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
Zepler [3.9K]
3 years ago
7

The angle measures and/or side lengths of a triangle are described. Determine whether the conditions given

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
8 0

(a) One unique triangle. This is an equilateral triangle since all sides are the same length. Through the SSS property, we can prove that only one triangle is possible here.

----------------------------------------------------

(b) Cannot make a triangle. The triangle inequality theorem says that adding any two sides of a triangle must result in a value larger than the third side. Add up the first two sides (1 and 2) to get 1+2 = 3, which is not larger than the third side (3 units long). I recommend cutting out strips of paper that are 1 inch, 2 inches and 3 inches long, and trying to form a triangle. You'll find that a triangle is not possible. The 1 inch and 2 inch strips will line up to form a straight line that is 3 inches long, and basically you have a flat line (or a triangle with area 0)

----------------------------------------------------

(c) More than one triangle. The angles add up to 180 since 35+60+85, so we can form a triangle. It turns out we can form infinitely many of them. The AA (angle angle) similarity theorem allows us to scale any triangle to make it larger or smaller compared to the original.

----------------------------------------------------

(d) Cannot make a triangle. I'm assuming the 509 should actually be 50°. If so, then a triangle is not possible because the three angles (50, 50, 50) do not add to 180. We have instead 50+50+50 = 150. For any triangle, the three angles must always add to 180 degrees.

You might be interested in
Which expression is represented by the model?<br> x-3<br> x+3<br> -X-3<br> -X+3
Crazy boy [7]
-x +3 i think , i hope that helps
5 0
3 years ago
Read 2 more answers
12 people can be of 30 chairs in eight hours how many chairs candy people build in 100 hours
ruslelena [56]
Hello!

Divide the amount of chairs (30) that 12 people can build by the number of hours (8) it takes to build them, to find out how many chairs they make per hour.

30 ÷ 8 = 3.75

This means that they make they make 3.75 chairs per hour. Multiply this by 100 hours.

3.75 × 100 = 375

ANSWER:

The people can build D. 375 chairs in 100 hours.
7 0
3 years ago
The scores on an exam are listed. If a teacher wants to explain how poorly the class did on the test, would she use the mean, me
Natasha_Volkova [10]
Mean because the mean is an average. That gives an overall understanding of what the entire class did.
4 0
3 years ago
Read 2 more answers
If m&lt;ECD is six less than five times m&lt;BCE. and m&lt;BCD = 162°, find each measure.(Sorry bout using the wrong signs, but
tia_tia [17]

Answer:

m∠BCE = 28° and m∠ECD = 134°

Step-by-step explanation:

* Lets explain how to solve the problem

- The figure has three angles: ∠BCE , ∠ECD , and ∠BCD

- m∠ECD is six less than five times m∠BCE

- That means when we multiply measure of angle BCE by five and

 then subtract six from this product the answer will be the measure

 of angle ECD

∴ m∠ECD = 5 m∠BCE - 6 ⇒ (1)

∵ m∠BCD = m∠BCE + m∠ECD

∵ m∠BCD = 162°

∴ m∠BCE + m∠ECD = 162 ⇒ (2)

- Substitute equation (1) in equation (2) to replace angle ECD by

  angle BCE

∴ m∠BCE + (5 m∠BCE - 6) = 162

- Add the like terms

∴ 6 m∠BCE - 6 = 162

- Add 6 to both sides

∴ 6 m∠BCE = 168

- Divide both sides by 6

∴ m∠BCE = 28°

- Substitute the measure of angle BCE in equation (1) to find the

  measure of angle ECD

∵ m∠ECD = 5 m∠BCE - 6

∵ m∠BCE = 28°

∴ m∠ECD = 5(28) - 6 = 140 - 6 = 134°

* m∠BCE = 28° and m∠ECD = 134°

3 0
3 years ago
Read 2 more answers
PLEASE HELP FAST...The dot plots show the numbers of children’s books purchased by customers at two different bookstores on one
Katena32 [7]

Answer:

The mode of the data for Store 2 is greater than the mode of the data for Store 1.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • For the differential equation s′′+bs′+6s=0, find all the values of b that make the general solution overdamped, those that make
    6·1 answer
  • 7. Ned took a test with 25 questions. He lost 4
    15·1 answer
  • What's an easier way from multiplication ?
    14·2 answers
  • What is the simplified form of ether following expression ?
    11·2 answers
  • Find a ratio equivalent to<br> 2/2 <br> X <br> 3/6<br> whose second quantity is 1.
    11·1 answer
  • 70% of the magic tricks that Jade knows are card tricks. If she knows 14 card tricks, how many magic tricks does Jade know in al
    10·1 answer
  • A root emerges from a seed because of the force of?
    15·1 answer
  • Please help. I just don’t feel like doing it rn
    8·1 answer
  • What is the area, in square centimeters, of the shape below? Express your answer as a fraction in simplest form.
    11·1 answer
  • What is lim x-&gt;3 x^2+x-12/x^2-3x<br><br> 0<br> 7/3<br> 4<br> DNE
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!