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
masya89 [10]
3 years ago
7

Triangle XYZ is shown, where n ≥ 5. Triangle X Y Z is shown. The length of side X Y is n + 4, the length of side Y Z is 2 n, and

the length of side Z X is n minus 2.
Mathematics
1 answer:
motikmotik3 years ago
6 0

Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

XY = n + 4

YZ = 2n

ZX = n - 2

According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3

YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2

ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that <em>n</em> ≥ 5.

Then the sides of the triangle are:

XY = n + 4 ≥ 5 + 4 = 9

YZ = 2n ≥ 2 × 5 = 10

ZX = n - 2 ≥ 5 - 2 = 3

So, the longest side of the triangle is YZ. And the shortest side is ZX.

The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

You might be interested in
The table shows the number of each type of toy in the store. the toys will be placed on shelves so that each shelf has the same
skelet666 [1.2K]
First, we compute the highest common factor between the numbers of toys. The highest common factor for 45, 105 and 75 is 15. Therefore, we will need 15 shelves. On each shelf, there will be 45/15 = 3 dolls, 105/15 = 7 footballs and 75/15 = 5 small cars
3 0
3 years ago
At a real estate​ agency, an agent sold a house for ​$360,000. The commission rate is 25% for the real estate agency and the com
Orlov [11]

Answer: See explanation

Step-by-step explanation:

a. The amount that the agency make on the​ house will be 25% of $360,000. This will be:

= 25% × $360,000

= 25/100 × $360,000

= 0.25 × $360,000

= $90,000

b. The amount that the agent earn in​ commission will be:

= 30% × $90,000

= 30/100 × $90,000

= 0.3 × $90,000

= $27,000

3 0
3 years ago
How many times greater is the value of 3 in 300
Tatiana [17]
The value of 3 in 300 is ten times I hope this helps you tell me if you want ,e to explain
7 0
3 years ago
Which of the following is true given that -4 &gt; -9?
xxMikexx [17]

Answer:

A. -4 is to the right of -9 on a horizontal number line.

Step-by-step explanation:

The order in a number line is:

-9 , -8 , -7 , -6 , -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

As shown above, -4 is to the right of -9 on the horizontal number line.

4 0
3 years ago
The graph shows the function of f(x)=(3.5)^x
GrogVix [38]
The one that passes through the origin. That one in the lower left part.
6 0
3 years ago
Read 2 more answers
Other questions:
  • PLS HELP ME ASAP FOR QUESTION 4!! (MUST SHOW WORK!!!) + LOTS OF POINTS! *brainliest*
    13·1 answer
  • Melanie made 72 peanut butter cookies and oatmeal cookies. She wants to make identical groups of cookies for her friends. Each g
    6·1 answer
  • Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –3 + (n – 1)(–2.2)
    14·1 answer
  • X-intercept = -1 Y-intercept =5
    5·1 answer
  • Roberto will save 1/6 of his allowance each day. If he gets $2.00 a day, about how much money will he save each day? Round your
    5·1 answer
  • What is the answer of 2/3-6/10
    15·2 answers
  • Identify the relationship and then solve for x
    15·1 answer
  • A customer buys bouquets of tulips and bouquets of roses for $.. What is the price of a bouquet of roses?
    10·1 answer
  • Help i,m suck and i cant find the answer
    10·1 answer
  • Please help I need help by the end of today
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!