All categories

3 years ago

Solve for the roots in simplest form by completing the square 6x^2+120x+2070=0

Mathematics

1 answer:

Kitty [74]3 years ago

8 0

Answer:

Step-by-step explanation:

First, we can divide out the common factor, 6

$6x^2 + 120x + 2070 = 0\\x^2 + 20x + 345 = 0\\$

Now we complete the square

$(x^2 + 20x + (\frac{20}{2})^2) + 345 - (\frac{20}{2})^2\\(x^2 + 20x + 100) + 345 - 100\\(x+10)^2 + 245\\$

$(x+10)^2 = -245\\x + 10 = \sqrt{-245}\\x = i\sqrt{245} - 10\\x = -10 \pm i\sqrt{245}$

You might be interested in

the measure of one acute angle is twice the difference of the measure of the other acute angle and 12

Dmitrij [34]

Is there a picture to find the measure of the acute angle? Or do you want an equation to solve it? If so than it is: 2b-12=a, where b is the measure of the other acute angle and a is the measure of the acute angle where it is twice the difference of the measurment of the other acute angle and 12.

3 0

4 years ago

Isolate w for the literal equation v = lwh

Serggg [28]

$\Large\textsf{\textbf{Answer\::}}$

view explanation please !

$\Large{\textsf{\textbf{Calculations\::}}$

<em>What are we asked to do ?</em>

We are asked to isolate w (get w by itself) .

To do that , divide by lh on both sides :

$\displaystyle\frac{V}{lh} = w$

So the right formula is :

$\bigcirc\!\!\!\!\!\!\bigstar$ $\displaystyle\frac{V}{lh} =w$

$\footnotesize\text{hope\:helpful~}$

4 0

2 years ago

Read 2 more answers

write the equation of the line that is perpendicular to the given line and that passes through the given point. y = -1/3x+5;(4,3

timama [110]

Answer:

The equation of line perpendicular to given line equation and passing through point (4,3) is y = 3 x - 9 .

Step-by-step explanation:

Given as :

The given equation of one line = y = $\dfrac{-1}{3}$ x + 5

∵ Equation of line in slope-intercept form is written as

y = m x + c

where m is the slope of line

And c is the intercept of y

Now, Comparing given line equation with standard slope intercept line equation

∴ m = $\dfrac{-1}{3}$

Slope of this line = m = $\dfrac{-1}{3}$

Now, another line is perpendicular to the given line

For perpendicular lines , the products of slope of lines = - 1

Let the slope of another line = M

So, from perpendicular lines condition

m × M = - 1

∴ M = $\dfrac{-1}{m}$

I.e M = $\frac{-1}{\frac{-1}{3}}$

So, M = 3

∴ The slope of other line = M = 3 , and the line passing through point (4,3)

Now, Again

The equation of line in slope-intercept form

I.e y = M x + c

Now, satisfying the points on line

So, 3 = 3 × 4 + c

Or, 3 = 12 + c

∴ c = 3 - 12

i.e c = - 9

or, The other line equation = y = 3 x - 9

Hence, The equation of line perpendicular to given line equation and passing through point (4,3) is y = 3 x - 9 . Answer

5 0

3 years ago

Helppppppp. Plers omggggggasappp

Veseljchak [2.6K]

Answer:

Step-by-step explanation:

The ratio of in- state : out- state = 96 : 56 ← divide both parts by 8

Thus 96 : 56 = 12 : 7 ← in simplest form → D

3 0

4 years ago

Read 2 more answers

What is the x-intercept of the line with this equation 13x+y=−15? Enter your answer in the box. ( , 0) plz first to answer get b

Mumz [18]

Answer:

(-15/13, 0)

Step-by-step explanation:

For x-intercept, ALWAYS put y=0, and vice versa is true.

Given equation: 13x+y=-15

X-intercept (Put y=0);

13x + (0) = -15

13x=-15

x=-15/13

Hence x=-15/13 and y=0 (for x-intercept)

In co-ordinate form, we will write it as:

(x,y) = (-15/13, 0)

3 0

3 years ago

Read 2 more answers