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2 years ago

Point B ∈ |AC| so that AB:BC=2:1. Point D ∈ |AB| so that AD:DB=3:2. Find AD:DC

Mathematics

2 answers:

grigory [225]2 years ago

6 0

Answer:

5:4

Step-by-step explanation:

If point B divides the segment AC in the ratio 2:1, then

AB=2x units and BC=x units.

If point D divides the segment AB in the ratio 3:2, then

AD=3y units and DB=2y units.

Since AD+DB=AB, then

$3y+2y=2x\\ \\5y=2x\\ \\y=\dfrac{2}{5}x$

Now,

$AD=3y\\ \\DC=DB+BC=2y+x=2y+\dfrac{2}{5}y=\dfrac{12}{5}y$

So,

$AD:DC=3y:\dfrac{12}{5}y=15:12=5:4$

katen-ka-za [31]2 years ago

5 0

Answer:

AD:DC=6:9

Step-by-step explanation:

We know that:

AB:BC=2:1

AD:DB=3:2

We can conclude that:

AB+BC=AC

Then:

AB=2/3AC

BC=1/3AC

AD+DB=AB

Then

AD=3/5AB

DB=2/5AB

From the above we can replace:

AD=(3/5)(2/3AC)=6/15AC

On the other hand:

DC= DB+BC

DC=2/5AB+1/3AC

In terms of AC

DC=((2/5)(2/3AC))+1/3AC=4/15AC+1/3AC

DC=27/45AC=9/15AC

From:

AD=6/15AC

DC=9/15AC

we can say that:

AD:DC=6:9

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Read 2 more answers

A given line has the equation 10x + 2y = −2.

worty [1.4K]

The equation is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<h3>Further explanation </h3>

This case asking the end result in the form of a slope-intercept.

<u>Step-1: find out the gradient. </u>

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2

Divide both sides by two

y = -5x -1

The slope-intercept form is $\boxed{ \ y = mx + c \ }$ , with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:

$\boxed{ \ ax + by = k \rightarrow m = - \frac{a}{b} \ }$

10x + 2y = −2 ⇒ a = 10, b = 2

$\boxed{m = - \frac{10}{2} \rightarrow m = -5}$

<u>Step-2:</u> the conditions of the two parallel lines

The gradient of parallel lines is the same $\boxed{ \ m_1 = m_2 \ }$ . So $\boxed{m_1 = m_2 = -5}.$

<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

$\boxed{ \ \boxed{ \ y - y_1 = m(x - x_1)} \ }$

Given that

m = -5
(x₁, y₁) = (0, 12)

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<u>Alternative steps </u>

Substitutes m = -5 and (0, 12) to slope-intercept form $\boxed{ \ y = mx + c \ }$

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e. $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

$\boxed{Standard \ form: ax + by = c, with \ a > 0}$

$\boxed{Point-slope \ form: y - y_1 = m(x - x_1)}$

$\boxed{Slope-intercept \ form: y = mx + k}$

<h3>Learn more </h3>

A similar problem brainly.com/question/10704388
Investigate the relationship between two lines brainly.com/question/3238013
Write the line equation from the graph brainly.com/question/2564656

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant