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almond37 [142]
3 years ago
10

Find the complex zeros of

E%7B2%7D%20%20%2B%2059x%20-%2087" id="TexFormula1" title=" f(x) = {x}^{3 } - 13 {x}^{2} + 59x - 87" alt=" f(x) = {x}^{3 } - 13 {x}^{2} + 59x - 87" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
timama [110]3 years ago
6 0

f(x) = 0 \\\\\implies x^3-13x^2+59x -87 =0\\\\\implies x^3 -3x^2 -10x^2 +30x +29x - 87=0\\\\\implies x^2(x-3)  - 10x(x-3) + 29(x-3) =0\\\\\implies (x-3)(x^2 -10x +29) =0\\\\\implies x - 3 = 0 ~~ \text{or}~~x^2 -10x +29 = 0\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{-(-10) \pm \sqrt{(-10)^2 -4 \cdot 1 \cdot 29}}{2(1)}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm \sqrt{-16}}{2}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm 4i }{2}\\

\\\implies x =3~~ \text{ or} ~~ x =5 \pm 2i\\\\\text{Hence the complex roots are,}~ 5- 2i ~~ \text{and} ~~5 + 2i

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Step by step explanation
vodka [1.7K]

Answer: x = 4 and y = -3

Step-by-step explanation:

2x + 4y = -4

2x = -4 - 4y

x = -2 - 2y

Now that we have solved the first equation for x, we plug (-2 - 2y) into the other equation in place of x and then solve for y.

3(-2 -2y) + 5y = -3

-6 - 6y + 5y = -3

-y = 3

y = -3

Now that we know y, we plug it into the original equation and solve for x.

2x + 4(-3) = -4

2x + -12 = -4

2x = 8

x = 4

You can check the answer by plugging both x and y into either of the original equations.

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3 years ago
Which inverse operation should be performed first?: m = 7 = 32.
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The answer is multiplication
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marin [14]

Answer:

As given in the problem statement,it should be treated as quantitative Students in the northeastern United States was measured and it is a correct option B is correct option.

3 0
3 years ago
An automobile firm wants to purchase either machine A or machine B. The intial cost of machines A and B are $40,000 and $50,000,
Fynjy0 [20]

Answer:

C. $118,000 and $110,000, respectively.

Step-by-step explanation:

Please consider the complete question.

An automobile firm wants to purchase either machine A or machine B. The intial cost of machines A and B are $40,000 and $50,000, respectively. The power consumption per year of machines A and B are 120 MWh and 100 MWh, respectively. The power cost is $40/MWh. The estimated operating and maintenance cost over 10 years is $30,000 for machine A and $20,000 for machine B.

First of all, we will find the amount spent on power consumption for 10 years by each machine as:

\text{Machine A}=10\cdot 120(\$40)\\\text{Machine A}=\$48,000

\text{Machine B}=10\cdot \$100(\$40)\\\text{Machine A}=\$40,000

Now, we will find overall cost of machines A and B by adding initial cost, power consumption for 10 years and maintenance cost as:

\text{Overall cost of machine A}=\$40,000+\$48,000+\$30,000

\text{Overall cost of machine A}=\$118,000

\text{Overall cost of machine B}=\$50,000+\$40,000+\$20,000

\text{Overall cost of machine B}=\$110,000

Therefore, the overall cost of machines A and B are $118,000 and $110,000, respectively and option C is the correct choice.

6 0
3 years ago
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Veseljchak [2.6K]

Answer:

5

Step-by-step explanation:

3 - 2 = 1

3 + 2 =5

5 x 1 =5

3 0
3 years ago
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