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Paul [167]
3 years ago
5

[Algebra 2] Find the quotient with the necessary restrictions.​

Mathematics
1 answer:
Tatiana [17]3 years ago
8 0

Answer:

The correct answer is:   3x² (4x - 1) / (x - 4) (x - 3) ∧ restriction x ≠ 3, x ≠ 4, x ≠ 0 and x ≠ 1/4

Step-by-step explanation:

Given:

((16x² - 8x + 1) / (x² - 7x + 12)) : ((20x² - 5x) / 15x³) =

dividing with one fraction is the same as multiplying with its reciprocal value

((16x² - 8x + 1) / (x² - 7x + 12)) · (15x³ / (20x² - 5x))

First we need to factorize both numerators and denominators

16x² - 8x + 1 = (4x - 1)²   This is square binomial

x² - 7x + 12 = x² - 4x - 3x + 12 = x (x - 4) - 3 (x - 4) = (x - 4) ( x - 3)

20x² - 5x = 5x (4x - 1)

(4x - 1)² / (x - 4) (x - 3) ·  15x³ / 5x (4x - 1)

The existence of this rational algebraic expression is possible only if it is:

x - 4 ≠ 0 and x - 3 ≠ 0 and x ≠ 0 and 4x - 1 ≠ 0  =>

x ≠ 4 and x ≠ 3 and x ≠ 0 and x ≠ 1/4  This is restriction

Finally we have:

3 x² (4x - 1) / (x - 4) (x - 3)

God with you!!!

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The food service manager conducted a random survey of students to determine their preference for new lunch menu items. Which of
gogolik [260]

Answer:

<u>Inferences A, B and C are correct.</u>

Complete question, data and inferences:

Item                         Number of students

Pizza                                   6

Salad Bar                           27

Pita Sandwiches                13

Burritos                             24

The food service manager conducted a random survey of students to determine their preference for new lunch menu items. Which of these inferences can be drawn from the manager’s data? Select all that apply.  

A. About twice as many students prefer salad bar as compared to pita sandwiches.  

B. About three-fourths of students prefer either salad bar or burritos.

C. About half as many students prefer pita sandwiches as compared to burritos.

D. Burritos are the most preferred item.

E. Twice as many students prefer pizza as compared to pita sandwiches.

Source:

Question that can be found at quizizz dot com. We can't copy and paste the exact URL because brainly will block it.

Step-by-step explanation:

A. About twice as many students prefer salad bar as compared to pita sandwiches.   True. Two times 13 is 26 and the number of students that prefer Salad Bar is 27.

B. About three-fourths of students prefer either salad bar or burritos.  True. 51 students are the 73% (about three-fourths of the students surveyed) of the total students surveyed, 70.

C. About half as many students prefer pita sandwiches as compared to burritos. True. 13 is almost the half of 24.

D. Burritos are the most preferred item.  False. Salad Bar is the most preferred item.

E. Twice as many students prefer pizza as compared to pita sandwiches.  False. It's the opposite actually; twice as many students prefer pita sandwiches as compared to pizza.

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Step-by-step explanation:

You need to find the total number of votes first. Just add 13 and 39 which would equal 52.

Then divide the number of people in favour by the total number of voters and multiply by a 100 to find the percentage.

39 + 13 = 52

39/52 = 0.75

0.75 x 100 = 75.0

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Step-by-step explanation:

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oel biked 9 miles east and then 12 miles north. If he biked back to his starting point using the most direct route, how many mil
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Answer:

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Step-by-step explanation:

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The dimensions of the two sides given are multiples of a classic Pythagorean Triple: 3, 4, 5.    3^{2} + 4^{2} = 5^{2}  

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