All categories

3 years ago

In the figure, BD is a median. If AD=6x+10 and CD=2x+12, find the length of AC. Show your work.

Mathematics

1 answer:

Valentin [98]3 years ago

6 0

Answer:

26.

Step-by-step explanation:

Given, BD is a median. As it divides the AC equally, that's why it will AD=CD. Given, AD= 6x+10 and CD= 2x+12

Now, AD= CD

or, 6x+10=2x+12

or, 6x-2x= 12-10

or, 4x= 2

or, x= 1/2

So the value of x is 1/2. As BD divided AC equally, both AD and CD will be equal and AD+CD= AC.

So, 6x+10+2x+12= AC

or, 8x+22= AC

or, 8 X (1/2) + 22= AC

or, 4+22 = AC

or, AC= 26.

You might be interested in

NEED HELP ASAP!!!<br> thank you.

Alex17521 [72]

Answer:

See explanation

Step-by-step explanation:

Consider triangles ACM and BCM. In these triangles,

$m\angle 3=m\angle 4$ - given;
$m\angle 1=m\angle 2=90^{\circ}$ - definition of perpendicular lines CM and AB;
$\overline{CM}\cong \overline{CM}$ - reflexive property.

So,

$\triangle ACM\cong \triangle BCM$ by ASA postulate (if one side and two angles adjacent to this side of one triangle are congruent to one side and two angles adjacent to this side of another triangle, then two triangles are congruent).

Two-column proof:

Statement Reason

1. $m\angle 3=m\angle 4$ Given

2. $CM\perp AB$ Given

3. $m\angle 1=m\angle 2=90^{\circ}$ Definition of perpendicular lines CM and AB

4. $\overline{CM}\cong \overline{CM}$ Reflexive property

5. $\triangle ACM\cong \triangle BCM$ ASA postulate

7 0

2 years ago

For the figure below, give the following.

Zepler [3.9K]

Answer:

Step-by-step explanation:

Just c cuz i smart

3 0

3 years ago

Giving brainliest for whoever gets it right

spayn [35]

Okay thanks I’ll try to help you

3 0

3 years ago

How to solve -12+7x=x

lord [1]

Answer:

x=2

Step-by-step explanation:

So if the equation is -12+7x=x, you need to subtract 7x, because you want to know the value of x. So the equation now looks like this: -12=-6x

you divide-6 to both sides because we want to iscolate the x

The answer is x=2

Hope it helps!

3 0

3 years ago

A coin favors heads when tossed and there are 15 heads in 18 tosses

Alexxandr [17]

This is not correct. You might think you are "on a roll" but the probability of heads on any toss is just as likely as the probability of tails because each coin toss is an independent event, meaning, two events related in such a way that knowing about the occurrence of one event has no effect on the probability of the the other event. This would hold true if you have tossed these 15 heads and you believe that tails "are due". It is an independent event.

7 0

3 years ago