1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rina8888 [55]
3 years ago
12

Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC

Mathematics
1 answer:
e-lub [12.9K]3 years ago
8 0

Answer:

DC=\frac{8}{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

BM^2=AB^2-AM^2

we have

AB=5\ units\\AM=x\ units

substitute

BM^2=5^2-x^2

BM^2=25-x^2 -----> equation A

<em>In the right triangle BMC</em>

Applying the Pythagorean Theorem

BM^2=BC^2-MC^2

we have

BC=7\ units\\MC=AC-AM=(9-x)\ units

substitute

BM^2=7^2-(9-x)^2

BM^2=49-(81-18x+x^2)  

BM^2=49-81+18x-x^2

BM^2=-x^2+18x-32 ----> equation B

equate equation A and equation B

-x^2+18x-32=25-x^2

solve for x

18x=25+32\\18x=57\\\\x=\frac{57}{18}

Simplify

x=\frac{19}{6}

<em>Find the length of DC</em>

DC=AC-2x

substitute the given values

DC=9-2(\frac{19}{6})

DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units

You might be interested in
A bag contains 9 marbles: 4 are green, 2 are red, and 3 are blue. Chris chooses a marble at random, and without putting it back,
Ivahew [28]

Answer:

1/12

Step-by-step explanation:

3/9 for the first

2/8 for the second

3/9= 1/3

2/8= 1/4

1/4 x 1/3= 1/12

4 0
2 years ago
Concider the graph of the polynomial function p(x)=(x-1)(x+2)(x+5)
yulyashka [42]
I need to see the horse??
4 0
3 years ago
If we solve h(x) = 36, one of the possible values of x is 1
Mademuasel [1]

Answer:

Step-by-step explanation:

(x+5)² = 36

x+ 5 = ±√36 = ±6

x = -5 ±6 = 1, -11

4 0
3 years ago
Express 2x squared - 3x - 5 as the product of two binomial factors
natita [175]

Answer:

(2x - 5) (x + 1)

Step-by-step explanation:

2x2 - 3x - 5 = 0

(2x - 5) (x + 1) = 0

4 0
2 years ago
An animal shelter has 910 of its crates filled with animals.
AnnZ [28]

12/910 which simplifies to 6/455.

Explanation:

Take the amount of crates holding dogs over the total amount of crates

5 0
3 years ago
Other questions:
  • In the figure on the right, STWC space is a square centered at the origin with side length 2a What are the coordinates of the ve
    14·1 answer
  • Please help! tell whether x and y are proportional. if so, identify the constant of proportionality
    5·1 answer
  • -4x=12<br>how do i awnser this​
    10·2 answers
  • A bikini and sunglasses cost 110 $ in total. The Bikini costs 100$ more the the glasses. How many much do the sunglasses cost?
    14·1 answer
  • Diego and Max are buying soft drinks for a neighborhood picnic. Each person is
    6·1 answer
  • It takes 7/12 foot of ribbon to make a bookmark. How many feet of ribbon will it take to make 15 bookmarks?
    14·1 answer
  • G Image result for pe.
    15·1 answer
  • HELP PLS<br> Raise 5 to the 9th power, then subtract j from the result
    15·2 answers
  • A certain forest covers an area of 4000km^2. Suppose that each year this area decreases by 3.5%. What will the area be after 9 y
    8·1 answer
  • (a + b)² = a² + 2ab + b2 with step by step explanation​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!