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
user100 [1]
3 years ago
8

Find the length of line segment UV.

Mathematics
1 answer:
pshichka [43]3 years ago
8 0

Answer:

The length of the line segment UV is 76 units

Step-by-step explanation:

In a triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length

In Δ ONT

∵ U is the mid-point of ON

∵ V is the mid-point of TN

→ That means UV is joining the mid-points of two sides

∴ UV // OT

∴ UV = \frac{1}{2} OT

∵ UV = 7x - 8

∵ OT = 12x + 8

∴ 7x - 8 = \frac{1}{2} (12x + 8)

→ Multiply the bracket by \frac{1}{2}

∵ \frac{1}{2} (12x + 8) =  \frac{1}{2} (12x) +  \frac{1}{2} (8) = 6x + 4

∴ 7x - 8 = 6x + 4

→ Add 8 to both sides

∴ 7x - 8 + 8 = 6x + 4 + 8

∴ 7x = 6x + 12

→ Subtract 6x from both sides

∴ 7x - 6x = 6x - 6x + 12

∴ x = 12

→ Substitute the value of x in the expression of UV to find it

∵ UV = 7(12) - 8 = 84 - 8

∴ UV = 76

∴ The length of the line segment UV is 76 units

You might be interested in
Which expression is equivalent to n(3+2n)?<br> a)2n²+3n+5<br> b)5n+5<br> c)2n+8<br> d)11n
denis23 [38]

Answer:

None of the above.

Step-by-step explanation:

n(3 + 2n)

Apply distributive property...

3n + 2n²

There are no extra numbers

5 0
3 years ago
Read 2 more answers
Describe and correct the error in finding the measure of the angle
DerKrebs [107]

Sorry, it's late, and I'm a bad explainer.

The error is adding (2x-12) with x and 30. This is wrong because you are adding the angles inside the triangle and you are assuming that (2x - 12) is the unlabeled angle INSIDE the triangle, when it is the exterior angle/outside of the triangle.

A straight line is also 180°.

(2x - 12) + ? = 180

30 + x + ? = 180

If you look at the equations, and put parentheses around 30 + x, (30 + x) and (2x - 12) should be the SAME NUMBER. So you could set them equal to each other to find x. (or you could also look at the picture and see that they both need/are missing the same angle)

2x - 12 = 30 + x

x = 42

Now you plug 42 into the exterior angle equation

2(42) - 12 = 84 - 12 = 72°

5 0
3 years ago
What is the area of the polygon below in square units?<br> 4 cm<br> 12 cm<br> 18 cm
stepan [7]
There is no polygon there
8 0
2 years ago
Mrs. Olga’s $250 investment earns 19% interest compounded annually. What will her balance be after 3 years?
Maurinko [17]

Answer:

The answer is A. $421.29

Step-by-step explanation:

Just keep finding 19% of the numbers next, and you add that all up and you get the answer.

250 x 19%=47.5. (250+47.5)=> 297.5x19%= 56.525. (297.5+56.525) =>354.025x19%=67.26475

354.025+67.26475=> 421.28975, which can round up to 421.29.

6 0
3 years ago
Read 2 more answers
The area of a rectangular garden is 5828 m
evablogger [386]

Answer:

The length of the garden is 94 m.

Step-by-step explanation:

you do 5828 m. divided by 62m. and that is how you get your answer of 94 m.

6 0
3 years ago
Read 2 more answers
Other questions:
  • the wall is 20ft deep, the snail goes up 4ft every day and drops 2 ft every night. how many days does it take the snail to reach
    7·2 answers
  • What is the value of 2 in 5,678.321
    7·2 answers
  • What is the equation of the line with x-intercpt 18 and y-intercpt 3​
    10·1 answer
  • A pencil at a stationery store costs $1, and a pen costs $1.50. Stefan spent $7 at the store. He bought a total of 6 items. Whic
    12·2 answers
  • What is equivalent to 6/7
    9·2 answers
  • Please help me with d.
    10·1 answer
  • Write the product using exponents. (pls help)
    14·2 answers
  • first to answer correctly gets brainleist if u put a link u get reported so yea. bye thx have a blessed day :).
    11·2 answers
  • Make the biggest possible number using the digits below only once2,9,4​
    10·1 answer
  • Suppose that the function f(x)=3 x+1.5 represents the cost to rent x movies a
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!