Which numbers will produce a rational number when multiplied by 1/5

1 answer:

3 0

A rational number times a rational number=rational numberan irrational number times a rational number=irrational number
remember, a rational number is a number that can be written as a/b where a and b are integers and b≠0

A is irrational because the pattern doesn't repeatb is irrational because it's a crazy square rootC is irrationalD is not irrational, it is a fraction

answer is D

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How many base pieces 8 1/4 inches long and 8 1/4 inches wide can Mr. Penny cut from a wooden plank 4 1/8 feet long and 4 1/8 fee

podryga [215]

Answer:

36 pieces

Step-by-step explanation:

4 1/8 ft x 4 1/8 ft = 49.5 in x 49.5 in = 2450.25 in^2

8.25 in x 8.25 in = 68.06 in^2

2450.25/68.06 = 36 pieces

checking for scrap loss:

49.5/8.25 = 6

so no scrap loss

3 0

3 years ago

which of the following expresses the possible number of positive real solutions for the polynomial equation shown below

Nookie1986 [14]

The polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.

In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.

To find the solutions, we do as follows:

x³ - 4x² - 7x + 28 = 0,

or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},

or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},

or, (x - 4)(x² - 7) = 0 {Grouping},

or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: $a^2 - b^2 = (a+b)(a-b)$ }.

By the zero-product rule, the solutions are:

x - 4 = 0, or, x = 4,

x + √7 = 0, or, x = -√7,

x - √7 = 0, or, x = √7.

Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.

Thus, the polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.

Learn more about polynomials at

brainly.com/question/1550365

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The complete question is:

"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?

x³-4x²-7x+28=0

a. two or zero

b. three or one

c. one

d. two"

5 0

2 years ago