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Free_Kalibri [48]
3 years ago
13

A rectangle has sides measuring (2x + 7) units and (5x + 9) units. Part A: What is the expression that represents the area of th

e rectangle? Show your work. (4 points) Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Mathematics
1 answer:
andrey2020 [161]3 years ago
3 0

Answer:

Part A:  

(2x+7)(5x+9)

=(2x+7)(5x+9)

=(2x)(5x)+(2x)(9)+(7)(5x)+(7)(9)

=10x2+18x+35x+63

=10x2+53x+63

A)

The formula for determining the area of a rectangle is given as

Area = length × width

Given that the length and width are (2x + 6) units and (5x + 3) units, the expression for the area is

(2x + 6)(5x + 3) = 10x² + 6x + 30x + 18

Area = 10x² + 36x + 18

B)

The degree is 2 because the highest power of the terms is 2. It is classified as a trinomial because it has 3 terms.

C) it is closed under multiplication. the exponents in the polynomials are whole numbers(2 and 1). The whole numbers are closed under addition, which means that the new exponents formed are also whole numbers. The exponents were whole numbers before multiplication and doesn't change after multiplication.

Step-by-step explanation:

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What is the approximate distance between points A and B?
Aleks04 [339]

Answer:

\displaystyle d \approx 7.62

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra II</u>

  • Distance Formula: \displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Find points from graph.</em>

Point A(1, 4)

Point B(-2, -3)

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance<em> d</em>

  1. Substitute in points [DF]:                    \displaystyle d = \sqrt{(-2-1)^2+(-3-4)^2}
  2. (Parenthesis) Subtract:                       \displaystyle d = \sqrt{(-3)^2+(-7)^2}
  3. [√Radical] Exponents:                        \displaystyle d = \sqrt{9+49}
  4. [√Radical] Add:                                   \displaystyle d = \sqrt{58}
  5. [√Radical] Evaluate:                           d = 7.61577
  6. Round:                                                 \displaystyle d \approx 7.62
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John made a small rectangular table for his workroom. If the sides of the table are 32 inches and 26 inches, what should the tab
matrenka [14]

Answer:

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Step-by-step explanation:

To find the diagonal of a rectangle we use the formula :

a^{2} + b^{2} = c^{2}

A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.

32^{2} + 26^{2} = c^{2}

1024 + 676 = c^{2}

1700 = c^{2}

The square root of 1700 is (rounded to the hundreth's place) = 41.23

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You can paint 75 square feet of a surface every 45 minutes. Determine how long it takes you to paint a wall with the given dimen
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Answer:

25.2 min

Step-by-step explanation:

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