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3 years ago

Solve for the roots in simplest form by completing the square x^2-12x+20=0

Mathematics

1 answer:

Alex17521 [72]3 years ago

5 0

Answer:

x = 10 or x = 2

Step-by-step explanation:

Solve for x:

x^2 - 12 x + 20 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 20 from both sides:

x^2 - 12 x = -20

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36 to both sides:

x^2 - 12 x + 36 = 16

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 6)^2 = 16

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 6 = 4 or x - 6 = -4

Hint: | Look at the first equation: Solve for x.

Add 6 to both sides:

x = 10 or x - 6 = -4

Hint: | Look at the second equation: Solve for x.

Add 6 to both sides:

Answer: x = 10 or x = 2

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2 years ago

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Maurinko [17]

So first we assume that half is adult and have is student.

So
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So there were
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I hope this helped. Have a great day!

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2 years ago

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3 years ago

How many solutions does the nonlinear system of equations graphed below have?

Ostrovityanka [42]

Answer:

Option (A)

Step-by-step explanation:

Solution of two functions represented by the graph are the common points or point of intersection of the graphs.

From the graph attached,

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Therefore, solutions of the given non linear functions will be FOUR.

Option (A) will be the correct option.

4 0

3 years ago

What is the equation of the line that passes through the point (4, 6) and is parallel to the line 2y - 4x = 1?

Cloud [144]

Answer:

D. y = 2x - 2

Step-by-step explanation:

1) First, find the slope of the given line. Place it in slope-intercept form to identify its slope easily. Isolate the y in the equation:

$2y-4x = 1\\2y = 4x+1\\y = 2x+\frac{1}{2}$

A line placed in slope-intercept form is represented by the formula $y = mx + b$ . The $m$ , or the coefficient of the x-term, represents the slope. Thus, the slope of this line is 2.

2) Lines that are parallel share the same slope. So, the slope of the parallel line will have 2 as its slope as well.

We now have enough information to write the equation of the line in point-slope form. From there, we can convert it to slope-intercept form and find out which option is correct.

Use the point-slope formula $y-y_1 = m (x-x_1)$ and substitute values for $m$ , $x_1$ , and $y_1$ . Since $m$ represents the slope of the line, substitute 2 in its place. Since $x_1$ and $y_1$ represent the x and y values of a point the line intersects, substitute the x and y values of (4,6) into the formula as well. Then, with the resulting equation, isolate y like before to find which option is correct:

$y-6 = 2(x-4)\\y-6 = 2x-8\\y = 2x-2$

So, option D is correct.

7 0

3 years ago