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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

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<h3>What is a pseudocode?</h3>

A pseudocode simply refers to a description of the steps contained in an algorithm, especially through the use of a plain (natural) language.

<u>Note:</u> π is equal to 3.14.

Since Nya assigns π, which isn't an integer, the program would determine the integer (n) as follows:

x - 1 < n < x

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Substituting the parameter (3.14) into the formula, we have;

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Read more on pseudocode here: brainly.com/question/13208346

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4 0
2 years ago
Lawrence is half as old as Jonathan. The sum of their ages is 54. How old is Jonathan?
schepotkina [342]

Answer:

Jonathan is 36 years old.

Step-by-step explanation:

Jonathan=2 Lawrence

J= 2L

54 divided by 3 equals 18.

18 times 2 equals 36.

Hope this helped! :)

5 0
3 years ago
Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for t
Anit [1.1K]

Answer:

Direction is missing

Step-by-step explanation:

Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. We know that velocity is a vector quantity. It has both magnitude as well as direction. Velocity is defined as the total distance per unit time I.e.  

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Here, only velocity is given but its direction is missing. So, the missing information is " the direction ".    

5 0
3 years ago
Read 2 more answers
An isosceles triangle always has three interior angles that measure 60° each.
Nataly [62]

Answer:

False

Step-by-step explanation:

The definition given is that of an equilateral triangle, NOT that of an isosceles triangle. An isosceles triangle has <em>at least</em> two angles that are equal by definiton. They need not be 60 degrees. For example, a triangle with angle measures of 140, 20, and 20 is an isosceles triangle because two of the angles are equal. Hope this helped!

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3 years ago
What is the scientific notation for 3800
BigorU [14]

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im pretty sure thats scientific notation

8 0
3 years ago
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