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Burka [1]
3 years ago
5

Pls giving brainlyist and 25 points

Mathematics
2 answers:
ZanzabumX [31]3 years ago
7 0

These angles are called vertical angles, and they are congruent. Therefore, the expression and the 55 degree angle are equal to each other.

5x + 15 = 55

5x = 40

x = 8

Correct Answer: B, 40

Hope this helps!

Nastasia [14]3 years ago
6 0

Answer:

x = 8

Step-by-step explanation:

Reorder the terms:

15 + 5x = 55

Solving

15 + 5x = 55

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + 5x = 55 + -15

Combine like terms: 15 + -15 = 0

0 + 5x = 55 + -15

5x = 55 + -15

Combine like terms: 55 + -15 = 40

5x = 40

Divide each side by '5'.

x = 8

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<u>Roots of a polynomial</u>

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)

Where a is an arbitrary constant.

We know three of the roots of the degree-5 polynomial are:

x_1=0;\ x_2=\sqrt{7}\boldsymbol{i}:\ x_3=-2\boldsymbol{i}

We can complete the two remaining roots by knowing the complex roots in a polynomial with real coefficients, always come paired with their conjugates. This means that the fourth and fifth roots are:

x_4=-\sqrt{7}\boldsymbol{i}:\ x_3=+2\boldsymbol{i}

Let's build up the polynomial, assuming a=1:

P(x)=(x-0)(x-\sqrt{7}\boldsymbol{i})(x+\sqrt{7}\boldsymbol{i})(x-2\boldsymbol{i})(x+2\boldsymbol{i})

Since:

(a+b\boldsymbol{i})\cdot (a-b\boldsymbol{i})=a^2+b^2

P(x)=(x)(x^2+7)(x^2+4)

Operating the last two factors:

P(x)=(x)(x^4+11x^2+28)

Operating, we have the required polynomial:

\boxed{P(x)=x^5+11x^3+28x}

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3 years ago
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