Mathematics College

Given the following rectangles, identify all combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping. You can't cut any of the rectangles but you may use some of them multiple times. More than one answer may be correct; mark all that apply.

Rectangles you are given:

answer options:


two C rectangles, two D rectangles, and two B rectangles

one each of rectangles A, B, C, and D

one A rectangle and four B rectangles

three E rectangles and two B rectangles

one E rectangle, one C, one D, and three B rectangles

Given The Following Rectangles, Identify All Combinations Of Assembling These Rectangles For Which It

Answers

Answer 1

The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:

One each of rectangles A, B, C, and D.One A rectangle and four B rectangles.

What is a rectangle?

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.

Required

Which group forms a rectangle of

[tex]\text{Length}=15[/tex]

[tex]\text{Width}=11[/tex]

First, calculate the area of the big rectangle

[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]

[tex]\text{A}_{\text{Big}}=15\times11[/tex]

[tex]\text{A}_{\text{Big}}=165[/tex]

Next, calculate the area of each rectangle A to E.

[tex]\text{A}_{\text{A}}=11\times7[/tex]

[tex]\text{A}_{\text{A}}=77[/tex]

[tex]\text{A}_{\text{B}}=2\times11[/tex]

[tex]\text{A}_{\text{B}}=22[/tex]

[tex]\text{A}_{\text{C}}=6\times6[/tex]

[tex]\text{A}_{\text{C}}=36[/tex]

[tex]\text{A}_{\text{D}}=6\times5[/tex]

[tex]\text{A}_{\text{D}}=30[/tex]

[tex]\text{A}_{\text{E}}=13\times4[/tex]

[tex]\text{A}_{\text{E}}=52[/tex]

Then consider each option.

(a) 2C + 2D + 2B

[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]

(b) A + B + C + D

[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

(c) A + 4B

[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]

[tex]\text{A} + 4\text{B}=77+88[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

(d) 3E + 2B

[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]

[tex]3\text{E}+2\text{B}=156+44[/tex]

[tex]3\text{E}+2\text{B}=200[/tex]

(e) E + C + D + 3B

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]

Recall that:

[tex]\text{A}_{\text{Big}}=165[/tex]

Only options (b) and (c) match this value.

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

Hence, options (b) and (c) are correct.

To know more on rectangles, visit:

https://brainly.com/question/31891759

Related Questions

Is the expression quadratic 3x+5y-2

Answers

No, the expression 3x + 5y - 2200 is not a quadratic expression.

A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.

It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.

"3x + 5y - 2" is a linear expression, not a quadratic expression.

In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.

The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.

It is a first-degree polynomial, meaning that the highest power of the variable is 1.

Linear expressions often have a graph that is a straight line.

For more related questions on quadratic expression.:

https://brainly.com/question/10025464

#SPJ8

No. The expression, 3x + 5y - 2, is not quadratic.

What are quadratic expressions?

The expression "3x+5y-2" is a linear expression, not quadratic.

Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.

The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.

More on quadratic expressions can be found here: https://brainly.com/question/14680354

#SPJ1

0.059 and 0.01 which is greater?

Answers

0.059 is greater than 0.01

Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?

