MATHEMATICS MIDDLE SCHOOL

A painter starts with a blank 24-inch by 12-inch piece of rice paper. The painter wants to leave a uniform border x inches wide along the outer edges so that the painting can be framed.a. Write a polynomial in standard form that represents the area of paper that can be painted.
b. What is the area of the paper that can be painted when the margin is 2 inches wide?

Answers

Answer 1

Answer:

Answer:

a. A = x² - 36x + 288

b. If x = 2; A = 220 in²

Step-by-step explanation:

a.

In this scenario, 'x' represents the width of the border. A "uniform border" means that the border has the same width all around.

The area of the paper that can be painted does not include the border. Since the border is on the original rice paper (not added to it), you subtract 'x' from each side of the rice paper.

The area of a rectangle is A = lw (Area is length times width). Each length and width is reduced by 'x'.

If the original rice paper's area is: 24 X 12, then,

the Area that can be painted is:

A = (24 - x) (12 - x)

A polynomial in standard form means the most expanded version of an expression, ordering the terms (numbers) from greatest to least degree. (The degree of a term is the value of its exponent).

Expand the expression. Multiply the numbers from each bracket in the order FOIL (first, outside, inside last):

A = (24 - x) (12 - x)

= 288 - 24x - 12x + x² Collect like terms (-24x - 12x = -36x)

= 288 - 36x + x² Rearrange ordering greatest to least exponent value

= x² - 36x + 288 Standard form polynomial

b.

The width of the margin is the same thing as the width of the border. Since 'x' is the width of the border,

x = 2

Using either the expanded or factored equation for area of that can be painted, substitute 'x' for 2.

I will use the factored form.

A = (24 - x) (12 - x) Substitute x for 2

= (24 - 2) (12 - 2) Solve inside each bracket first by subtracting

= (22) (10) Multiply

= 220 Area that can be painted

Remember to include the units: 220 in²

Therefore if the margin is 2 inches wide, then the area that can be painted in 220 square inches.

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Answers

Surface Area formula of a cylinder:
S.A = 2 × Area of base + Perimeter of base × Height of prism
= 2 $\pi$ r² + 2 $\pi$ rh
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What is the coefficient in this expression?
17 + 5a

Answers

the answer is the a next to the 5

The coefficient of the expression is 5 because a coefficient is the number multiplied by the variable.

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Answers

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Select all of the given values of m that make the inequality 4z 17 true.4

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Answers

i think it’s 4.25 :)

The TOTAL NUMBER of students who chose the ZOO is how many times as great as the TOTAL NUMBER of students who chose the PLANETARIUM?CLASS Students who chose the Zoo Students who chose the Museum Students who chose the Planetarium CLASSStudents who chose the Zoo

Students who chose the Museum

Students who chose the Planetarium

A

10

9

8

B

8

11

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C

12

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D

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Answers

Okay I just do part A as an example.

The number of students who chose the zoo, students who chose the museum, and students who chose the planetarium is 10, 9, and 8 respectively.

10 students /8 students= 1.25.

The number of students who chose the zoo is 1.25 times as many as the students who chose the planetarium.

We do the same thing for B, C, and D.

Hope this helps~

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