Determine whether it is possible to draw a triangle with sides having the given measures. If possible, write yes. If not possible write no and make a sketch demonstrating why it isn’t possible
Answers
Answer: No, it is not possible to form a triangle with these side lengths.
The sketch is provided below
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Explanation:
The triangle inequality theorem says that the sum of any two sides must be larger than the third side.
But notice that 5+6 = 11 which is not larger than 12.
I recommend cutting out slips of paper that are 5 inches, 6 inches and 12 inches long. You can also use software to get the job done, which is what I did. You should see that it is impossible to form a triangle. If you place the 5 inch and 6 inch slips on either end of the 12 inch portion, then you should see the we effectively have an open-ended "triangle". I'm putting it in quotes because we don't have a triangle forming, but instead what looks to be an incomplete version of it.
The sketch of what I'm referring to is shown below. I used Geogebra to make the drawing. Imagine the red and blue segments able to swing freely while the green horizontal segment stays completely still. No matter how the red and blue segments rotate, they will never meet up to form a triangle.
The dashed circles show the range of motion that is possible for each swinging red and blue segment. If the red and blue segments lay perfectly on top of the green segment, they add to 5+6 = 11, which comes up short of the 12 inch segment.
No, it is not possible to draw a triangle with sides measuring 5ft, 6ft, and 12ft.
What is a Triangle?The polygon known as a triangle has three sides and three vertices.
The triangle's total angle is 180 degrees.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
The reason is that according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
However, in this case, 5ft + 6ft = 11ft, which is less than the length of the third side, 12ft.
Therefore, a triangle cannot be formed with these side lengths.
To demonstrate why it isn't possible, you can draw a line segment of length 12ft and label it as the third side of the triangle.
Then, try to draw the other two sides (5ft and 6ft) originating from the same endpoint as the 12ft side.
You will notice that the two sides will never meet to form a triangle, since they are too short to bridge the gap between the two endpoints of the 12ft side.
To learn more about the triangle;
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Related Questions
where is the opposite of the opposite of -1.9 situated on the number line
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Answer:
b
Step-by-step explanation:
HELP!!!!i will give BRAINLIEST
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Answer:
2.9
Step-by-step explanation:
2 9/10 as an improper fraction is 29/10
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What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
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Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
Learn more about quadratic equations here: brainly.com/question/1863222
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I need help for this
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Answer:
not sure
Step-by-step explanation:
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[tex]a = \frac{cde}{b} \\ [/tex]
[tex]c = \frac{ab}{de} \\ [/tex]
[tex] \frac{ab}{e} = cd \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
can someone help me !?
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Y=-8
Z= 1
hope that helps
2 1/7 divided by 1 2/5
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which number are composite numbers-49,35,32,41,47
Answers
Answer:
49, 35, 32
Step-by-step explanation:
A prime number is a number whose factors are 1 and itself
Eg 7
7 is a prime number because it only comes in table one and 7
Or it’s only factors are 1 and itself
A composite number comes in 1, itself and other tables
Eg. 16
It comes in table 1, 2, 4 and 16
Answer: 49,32,35.
Hope this helps!
Mr Thompson wants to cut a 5-ft rope into a 1/4-ft sections how many 1/4 sections will he have
Answers
Answer:
20 pieces of rope
Step-by-step explanation:
Mr. Thompson has a 5-ft rope. If he cuts the rope into 1/4-ft pieces, that means for every foot, there are 4 pieces of rope. There are 5-ft of rope, so we multiply 5 and 4 to get the number of pieces of rope.
5 x 4 = 20 pieces of rope.
I hope that this helps! :)
Ramen noodles. There are 20 ramen noodle packages in a bag. There are 10 beef flavored, and the other 10 are chicken flavored. What is the probability of getting at least one chicken and at least one beef flavor when you grab 3 packages randomly?
Answers
Answer:
0.789
Step-by-step explanation:
Number of beef flavored Ramen noodles = 10
Number of chicken flavored Ramen noodles = 10
Total number of noodles = 20
Number of ways to select 3 packages:
[tex]_{20}C_3= \dfrac{20\times 19\times 18}{3\times 2\times 1}=1140[/tex]
Number of ways to select two beef flavored Ramen noodle = [tex]_{10}C_2[/tex] = 45
Number of ways to select one chicken flavored Ramen noodle = 10
Number of ways to select two chicken flavored Ramen noodle = [tex]_{10}C_2[/tex] = 45
Number of ways to select one chicken flavored Ramen noodle = 10
Total number of ways so that one chicken and one beef Ramen selected = 450 + 450 = 900
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Required probability is:
[tex]\dfrac{900}{1140} = 0.789[/tex]
Convert 12 ounces to pounds use the conversion rate 16 ounces = 1 pound
Answers
Answer:
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Step-by-step explanation:
12/ 16
÷4 on top and bottom
Answer:
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Step-by-step explanation:
GIVING BRAINLIEST IF CORRECT PLEASE HELP ASA[P
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Answer:
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Step-by-step explanation:
I'm sorry if I'm getting this whole concept wrong cause it felt way too easy to be right so I'm sorry if you get it wrong.
