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Temka [501]
2 years ago
9

Solve 3x2 + 18x + 15 = 0 by completing the square. 3(x + 3)2 = 6; x = −3 + square root 2, x = −3 − square root 2 3(x + 9)2 = 12;

x = −11, x = −7 3(x + 3)2 = 12; x = −5, x = −1 3(x + 9)2 = 228; x = −9 + square root 76, x = −9 − square root 76
Mathematics
2 answers:
Rzqust [24]2 years ago
7 0

Hey there!

I took the test, and I can confirm that 3(x + 3)2 = 12; x = -5, x = -1 is the CORRECT answer

xXxGolferGirlxXx

Damm [24]2 years ago
5 0
3(x + 3)2 = 12; x = -5, x = -1
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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]

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Step-by-step explanation:

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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.

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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

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Bezzdna [24]

Answer:

Length = 25cm

Step-by-step explanation:

Given

Brass Shape: Square

Density = 4.2g/cm^3

Mass = 1.05kg

Height = 4mm

Required

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First, we need to calculate the Volume of the Brass using

Density = \frac{Mass}{Volume}

Make Volume the subject of formula

Volume = \frac{Mass}{Density}

Substitute 1.05kg for Mass and 4.2g/cm³ for Density

Volume = \frac{1,05\ kg}{4.2\ g/cm^3}

Convert 1.05 kg to grams

Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}

Volume = \frac{1050 \ kg}{4.2\ g/cm^3}

Volume = \frac{1050 \ kg}{4.2\ g/cm^3}

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Next is to determine the Area of the brass;

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Convert mm to cm

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Divide both sides by 0.4cm

\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}

\frac{250cm^3}{0.4cm} =Area

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Lastly, we'll calculate the length of the brass

Since the brass is square based;

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Substitute 625cm² for Area

625cm^2 = Length^2

Take square root of both sides

\sqrt{625cm^2} = Length

25cm = Length

Length = 25cm

<em>Hence, the length of the square brass is 25cm</em>

5 0
2 years ago
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