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3 years ago

The following system of equations is _____.

1 answer:

3 0

The correct answer among the choices listed above is the second option. The following system of equations is equivalent. This is because when written in the same form, one equation will yield to the same equation as the other.

y = -1/3x +2/3

2x + 6y = 4
6y = 4 - 2x
y = 2/3 - 1/3x
y = -1/3x +2/3

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Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer

mars1129 [50]

Answer:

2, 2, 4, 6, 4

Step-by-step explanation:

Fundamental Theorem of Algebra states that 'An 'n' degree polynomial will have n number of real roots'.

1. The polynomial is given by $x(x^2-4)(x^2+16) = 0$

So, on simplifying we get that, $x(x+2)(x-2)(x^2+16)=0$ .

Since, degree of polynomial is 5, it will have 5 roots.

This gives us that the roots of the equation are x = 0, -2, 2, 4i and -4i

So, the number of complex roots are 2.

2. The polynomial is given by $(x^2+4)(x+5)^2 = 0$

Since, degree of polynomial is 4, it will have 4 roots.

Equating them both by zero, $(x^2+4)= 0$ and $(x+5)^2=0$ gives that the roots of the polynomial are x = 2i, -2i, -5, -5.

So, the number of complex roots are 2.

3. The polynomial is given by $x^6-4x^5-24x^2+10x-3=0$

Since, degree of polynomial is 6, it will have 6 roots.

On simplifying, we get that the real roots of the polynomial are x = -1.75 and x = 4.28.

So, the number of complex roots are 6-2 = 4.

4. The polynomial is given by $x^7+128=0$

Since, degree of polynomial is 7, it will have 7 roots.

On simplifying, we get that the only real root of the polynomial is x = -2.

So, the number of complex roots are 7-1 = 6.

5. The polynomial is given by $(x^3+9)(x^2-4)=0$

Since, degree of polynomial is 5, it will have 5 roots.

Simplifying the equation gives $(x+2)(x-2)(x+\sqrt[3]{9})(x^2-\sqrt[3]{9x}+9^{\frac{2}{3}})=0$

Equating each to 0, we get the real roots of the polynomial is $x=-3^{\frac{2}{3}}$

So, the number of complex roots are 5-1 = 4

6 0

3 years ago

Read 2 more answers

Abe ate 1/6 of a small pizza. Aisha ate 1/8 of a small pizza. Who ate more?

Papessa [141]

abe

Step-by-step explanation:

aisha ate more because aisha slice was cut into more pieces. then leaving her with the smallest peice and abe had less slices then leaving him with bigger slices so in conclusion abe ate more

6 0

3 years ago

Help please i will give brainlest

Anton [14]

Your answer is B. 3 13/24

Hoped this helped :)

Have a wonderful day-

8 0

2 years ago

Read 2 more answers

PLSS HELPP Probability statistics

Lisa [10]

So okay, in stats when there is probability that looks like p(fem/type b) it means what is the probability that they are female given they are type b, so it would be where they intersect. Therefore where they intersect on the table is 22 out of the total of 200 people so 1/10. Now that we know that probability let's look at the "or" one, when it says or it means it could be a female or a type b so we would include both totals of each:

97 females+70 type b= 167

now we divide that by the total amount of people so it simplifies down to a probability of 0.835.

Finally, looking at these 2 probability we can see that the "or" probability is far greater than the one previous discussed so it would be the last option if I remeber correctly!!

7 0

3 years ago

In the figure below, what is the length of MN?

Diano4ka-milaya [45]

There is no figure below.

6 0

3 years ago