The reason the first question is 8 is because of the fact that you first have to add the students charted on the Venn-diagram and subtract that from 55, getting you to 8 students.
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Same thing for part two except the fact that you have to add the students who only passed one subject, so combine 17 and 11, getting you to 28, thus getting the answer 28/55.
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What is the perimeter of an equilateral triangle which has an area of 96\sqrt{3}96
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Step-by-step explanation:
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Write the next three terms in each sequence. Make sure your
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Answer:
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HELP PLEASE!!!!! I ONLY HAVE 10 MIN FOR 3 QUESTIONS
Jo estimated the quotient of –41.71 divided by –6.03 by rounding each to the nearest integer. What is Jo’s error?
Negative 42 divided by negative 7 = 6
Jo should have rounded the dividend to –40.
Jo should have rounded the divisor to –6.
Jo should have divided –7 by –42.
Jo should have divided –7 by –7.
Answers
Answer:
Its Jo should have rounded the divisor to –6.I cant see Jo's error...but the correct way is this :
-41.71 rounds to -42
-6.03 rounds to -6
so the quotient is : -42/-6 = 7 <==Step-by-step explanation:
brainliest would be nice!
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Step-by-step explanation:
if im wrong im wrong dont yell at me
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Step-by-step explanation:
Mathematics value in words
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When full, a cinema house has n people. When 280 people have taken seat the remaining seats comes to $384 if each tickets cost $1.20 find the number of seats in the cinema house?
Answers
Answer: 600 seats
Step-by-step explanation:
384/$1.20 = 320 seats
N - 280 = 320
+280. +280
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The total number of seats in the cinema house will be 600 seats.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
When full, a cinema house has n people. When 280 people have taken a seat the remaining seats come to $384 if each ticket cost $1.20.
Then the total number of seats in the cinema house will be given as,
⇒ 280 + $384 / $1.20
⇒ 280 + 320
⇒ 600 seats
The total number of seats in the cinema house will be 600 seats.
More about the Algebra link is given below.
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If you use 12g of Kool-Aid powder to make 5 liters of juice, how many grams of powder will it take to make 20 liters of juice?
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
62 is divisible by which of the following numbers? (1 point)
O 1, 3, 31, 62
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Step-by-step explanation:
Unit review practice: (from connexus)
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(0,-9) (3, -4) (-3,-14)
Plug those points in and draw a straight line going through them that should be your graph :)
Talya wanted to hit 20 homeruns this season. She ended up hitting 150% of her goal. How many homeruns did Talya hit this season?
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Answer:
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Step-by-step explanation:
tell me if im wrong
sorry if i am TmT
I don’t understand plz help me
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Answer:
C×6=D
Step-by-step explanation:
You don't know her me calculators they have or they bought so you take C for the calculators multiply by 6 and D is the product or answer.
Select all simplified expressions of 3^4 ÷ 3^9.
3^13
3^5
1/243
1/3^5
1^5
Answers
Explanation
Subtract the exponents
Since the exponent is negative
It stays in the bottom hence why the one is added
Three cards—one red, one green, and one blue—are to be arranged in a stack. Using R for red, G for green, and B for blue, make a list of all the different stacks that can be formed. (Some computer monitors are called RGB monitors for the colors red, green, and blue. Enter your answers as a comma-separated list.)
Answers
Answer:
RGB. RBG, BRG, BGR, GBR, GRB
Step-by-step explanation:
Given
R, G and B
Required
List all possible arrangement
First, we need to calculate the number of arrangement
There are 3 letters and they are to be arranged in order of 3.
So, we have:
[tex]n = 3[/tex] and [tex]r =3[/tex]
Number of arrangement is:
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
[tex]^3P_3 = \frac{3!}{(3 - 3)!}[/tex]
[tex]^3P_3 = \frac{3!}{0!}[/tex]
[tex]^3P_3 = \frac{3*2*1}{1}[/tex]
[tex]^3P_3 = \frac{6}{1}[/tex]
[tex]^3P_3 = 6[/tex]
Hence, number of arrangements is 6 and the arrangements are:
RGB. RBG, BRG, BGR, GBR, GRB
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
two to the seven eighths power, all over two to the one fourth power
the eighth root of two to the fifth power
the fifth root of two to the eighth power
the square root of two to the five eighths power
the fourth root of two to the sixth power
Answers
Answer:
Eight root of to the fifth power.
Step-by-step explanation:
2^7/8 / 2^1/4
= 2^(7/8 - 1/4)
= 2^5/8
= eight root of to the fifth power.
Answer:
the eighth root of 2 to the fifth power .
