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IRISSAK [1]
3 years ago
10

How to get x when x^3-x^2+x-1=0?

Mathematics
1 answer:
Art [367]3 years ago
6 0

Answer:

x = 1 or x = ± i

Step-by-step explanation:

Note the sum of the coefficients

1 - 1 + 1 - 1 = 0

This indicates that x = 1 is a root, thus (x - 1) is a factor

Using long division or synthetic division, then

x³ - x² + x - 1 = (x - 1)(x² + 1), thus

(x - 1)(x² + 1) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x² + 1 = 0 ⇒ x² = - 1 ⇒ x = ± \sqrt{-1} = ± i

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Time has a total of $28 after spending half of his weekly earnings on a video game and earning $10 additional dollars for mowing
Korolek [52]

Given:

Time has a total of $28 after spending half of his weekly earnings on a video game and earning $10 additional dollars for mowing the lawn.

To find:

Weekly earnings at his part time job.

Solution:

Let x be the weekly earning.

He spend half of his weekly earning, i.e., \dfrac{x}{2}

He earns $10 additional dollars for mowing the lawn.

According to the question,

\dfrac{x}{2}+10=28

\dfrac{x}{2}=28-10

\dfrac{x}{2}=18

Multiply both sides by 2.

x=36

Therefore, his weekly earnings is $36.

5 0
3 years ago
Cindy plans to shop for her school supplies and wants to know how much money she would need to spend. from her friend she knows
vlabodo [156]

Let the cost of 1 notebook be x and the cost of 1 binder be y.

4 notebooks and 3 binders would cost 23.5

Therefore, 4x + 3y = 23.5     (1)

7 notebooks and 6 binders would cost 44.5

Therefore, 7x + 6y = 44.5     (2)

Multiply the first equation by 2.

8x + 6y = 47     (3)

(3) - (2) gives

x = 2.5

Substitute the value of x in (1), we get,

4(2.5) + 3y = 23.5

10 + 3y = 23.5

3y = 23.5 - 10

3y = 13.5

y = 13.5/3

y = 4.5

Hence, cost of 5 notebooks and 3 binders is:

5x + 3y = 5(2.5) + 3(4.5)

           = 12.5 + 13.5

           = 26

Hence, cost of 5 notebooks and 3 binders is $26.

4 0
3 years ago
Assume that random guesses are made for nine multiple choice questions on an SAT​ test, so that there are nequals9 ​trials, each
Marina86 [1]

Answer:  Find the probability that the number x of correct answers is fewer than 4 = 0.6087

Step-by-step explanation: Please find the attached files for the solution

6 0
3 years ago
In a survey of first graders, their mean height was 51.6 inches with a standard deviation of 3.6 inches. Assuming the heights ar
ki77a [65]

Answer:

Step-by-step explanation:

In a survey of first graders, their mean height was 51.6 inches with a standard deviation of 3.6 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?

54.03 inches

48.57 inches

48.00 inches

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6 0
2 years ago
Simplify the expression:<br> 2a+4b=9c
fomenos

Answer:

a=\frac{9c}{2}-b

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

4 0
2 years ago
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