1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nikdorinn [45]
3 years ago
13

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?
Mathematics
1 answer:
ddd [48]3 years ago
5 0

Answer:

a. A = x² - 36x + 288

b. If x = 2; A = 220 in²

Step-by-step explanation:

<h2>a.</h2>

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). <u>Each length and width is reduced by 'x'.</u>

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

<h2>b.</h2>

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.

You might be interested in
What are the benefits if you pay off all your high-interest debt such as credit cards and store cards?
jekas [21]

Answer:  The law required that 100% of your payment go toward your most expensive debt. ... The excess payment is everything you pay above the minimum. The Card Act requires issuers to apply this part of your payment to the highest-interest balance first.

6 0
3 years ago
Mary eats her dinner off a plate that has a radius of 4 inches. What is the exact area of the plate
Alik [6]
I cant get an exact area because pi is a never ending number but i got about 50.27 in 
5 0
3 years ago
Read 2 more answers
Write the equation for an absolute value function with the following transformations:
Kipish [7]

Answer:

j(x) = 5 |x+9|-23

Step-by-step explanation:

f(x) = |x|

translate left 9 units

y = f(x + C)  C > 0 moves it left

g(x) = |x+9|

translate down 23 units

y = f(x) + C C < 0 moves it down

h(x)= |x+9|-23

stretch by a factor of 5  

y = Cf(x)   C > 1 stretches it in the y-direction

j(x) = 5 |x+9|-23

5 0
3 years ago
I need help im going to post later a 3 more times 10 points
SashulF [63]

Answer:

X=9  Y= 3

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Find f ′(x) for f(x) = sin (3x2).
Ne4ueva [31]

Answer:

  f'(x) = cos(3x^2)(6x)

Step-by-step explanation:

(d/dx)(sin u) = cos(u)·du/dx . . . . . chain rule

For f(x) = sin(3x^2), this means ...

  f'(x) = cos(3x^2)(6x)

3 0
3 years ago
Other questions:
  • A air freshener used 3 3/4 milliliter of perfume. If Wendy wanted to make 3 air fresheners, how many milliliter a of perfume wou
    8·1 answer
  • Solve 5(r—1)=2(r-4)-6 step by step
    6·1 answer
  • Leah's house has a media room with a large flat-screen television to watch movies. The media room television has a width of 8 fe
    12·1 answer
  • 5 types of kitchen accidents and how to prevent them​
    13·2 answers
  • Follow the rule to find the next three numbers in the pattern describe the pattern using the terms even and odd 1,6,11
    14·1 answer
  • A piece of candy weighs 30 grams. All of the candy in a bag weighs 750 grams. How many pieces of candy are in the bag? A) 15 B)
    5·2 answers
  • Find the equation of the line passing through the points (7, 16) and (2, −4). Then state the slope and coordinates of the x- and
    8·1 answer
  • Keep gettin those wrong. Please help!!!
    5·1 answer
  • Please help asap i do not understand this i just need an answer WILL GIVE BRAINLIEST
    13·2 answers
  • A) side angle side<br> b) side side side <br> c) angle side angle<br> d) not congruent
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!