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3 years ago

which method of solving the quadratic equation would be the easiest to find the soulution for 2x^2 - 4x-3=0

1 answer:

6 0

Solve for x over the real numbers:
2 x^2 - 4 x - 3 = 0

Divide both sides by 2:
x^2 - 2 x - 3/2 = 0

Add 3/2 to both sides:
x^2 - 2 x = 3/2

Add 1 to both sides:
x^2 - 2 x + 1 = 5/2

Write the left hand side as a square:
(x - 1)^2 = 5/2

Take the square root of both sides:
x - 1 = sqrt(5/2) or x - 1 = -sqrt(5/2)

Add 1 to both sides:
x = 1 + sqrt(5/2) or x - 1 = -sqrt(5/2)

Add 1 to both sides:
Answer: x = 1 + sqrt(5/2) or x = 1 - sqrt(5/2)

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Write an equation for a line perpendicular to y = -5x – 4 and passing through the point (15,5)

3241004551 [841]

The equation for the line in point-slope form that passes through (15, 5) and is perpendicular to $y = -5x - 4$ is $\mathbf{y -5 = \frac{1}{5} (x - 15)}$

Recall:

The equation of the line can be written in point-slope form (y - b = m(x - a)) and also in slope-intercept form (y = mx + b).

Given:

the point the line passes through: (15, 5)
the line it is perpendicular to: y = -5x - 4

Find the slope (m):

The slope value will be the negative reciprocal of the slope value of y = -5x - 4.

The slope of y = -5x - 4 is -5.

Therefore, the slope of the line perpendicular to y = -5x - 4 will be the negative reciprocal of -5 which is: 1/2.

Write the equation in point-slope form by substituting m = 1/2 and (a, b) = (15, 5) into y - b = m(x - a)

Thus:

$y -5 = \frac{1}{5} (x - 15)$

Therefore, the equation for the line that passes through (15, 5) and is perpendicular to $y = -5x - 4$ is $\mathbf{y -5 = \frac{1}{5} (x - 15)}$

Learn more here:

brainly.com/question/11624671

7 0

3 years ago

Any help please and thank you (picture included)

lina2011 [118]

Answer:

15 units

Step-by-step explanation:

1. Find the corresponding lengths of the triangles.

9/x = x/ (9+16)

9/x = x/25

2. Solve for x.

Multiply both sides by x.

9 = x²/25

Multiply both sides by 25.

225 = x²

Square root both sides to solve for x.

√225 = √x²

x = 15

3 0

3 years ago

Is the answer to -8/-8 positive or negative?

NeTakaya

Answer: positive

Step-by-step explanation:

A negative divided by another negative is always positive. Same rule applies to multiplication. Double negatives equal positives

5 0

2 years ago

The larger of two consecutive integers is 7 greater than twice the smaller. Find the integers. ( 4, 5)( -8, -9)(-5, -6)

igor_vitrenko [27]

Answer:

(-5, -6)

Step-by-step explanation:

The smaller integer is x.

The larger integer is x + 1.

x + 1 = 7 + 2x

-x = 6

x = -6

x + 1 = -6 + 1 = -5

Answer: (-5, -6)

8 0

1 year ago

If f(x)=3x-1 and g(x)= x+2, find (f-g)(x)

il63 [147K]

Answer:

Step-by-step explanation:

(f-g)(x) = f(x)- g(x)

= 3x - 1 - ( x + 2)

=3x - 1 - x - 2

= 2x - 3

8 0

2 years ago