Answers

Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

Other Questions
jesse has three one gallon containers. The first one has (5)/(9 ) of a gallon of juice, the second has (1)/(9) gallon of juice and the third has (1)/(9) gallon of juice. How many gallons of juice does Jesse have Question 5 (1 point ) a ,x-intercept (s): 1y-intercept (s): 1&3 b ,x-intercept (s): 6y-intercept (s): 6&18 c ,x-intercept (s): 1 & 3y-intercept (s): 1 d ,x-intercept (s): 6 & 18y-intercept (s): - 18 Question 6 ( 1 point ) A Fraction denominator must not ever become 0. You can enforce this invariant through:class Fraction {. . .public:Fraction(int, int);Fraction get() const;Fraction set(int, int);};a) the implementation of the accessor memberb) the selection of data membersc) the implementation of the mutator memberd) by using the access modifier private in place of publice) the implementation of a destructor Use split function in python to create two list from list = "200 73.86 210 45.25 220 38.44". One list showing the whole number and the other the decimal amount.ex.whole = [200, 210, 220]decimal = [73.86, 45.25, 38.44] A B C D Rolf added 20 g of solute to 100 g of water and mixed the solution. Rolf added 10 g of solute to 100 g of water and mixed the solution. Rolf added 65 g of solute to 100g of water, mixed the solution, and then heated the solution. Rolf added 7 g of solute to 100 g of water, mixed the solution, and then heated the solution. Which solution is unsaturated? O Solution A O Solution B O Solution C Solution D The solute in solution A has a solubility of 37 g/100 g HO at 20C. The solute in solution B has a solubility of 10 g/100 g HO at 20C. The solute in solution C has a solubility of 32 g/100 g HO at 20C The solute in solution D has a solubility of 4 g/100 g HO at 20C. the center of the multicausation disease model is behavioral choices. true or false Identify one real-world problem, for example like this --> "It is difficult to recruit good wait staff who provide the level of customer service to which we have become accustomed." Then, analyze the problem space by answering some questions such as What are the reasons for these problems? Design a conceptual model for your addressed problem. The parent of a toddler comments that the child is not toilet trained. Which comment by the nurse is correct?A What are you doing to scare the child?B The child must have psychological problems.c Bowel control is usually achieved before bladder.*D Bowel and bladder control are achleved on average between 24-36 months A ______ is designed to correct a known bug or fix a known vulnerability in a piece of software.A) tapB) patchC) fix one study of ninth to twelfth graders found those who attended church regularly in one grade were more likely to have lower levels of abuse in the next grade. acknowledgment that only a small amount of time is actually under one's control and that most of one's time is taken up by others is known as the: what are cumulative and no cumulative, local, global and continuousemissions pollutants when produced, free catecholamines (NE and EPI) are short lived. They are best measured in the urine, though catecholamine metabolites are best measured in the serum True or false? chemistry the size of a companys tax bill is determined by the tax _______. multiple choice a)practice b)laws c)process d)economics e)code Circles h and i have the same radius. jk, a perpendicular bisector to hi, goes through l and is twice the length of hi. if hi acts as a bisector to jk, what type of triangle would hki be? in satirs communication roles, the _____ avoids conflict at the cost of his or her integrity. A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A)=P(B)=0.95,P(C)=0.99, and P(D)=0.91. Find the probability that the machine works properly. Round to the nearest ten-thousandth. A) 0.8131 B) 0.8935 C) 0.1869 D) 0.8559 You may need to use the appropriate appendix table or technology to answer this question. Fewer young people are driving. In year A, 62.9% of people under 20 years old who were eligible had a driver's license. Twenty years later in year B that percentage had dropped to 42.7%. Suppose these results are based on a random sample of 1,900 people under 20 years old who were eligible to have a driver's license in year A and an year B. (a) At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answer to four decimal places.) At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answers to four decimal places.) to (b) At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answer to four decimal places.) At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answers to four decimal places.) to (c) Is the margin of error the same in parts (a) and (b)? Why or why not? The margin of error in part (a) is -- Select-- V than the margin of error in part (b). This is because the sample proportion of eligible people under 20 years old whad a driver's license in year B is than the sample proportion of eligible people under 20 years old who had a driver's license in year A. This leads to a -- Select--- interval estimate in part (b). Draw a product positioning map for Chocolate bars and explainit.No plagiarism please, reply in own words. a yo-yo is constructed of three disks: two outer disks of mass m, radius r and thickness d, and an inner disk of mass m, radius r and thickness d. the yo-yo is suspended from the ceiling and then released with the string vertical. calculate the tension in the string as the yo-yo falls. note that when the center of the yo-yo moves down a distance y, the yo-yo turns through an angle y/r, which in turn means that the angular speed w is equal to vcm/4