Mathematics, 10.10.2019 20:30 majj979

Written assignment
the perimeter of a rectangle must be greater than 70 cm, but the length cannot be greater than 30 cm and the width cannot be greater than 20 cm. represent the length with x and the width with y
a) write 3 constraints (inequalities) for this problem
b) graph all 3 constraints (edit the image or tell me where to plot)
c) what are two possible combinations for the length and width of the rectangle

Answers: 3

Show answers

Answers

Answer from: kingteron6166

Part a)

(x+y) 35

$x \leq 30$

$y \leq 20$

Part b) The graph in the attached figure

Part c) (30,20) and (25,15)

Step-by-step explanation:

Part a) write 3 constraints (inequalities) for this problem

Let

x -----> the length of the rectangle

y -----> the width of the rectangle

we know that

The perimeter of rectangle is

P=2(x+y)

$P 70\ cm$

2(x+y) 70 ---> the perimeter of a rectangle must be greater than 70 cm

Simplify

(x+y) 35 ----> inequality A

$x \leq 30$ ----> inequality B (the length cannot be greater than 30 cm)

$y \leq 20$ ----> inequality C (the width cannot be greater than 20 cm)

Part b) Graph all 3 constraints

we have

(x+y) 35

$x \leq 30$

$y \leq 20$

using a graphing tool

The solution is the triangular shaded area

see the attached figure

Part c) what are two possible combinations for the length and width of the rectangle

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy all the inequalities of the system (The ordered pair must lie on the shaded area of the graph)

First possible combination

point (30,20) ----> the point lie on the shaded area

x=30 cm, y=20 cm

Verify if the ordered pair satisfy the inequalities

Inequality A

(x+y) 35

(30+20) 35

(50) 35 ----> is true

The ordered pair satisfy the inequality A

Inequality B

$x \leq 30$

$30 \leq 30$ ---> is true

The ordered pair satisfy the inequality B

Inequality C

$y \leq 20$

$20 \leq 20$ ----> is true

The ordered pair satisfy the inequality C

The ordered pair satisfy all the inequalities of the system

therefore

The ordered pair (30,20) is a possible combinations for the length and width of the rectangle

Second possible combination

point (25,15) ----> the point lie on the shaded area

x=25 cm, y=15 cm

Verify if the ordered pair satisfy the inequalities

Inequality A

(x+y) 35

(25+15) 35

(40) 35 ----> is true

The ordered pair satisfy the inequality A

Inequality B

$x \leq 30$

$25 \leq 30$ ---> is true

The ordered pair satisfy the inequality B

Inequality C

$y \leq 20$

$15 \leq 20$ ----> is true

The ordered pair satisfy the inequality C

The ordered pair satisfy all the inequalities of the system

therefore

The ordered pair (25,15) is a possible combinations for the length and width of the rectangle

Written assignment the perimeter of a rectangle must be greater than 70 cm, but the length cannot b

Answer from: Quest

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

$\frac{48}{4}$ = 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

Answer from: Quest

what is the question?

step-by-step explanation:

Questions in other subjects:

Mathematics, 15.04.2020 03:13

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $48,000 and a standard deviation of $5,400. We randomly survey ten teachers...

Mathematics, 15.04.2020 03:13

A local maximum of the function f(x) occurs for which x-value? A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative...

Mathematics, 15.04.2020 03:13

A true/false test has 90 questions. Suppose a passing grade is 58 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessin...

Business, 15.04.2020 03:13

LaToya is buying con chips and soda. She has 4 bags of corn chips and 5 bottles of soda in her shopping cart. The marginal utility of the fourth bag of corn chips is 10, and the ma...

Social Studies, 15.04.2020 03:13

In your course you are instructed to design a fundraiser for a local school. As part of the assignment, you are to (1) write a letter about the fundraiser, (2) create a budget to t...

English, 15.04.2020 03:13

Ammu orphan who lives on the city streets 2. Das landowner’s merchant who informs Nathan that he must leave the land 3. Sacrabani servant of Muru...

Mathematics, 15.04.2020 03:13

Yesterday 37 1/2% of the customers in Mall Mart paid by credit card. If 582 customers paid by credit card ,how many customers were there in all...

Business, 15.04.2020 03:13

A Firm needs to replace most of its machinery in five years at a cost of $500,000. The company wishes to create a sinking fund to have this money available in five years. How much...

Social Studies, 15.04.2020 03:13

Regarding the length of questionnaires to be used in survey research, which of the following statements is most accurate? a. A relatively lengthy survey communicates your seriousne...

English, 15.04.2020 03:13

How does FDR make his audience feel united and ready to take action with his inaugural speech? A. By implying that Americans can improve on the pioneer's work B....

More questions: Mathematics Another questions

Answers

Other questions on the subject: Mathematics

Questions in other subjects: