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Vilka [71]
2 years ago
10

Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning.

Mathematics
1 answer:
STALIN [3.7K]2 years ago
5 0

A. it forms a triangle

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Plss answer!! <br>MERRY Christmas!!! <br>Critical Question. AAAAA​
liberstina [14]

Answer:

Step-by-step explanation:

abc = 1

We have to prove that,

\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1

We take left hand side of the given equation and solve it,

\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}

Since, abc = 1,

\frac{1}{c}=ab and c = \frac{1}{ab}

By substituting these values in the expression,

\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}

                                       =\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}

                                       =\frac{1+b+ab}{1+b+ab}

                                       =1

Which equal to the right hand side of the equation.

Hence, \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1

5 0
3 years ago
-6x-y=11<br> What’s the answer?
Serhud [2]

Answer:

_6x-y=11/ 6x+y+11=0 this is the answer

3 0
3 years ago
Read 2 more answers
James knows that when he walks, he takes about 120
Tpy6a [65]

Answer:

speed of James is: 3.75 miles/hour.

Step-by-step explanation:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

19800feet=\frac{19800}{5280} miles=3.65miles

hence speed of James= (distance covered by james in 1 hour)/1 hour

speed of James=3.75 miles/hour.

Thanks!!

Mark me brainliest!

~FieryAnswererGT~

7 0
2 years ago
Read 2 more answers
In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak
Svetradugi [14.3K]

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Information \: provided \:  with  \: us }}}}}\: \bigstar}

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{What \: we \:  have  \: to \: find ? }}}}}\: \bigstar}

➻ The required number of people who can speak both English and Spanish .

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}

<u>Consider</u> ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}

  • ➻ n (A) = 27

  • ➻ n (B) = 25

  • ➻ n (A∪B) = 40

  • ➻ n(A∩B) = ?

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}

∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>

━━━━━━━━━━━━━━━━━━━━━━

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

━━━━━━━━━━━━━━━━━━━━━━

6 0
2 years ago
What is the solution to the system of equations? you must show all work to recieve full credit!
earnstyle [38]
Use the substitution method:
2x - 6y = -12
x - 2y = -8
Then x = 2y - 8
Substitute in the first equation:
2(2y - 8) - 6y = -12
4y - 16 - 6y = -12
-2y = 4
y = -2
Now substitute y in one of the two equations given you prefer:
For example x-2*(-2) = -8
x + 4 = -8
x = -12
The solutions are x = -12 and y = -2
5 0
3 years ago
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