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3 years ago

Solve 6x^2 - 12x + 24 = 0 by completing the square

Mathematics

1 answer:

IrinaVladis [17]3 years ago

4 0

Answer: $\quad x=1+\sqrt{3}i,\:x=1-\sqrt{3}i$

Step-by-step explanation: $x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:6\cdot \:24}}{2\cdot \:6}$

$x_{1,\:2}=\frac{-\left(-12\right)\pm \:12\sqrt{3}i}{2\cdot \:6}$

$x_1=\frac{-\left(-12\right)+12\sqrt{3}i}{2\cdot \:6},\:x_2=\frac{-\left(-12\right)-12\sqrt{3}i}{2\cdot \:6}$

$x=1+\sqrt{3}i,\:x=1-\sqrt{3}i$

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A line passes through the points (1, 4) and (3, 4). Which is the equation of the line?

xeze [42]

Answer:

y = -4x + 8

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step 1: Find slope m

$m=\frac{-4-4}{3-1}$

$m=\frac{-8}{2}$

m = -4

y = -4x + b

Step 2: Find y-intercept b

4 = -4(1) + b

4 = -4 + b

8 = b

Step 3: Rewrite linear equation

y = -4x + 8

8 0

3 years ago

PLEASE HELP 2O POINTS

vovangra [49]

C. The first is a solution, but the second is not.

5x - y/3 = 13 ; (2,-9)
substitute the letters:
5(2) - (-9/3) = 13
10 - (-3) = 13 : note that deducting a number with a negative sign turns both sign as positive.
10 + 3 = 13 ;
13 = 13

5x - y/3 = 13 ; (3,-6)
5(3) - (-6/3) = 13
15 - (-2) = 13
15 + 2 = 13
17 = 13 not equal. not a solution

hope i could help

4 0

3 years ago

Read 2 more answers

A school district is considering moving the start of the school day at Groveland High from 8:00 a.m. to 9:00 a.m. to allow stude

DaniilM [7]

Answer:

The answer is " $\bold{(7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} }\\\\$ "

Step-by-step explanation:

Given values:

$\bar{x_1}=7.1\\\\\bar{x_2}=8.3\\\\s_1=1.7\\\\s_2=1.9\\\\n_1=50\\\\n_2=39$

Using formula:

$\to (\bar{x_1} -\bar{x_2}) \pm t \sqrt{\frac{(s_1)^2}{n_1}+\frac{(s_1)^2}{n_2}} \\\\$

Put the values in the above formula:

$\to (7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} \\\\$

4 0

3 years ago

Which expression represents each mathematical phrase?

olganol [36]

Answer:

Step-by-step explanation:

add 12 and a number: 12 + c

subtract a number from 12: 12 - c

divide a number by 12: c : 12 or c/12

multiply 12 by a number: 12 · c = 12c

5 0

2 years ago

What two numbers multiply to 54 and add up to 7

k0ka [10]

Xy = 54
x + y = 7

$xy = 54$
$\frac{xy}{x} = \frac{54}{x}$
$y = \frac{54}{x}$

$x + y = 7$
$x + \frac{54}{x} = 7$
$\frac{x^{2}}{x} + \frac{54}{x} = 7$
$\frac{x^{2} + 54}{x} = 7$
$x^{2} + 54 = 7x$
$x^{2} - 7x + 54 = 0$
$x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}$
$x = \frac{7 \± \sqrt{49 - 216}}{2}$
$x = \frac{7 \± \sqrt{-167}}{2}$
$x = \frac{7 \± i\sqrt{167}}{2}$
$x = \frac{7 \± 12.9i}{2}$
$x = 3.5 \± 6.45i$
$x = 3.5 + 6.45i$ $or$ $3.5 - 6.45i$

x + y = 7
3.5 + 6.45i + y = 7
- (3.5 + 6.45i) - (3.5 + 6.45i)
y = 3.5 - 6.45i
  (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)

  or

  x + y = 7
3.5 - 6.45i + y = 7
- (3.5 - 6.45i)   - (3.5 - 6.45i)
y = 3.5 + 6.45i
(x, y) = (3.5 - 6.45i, 3.5 + 6.45i)

The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.

5 0

3 years ago