2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.

Let x be the number of toppings to be added to each pizza and y be the total cost of pizza.

A large pizza at Palanxio's Pizzeria cot $6. 80 plu $. 90 for each topping.

So, we get an equation,

y = 6.80 + 0.90x

The cot of a large pizza at Guido's Pizza i $7. 30 plu $. 65 for eachtopping.

So, we get an equation,

y = 7.30 + 0.65x

 We need to find the number of toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.

Now let's equate the costs of both pizzas and solve for x.

6.80 + 0.90x = 7.30 + 0.65x

0.25x = 0.50

x = 2

Therefore, 2 toppings to be added to each pizza

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A hospital is going to be built in the land of the shape of a rhomus having its
diagonals 250 m and 480 m respectively in a mountainous district of Nepal. Find
the area covered by the hospital in Ropani. (1 Ropani = 508.72 m²).

Answers

Answer:

117.94 Ropani

Step-by-step explanation:

Area Of Rhombus=½×d1×d2

=½×480×250

=60,000m²

1Ropani=508.72 {As Given}

60,000m²=(60,000÷508.72)Ropani

=117.94 Ropani

Answer:

60000 m^2

117.943 ropani

Step-by-step explanation:

the area of rhombus = 250 × 480 ÷2=60000 m^2

60000 m^2 = 117.943 ropani



Show the work please! Thanks!!

Answers

Simplifying

2x + 5y = 2

Solving

2x + 5y = 2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5y' to each side of the equation.

2x + 5y + -5y = 2 + -5y

Combine like terms: 5y + -5y = 0

2x + 0 = 2 + -5y

2x = 2 + -5y

Divide each side by '2'.

x = 1 + -2.5y

Simplifying

x = 1 + -2.5y

Simplifying

5X + 10y = 17

Solving

5X + 10y = 17

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-10y' to each side of the equation.

5X + 10y + -10y = 17 + -10y

Combine like terms: 10y + -10y = 0

5X + 0 = 17 + -10y

5X = 17 + -10y

Divide each side by '5'.

X = 3.4 + -2y

Simplifying

X = 3.4 + -2y

three solutions of the equation y= -2x

Answers

Answer:

three solutions of the equation:

y = -2x - 1

=>

1) (0, -1)

2) (1, -3)

3) ( -1, 1)

Step-by-step explanation:

Olivia want to have a 90 average in algebra, where tet count for 55%, quizze count for 30ge % and homework count for 15%. If he ha a 92 tet average and 100% HW average, what mut her quiz average be? Let x = the average of the

Answers

In order to score 90 average in algebra her quiz average should be  82%.

It involves calculating the result of multiplying a number of quantities by their sum, then dividing the result by the total number of quantities.

Given,

She has a test grade of 55%, a quiz grade of 30%, and a homework grade of 15%.

If she achieved a score of 92% on the test

Make x the number of tests,

x = (90 - (0.55(92) + 0.15(100)))/0.30

x = 82

To receive a 90 in math, Olivia needs to have a quiz average of 82.

One of the oldest subfields of mathematics, algebra covers number theory, geometry, and analysis. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

Algebra covers a wide range of topics, from the study of abstractions to the solution of simple equations.

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Determine the equation of the parabola with vertex (7,4) and a directrix y=10.

Answers

The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application",

What is the parabola?pa·​rab·​o·​la pə-ˈrab-ə-lə : a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface : a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. : something that is bowl-shaped.This form is called the standard form of a quadratic function. The graph of the quadratic function is a U-shaped curve is called a parabola. The graph of the equation y=x2, shown below, is a parabola.The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola.

The equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .

It is given to us that -

The vertex of the parabola = (-8,5)

The directrix of the parabola is y = -3

We have to find the equation of the parabola with the given vertex and directrix.

We know that any point on a given parabola represented as () is equidistant from the directrix and the focus.

So, the equation for the point can be represented as

[tex][y-(-3)]=\sqrt{([x-(-8} ]^{2} +(y-5)^{2}[/tex]

[tex](y+3)^2} =(x+8)^{2} +(y-5)^{2} \\=y^{2}+9+2*y*3=(x+8)^{2} +y^{2}+25-2*y*(-5)=6y-10y=(x+8)^{2} +16=-4y=(xx+8)^{2} +16=y=\frac{-1}{4} (x+8)^{2}+4[/tex]

Thus, the equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .[tex]=y=\frac{-1}{4} (x+8)^{2} +4[/tex]

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Using the unit circle, on what interval is the cosine function increasing? (0, startfraction pi over 2 endfraction) (0, pi) (startfraction pi over 2 endfraction, startfraction 3 pi over 2 endfraction) (pi, 2 pi)

Answers

The interval where the cosine function is increasing is (π, 2π).

