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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.

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Plz help me !!!!!!!!!!!
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Split the second term in 3a^2 - 8a + 4 into two terms

3a^2 - 2a - 6a + 4 = 0

Factor out common terms in the first two terms, then in the last two terms.

a(3a - 2) -2(3a - 2) = 0

Factor out the common term 3a - 2

(3a - 2)(a - 2) = 0

Solve for a;

a = 2/3,2

<u>Answer : B. (2/3,2)</u>

6 0
3 years ago
Factor completely and then place the factors in the proper location on the grid. 36x 2 + 60x + 25
Aleonysh [2.5K]
Since 36x² + 60x + 25 is the perfect square trinomial, we use this formula a² + 2ab + b² = (a + b)². Hence, the solution is (6x + 5)² 
4 0
3 years ago
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Making handcrafted pottery usually takes two major steps:wheel throwing and firing. The time of wheel throwing and thetime of fi
levacccp [35]

Answer:

a) P(R

And we can find this probability using the normal standard table or excel and we got:

P(z

b) P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)

And we can find this probability using the complement rule and the normal standard table or excel and we got:

P(z>2.774)=1-P(Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:

R \sim N(40+60 = 100,\sqrt{2^2 +3^2}= 3.606 s)  

Where \mu=65.5 and \sigma=2.6

We are interested on this probability

P(R

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{R-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(R

And we can find this probability using the normal standard table or excel and we got:

P(z

Part b

P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)

And we can find this probability using the complement rule and the normal standard table or excel and we got:

P(z>2.774)=1-P(Z

8 0
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aev [14]

Answer:

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Step-by-step explanation:

Simplify the following:

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Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:

(3 x - 2 x) + 12

3 x - 2 x = x:

Answer: x + 12

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just olya [345]
(5, 3) (-6, 3)
The slope is 0 Slope = m = (Y2<span> -Y</span>1<span>) </span>÷<span> (X</span>2<span> -X</span>1<span>) (Y2 -Y1)=0
SO, the distance is just the difference in the x values.
distance = 5 --6 = 11

</span>
7 0
3 years ago
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