What is reciprocal of the fraction in the equation 3/5(2x+8)=18?

Question 1 (Essay Worth 10 points)

stira [4]

Answer:

Question 1

Part A: The total length of sides 1, 2, and 3 is (8y² + 8y - 10)

Part B: The length of the fourth side is 22y³ + 2y² + 2y - 7

Part C: Yes the answers for Part A and Part B show that the polynomials are closed under addition and subtraction

Question 2

Part A: The expression of the area of the square is 4x² - 20x + 25

Part B: The degree and classification of the expression obtained in part A

are second degree and trinomial

Part C: The polynomials are closed under multiplication

Question 3

Part A: The function of the area of the circle of spilled oil is 49 πt²

Part B: The area of the spilled oil after 8 minutes is 9847.04 units²

Step-by-step explanation:

* Lets explain how to solve the problems

# Question 1

∵ The length of the three sides of a quadrilateral are

- Side 1: 4y + 2y² - 3

- Side 2: -4 + 2y² + 2y

- Side 3: 4y² - 3 + 2y

- The perimeter of the quadrilateral is 22y³ + 10y² + 10y − 17

* Part A:

- To find the total length of sides 1, 2, and 3 of the quadrilateral

add them

∴ s1 + s2 + s3 = (4y + 2y² - 3) + (-4 + 2y² + 2y) + (4y² - 3 + 2y)

- Collect the like terms

∴ S1 + S2 + S3 = (2y² + 2y² + 4y²) + (4y + 2y + 2y) + (-3 + -4 + -3)

∴ S1 + S2 + S3 = 8y² + 8y + (-10) = 8y² + 8y - 10

* The total length of sides 1, 2, and 3 is (8y² + 8y - 10)

* Part B:

∵ The perimeter of the quadrilateral is the sum of its 4 sides

∴ The length of its fourth side is the difference between its

perimeter and the sum of the other 3 sides

∵ The perimeter of the quadrilateral is 22y³ + 10y² + 10y − 17

∵ The sum of the three sides is (8y² + 8y - 10)

∴ The length of the 4th side = (22y³ + 10y² + 10y − 17) - (8y² + 8y - 10)

- Remember that (-)(+) = (-) and (-)(-) = (+)

∴ S4 = 22y³ + 10y² + 10y - 17 - 8y² - 8y + 10

- Collect the like terms

∴ S4 = (22y³) + (10y² - 8y²) + (10y - 8y) + (-17 + 10)

∴ S4 = 22y³ + 2y² + 2y + (-7) = 22y³ + 2y² + 2y - 7

* The length of the fourth side is 22y³ + 2y² + 2y - 7

* Part C:

- Polynomials will be closed under an operation if the operation

produces another polynomial

∵ In part A there are 3 polynomials add to each other and the answer

is also polynomial

∴ The polynomials are closed under addition

∵ In part B there are 2 polynomial one subtracted from the other and

the answer is also polynomial

∴ The polynomials are closed under subtraction

* Yes the answers for Part A and Part B show that the polynomials

are closed under addition and subtraction

# Question 2

∵ The side of a square measure (2x - 5) units

* Part A:

∵ The are of the square = S × S, where S is the length of its side

∵ S = 2x - 5

∴ The area of the square = (2x - 5) × (2x - 5)

- Multiply the two brackets using the foil method

∵ (2x - 5)(2x - 5) = (2x)(2x) + (2x)(-5) + (-5)(2x) + (-5)(-5)

∴ (2x - 5)(2x - 5) = 4x² + (-10x) + (-10x) + 25

- Add the like terms

∴ (2x - 5)(2x - 5) = 4x² + (-20x) + 25 = 4x² - 20x + 25

∴ The area of the square = 4x² - 20x + 25

* The expression of the area of the square is 4x² - 20x + 25

* Part B:

∵ The greatest power in the expression obtained in Part A is 2

∴ Its degree is second

∵ The expression obtained in part A has three terms

∴ The expression obtained in Part A is trinomial

* The degree and classification of the expression obtained in Part A

are second degree and trinomial

* Part C:

- Polynomials will be closed under an operation if the operation

produces another polynomial

∵ (2x - 5) is polynomial

∵ (4x² - 20x + 25) is polynomial

∴ The product of two polynomials give a polynomial

∴ The polynomials are closed under multiplication

# Question 3

∵ n(t) = 7t, where t represents time in minutes and n represents how

far the oil is spreading

∵ The area of the pattern can be expressed as A(n) = πn²

* Part A:

- To find the area of the circle of spilled oil as a function of time, then

find the composite function A[n(t)]

- That means replace n in A(n) by the function n(t)

∵ n(t) = 7t

∴ A[n(t)] = A(7t)

∵ A(n) = πn²

- Replace n by 7t

∴ A(7t) = π (7t)² = 49 πt²

∴ A[n(t)] = 49 πt²

* The function of the area of the circle of spilled oil is 49 πt²

* Part B:

∵ The area of the circle of spilled oil in t minutes = 49 πt²

- To find the area of the circle of spilled oil after 8 minutes substitute

t by 8

∴ Area of the spilled oil after 8 minutes = 49 π (8)²

∵ π = 3.14

∴ Area of the spilled oil after 8 minutes = 49(3.14)(64) = 9847.04

* The area of the spilled oil after 8 minutes is 9847.04 units²

8 0

3 years ago

A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers put an ad online

telo118 [61]

Answer:

Single Blind (option 1)

Step-by-step explanation:

The subjects don't know which cream they have but the technicians do.

If the subject knows which cream they have then they can be influenced by the placebo effect. If they don't know but the technicians do then the technicians will be able to look at unbiased responses from the subjects and tell if it works or not. If the technicians don't know which cream each subject has then they won't be able to learn anything from the responses. The technicians need to know which cream each subject has and the subjects can't know which cream they had.

4 0

3 years ago

Manuel bought a balloon (that is a perfect sphere) with a radius of 2 cm. He wanted his balloon to be bigger, so he blew 2 big b

USPshnik [31]

well, the balloon original was of radius = 2 = r, he then put it 1 cm extra twice, so it went up to 4 = r. The balloon original had a radius of 2 and then it went up to 4.

$\bf \textit{volume of a sphere, \underline{originally}}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r = 2 \end{cases}\implies V=\cfrac{4\pi (2)^3}{3}\implies V=\cfrac{32\pi }{3} \\\\\\ \textit{volume of a sphere, \underline{later on}}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r = 4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V=\cfrac{256\pi }{3} \\\\[-0.35em] ~\dotfill$

$\bf \cfrac{\textit{later on}}{\textit{originally}}\qquad \qquad \cfrac{\frac{256\pi }{3}}{~~ \frac{32\pi }{3}~~}\implies \cfrac{256\pi }{3}\cdot \cfrac{3}{32\pi }\implies 8$

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180-320/9 Answer me please

Svetradugi [14.3K]

144.4 recurring (dot on top of the 4 if your writing it out)

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25 minutes before 9 at night is written as _:__p.m.

Natali [406]

The answer is 8:35 pm

6 0

3 years ago