Finding the value of the cosine function in different intervals:

The cosine function for the interval (0, π/2) gives

cos(x) = cos(0) = 1

cos(x) = cos(π/2) = 0

So, the value of the function is decreasing in this interval.

Then, for the interval (0, π), it gives

cos(0) = 1; cos(π) = -1

So, the value of the cosine function is decreasing in this interval.

Then, for the interval (π/2, 3π/2), it gives

cos(π/2) = 0

cos(π) = -1

cos(3π/2) = 0

So, the value of the function decreases up to x = π and then increases up to the same value as before i.e., cos(π/2) = cos(3π/2).

Then, for the interval (π, 2π), the cosine function gives

cos(π) = -1

cos(2π) = 1

Thus, the cosine function in this interval increase from -1 to 1.

Therefore, in the interval (π, 2π), the cosine function is increasing.

This is explained by using a unit circle below:

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Answer:

D

Step-by-step explanation:

got it right

. if you start with 1/4, you can create an entire class of fractions equivalent to 1/4 like the one above, by multiplying 1/4 by different forms of what number?

Answers

If you start with 1/4, you can create an entire class of fractions equivalent to 1/4 by multiplying 1/4 by different forms of the number 1.

What are fractions?

The connection between two numbers, known as the numerator and the denominator, is expressed mathematically as fractions. The number of pieces is represented by the numerator, while the total number of components is represented by the denominator. For instance, if a pizza is cut into 8 slices and someone eats 3 of them, the fraction corresponding to the quantity consumed would be 3/8.

Diverse mathematical ideas, including division, ratios, and proportions, can be represented using fractions. They can also be used to represent decimal and percentage values, with the decimal point placed to the right of the numerator and the number of decimal places represented by the denominator.

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Solve each system by elimination: x+5y=4 3x-7y=-10

Answers

Answer: x= -1  y= 1

Step-by-step explanation: Times  -3 to get the same x

-3x - 15y = -12

3x - 7y = -10

      -22y = -22

            y= 1

Then put 1 back in for letter y and you get x= - 1

A shopper at a clearance sale is pleased to discover some lamps on sale for $9 each. The original price tags read $30. What percentage is the discount?

Answers

The answer is 70% and ypur saved $21

Answer: 70% of a discount

Step-by-step explanation:

for every 8chin ups Melanie can do Theresa can do 5. If Melanie did 48 chin ups, how many fewer did Theresa do

Answers

Answer: Theresa did 18 fewer chin-ups.

Step-by-step explanation:

Melanie 8,16,24,32,40,48

Theresa 5,10,15,20,25,30

48-30=18

1/2 of a 360
circle in degrees

Answers

Answer:

Step-by-step explanation:

180 because if you add 180 + 180 = 360

Hillary is using the figure shown below to prove Pythagorean Theorem using triangle similarity: In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC. The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC. Which of these could be a step to prove that BC2 = AB2 + AC2? (6 points) By the addition property of equality, AC2 plus AD2 = AB multiplied by DC plus AD2. By the addition property of equality, AC2 plus AD2 = BC multiplied by DC plus AD2. By the addition property of equality, AC2 plus AB2 = AB multiplied by DC plus AB2. By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.

Answers

Answer: By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.

Are any of these numbers linear expressions? 5x+3, 8xy, 14, or 3x^2​

Answers

Answer: 5x+3 is a linear expression

Step-by-step explanation:

The linear expression is y=mx+b

5x +3 has a slope and y-intercept, so it is a linear expression!

8xy is not because it is just a variable

3x^2 is not because it has ^2

Roger is moving 40 1/2pounds of bricks for a landscaping project. He moves 7 1/3 pounds of bricks in each load, then takes a short break. Which equation will help you solve to find out how many whole loads of bricks, b, Roger will move?

Answers

The equation to find how many loads of bricks that Roger move will be 44x=243.

What does linear equation mean?

A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.

This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."

In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.

Given,

Total amount of bricks load carried by Roger=40 1/2pounds

=81/2 pounds

Per each load --- 7 1/3pounds

1 load --------- 22/3 pounds

x   -----81/2 pounds

(81/2)(3/22)=x

243=44x

44x=243

Therefore, the equation to find how many loads of bricks that Roger move will be 44x=243.

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1/2 - 1/7 =
3/5 - 1/2

Answers

Answer:

1/2 - 1/7 = 5/14

3/5 - 1/2 = 1/10

Step-by-step explanation:

Find the measure of angle f given the information below.


