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Elena L [17]
3 years ago
11

Solve the following equation by completing the square. 1/4x^2+x+1/4=0

Mathematics
1 answer:
fenix001 [56]3 years ago
8 0

Answer:

D. X=-2+sqrt(3) or -2-sqrt(3)

x_{1} =-2+\sqrt{3} \\x_{2} =-2-\sqrt{3}

Step-by-step explanation:

Quadratic Equation given:

$\frac{1}{4} x^2+x+\frac{1}{4}=0$

In order to get rid of the fractions, multiply both sides by 4.

$\frac{1}{4}x^2\cdot \:4+x\cdot \:4+\frac{1}{4}\cdot \:4=0\cdot \:4$

We get:

x^2+4x+1=0

x^2+4x+4-4+1=0

Completing the square:

(x+2)^2-4+1=0\\

(x+2)^2-3=0

(x+2)^2=3

x+2=\pm\sqrt{3}

x=-2\pm\sqrt{3}

x_{1} =-2+\sqrt{3} \\x_{2} =-2-\sqrt{3}

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One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle. Then the lines are parallel

<h3><u>Solution:</u></h3>

Given that, One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle.  

We have to prove that the lines are parallel.

If they are parallel, sum of the described angles should be equal to 180 as they are same side exterior angles.

Now, the 1st angle will be 1/6 of right angle is given as:

\begin{array}{l}{\rightarrow 1^{\text {st }} \text { angle }=\frac{1}{6} \times 90} \\\\ {\rightarrow 1^{\text {st }} \text { angle }=15 \text { degrees }}\end{array}

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5 0
3 years ago
If f(x) = -3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true. ​
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Step-by-step explanation:

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