A= 122 degrees
E=48 degrees the image is below!!

Answers

Answer:

74

Step-by-step explanation:

if a is 122 b is 58

b is congruent to g to g=58

58+48=106

180-106=f

180-106=74

choose the best graph to match the given expression.
F(x)= [x+1]

Answers

Answer:

Step-by-step explanation:

I don't see a graph from which to choose.  Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?

The graph of functions

(F(x) = (x+1), and

(F(x) = |x+1| are both attached.

Write a rule for the n th term of the sequence. Then find a_{20}

$51,48,45,42,...$

Answers

The rule for the nth term of arithmetic sequence is a + (n - 1)d.

What is the nth term of arithmetic sequence?The difference between consecutive terms in an arithmetic sequence is always the same.An arithmetic sequence's nth term is given by a = a + (n - 1)d. The number d is known as the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it can be found by subtracting any two terms a and an+1.

Here also,

We use the definition for the nth term of an arithmetic sequence:

an = a1 + (n - 1) d

Here first term (a1) = 51

common difference (d) = a2 - a1

                                      = 48 - 51

                                      = -3

We have to find 20th term,

a[20] = a1 + (20 - 1) d

         = 51 + 19 x -3

         = 51 - 57

         = - 6

Therefore 20th term of the sequence 51,48,45,42,... is -6.

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Harmony pays $64.00 per month for a base cable package and an additional amount for on-demand programming. Last month, Harmony received a $67.36 cable bill.

$64.00 + x = $67.36

Ignoring sales tax and additional fees, how much did she spend for on-demand programming?
A) $3.36
B) $6.36
C) $70.72
D.) $131.36

Answers

Should be A!!??!!????!!

Jimmy, Johny, and Jolly worked part-time on the weekend to earn some extra money. Three of them together earned $57. If Johny earned twice as much as Jolly did and Jimmy earned $3 less than Johny did, how much did Jimmy earn?

Answers

On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30  =4.8 and Johnny = 2x=34.8

What is a linear equation?

A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".

Take Jolly's expenditure as x.

Jimmy would have spent twice as much as Jolly.

Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.

Total amount spent: $57

Therefore,

[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]

x = 87/5

x= 17.4

Now take is that - X= 17.4.

Jolly is that -  x= $17.4

Jimmy is that - =4.8

Johnny is that = =34.8

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The rate of change is how a quantity is changing with respect to a change in another quantity.
True false question.
True
False

Answers

Answer: True

Step-by-step explanation:

The rate of change or the slope is the changes to another quantity with a constant.

power 121.three consecutive prime numbers, each less than $100$, have a sum that is a multiple of $5$. what is the greatest possible sum?

Answers

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

We have,

To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Check each combination:

(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)

(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)

(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)

(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)

(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)

(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)

(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)

(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)

(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)

(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)

(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)

(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)

(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)

(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)

(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)

(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)

(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)

(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)

(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)

(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)

(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)

(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)

(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)

Thus,

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

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The angles of a triangle are 44 degrees, 110 degrees, and 26 degrees. Classify the triangle

Answers

The measure of angles form an scalene triangle.

What is the angle sum property?

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

An angle requires two straight line, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle.

We are given that the angles of a triangle are 44 degrees, 110 degrees, and 26 degrees.

Since we know that angle sum property of a triangle;

44 + 110 + 26

180

Therefore, the measure of angles form an scalene triangle.

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At a football stadium, 25% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was the total number of people at the stadium?

Answers

Answer:

40 people

Step-by-step explanation:

25% = 10

50% = 20

100% = 40

Consider the system of equations

5x+3y=30

−5x−2y=−25

Part A: Solve the system. Show your work.


Part B: Use the solution to your equation to find the value of x – y. Show your work.

x−y =

Answers

The solution for the system of equations is the point (3, 5), and the difference x - y gives:

x - y = -2

How to solve the system of equations?

Here we have the following system of equations:

5x + 3y = 30

-5x - 2y = -25

Notice that in the two equations we have the "5x", but in one case is positive and in the other negative, then we can just add them so we get:

(5x + 3y) + (-5x - 2y) = 30 - 25

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

0 + y = 5

y = 5

So we found the value of y, by evaluating the second linear equation in y = 5 we will get:

-5*x - 2*5 = - 25

-5x = -25 + 2*5

-5x = -25 + 10

-5x = -15

x = -15/-5 = 3

So y = 5 and x = 3, the difference x - y gives:

3 - 5 = -2

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