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Luden [163]
3 years ago
5

Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the

measure of each angle of the triangle.
Mathematics
1 answer:
zimovet [89]3 years ago
8 0
<span>Draw a triangle and label is ABC.
Let angle A = x
let angle B = x
let angle C = 2x - 36
2x - 36 means that angle C is 36 degrees less than the sum of angle A and B.
Since the sum of the interior angles of a triangle is 180 degrees, then 2x + 2x - 36 = 180.

combine like terms in that equation and you get 4x - 36 = 180
add 36 to both sides of that equation and you get 4x = 216
divide both sides of that equation by 4 and you get x = 54 degrees
angle A = 54 degrees
angle B = 54 degrees
angle C = 108 - 36 = 72 degrees
54 + 54 + 72 = 108 + 72 = 180 degrees so the angles are good because they add up to 180 degrees and the third angle is 36 degrees less than the sum of the other 2. </span>
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Can someone please help me factor this
Dmitry_Shevchenko [17]

Answer:

\huge\boxed{\bf\:1}

Step-by-step explanation:

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }

Take \frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  } & factorise it at first.

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}

Now factorise the next set : \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }.

\frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\=  \frac{x-4}{x-1}

Now, multiply the two simplified results.

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}

\rule{150pt}{2pt}

7 0
2 years ago
Please Help !!!!!!!!
sdas [7]
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area of the cone base: pi*3*3
they are equal, so 9pi=(1/2)*3.3x
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4 0
3 years ago
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2. After the American Revolution why was there a need to establish a stable banking system?
lora16 [44]

Answer:

Federalists wanted a

centralized banking

system and Alexander

Hamilton, as Secretary of

the Treasury, proposed a

national bank in 1789.

• Antifederalists, like

Thomas Jefferson,

opposed this plan.

– They favored a

decentralized banking

system in which states

established and

regulated banks within

their borders.

Step-by-step explanation:

5 0
3 years ago
Find the midpoint of the segment with the given endpoints. (9.-9) and (2.-10)​
kondor19780726 [428]

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{(5.5 \: , \: -  9.5)}}}}}

Step-by-step explanation:

Let the points be A and B

Let A ( 9 , -9 ) be ( x₁ , y₁ ) and B ( 2 , - 10 ) be ( x₂ , y₂ )

<u>Finding</u><u> </u><u>the</u><u> </u><u>midpoi</u><u>nt</u>

\boxed{ \sf{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} }}

\longrightarrow{ \sf{midpoint = ( \frac{9 + 2}{2} , \:  \frac{ - 9  + ( - 10)}{2}}} )

\longrightarrow{ \sf {midpoint = ( \frac{11}{2} \: , \:  \frac{ - 9 - 10}{2}})}

\longrightarrow{  \sf{midpoint = (5.5 \: , \:  \frac{ - 19}{2}}} )

\longrightarrow{ \sf{midpoint = (5.5 \: , - 9.5}})

Hope I helped!

Best regards! :D

5 0
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Given function: f(x) = (3x+5)/7

y = f(x) so it's the same as y = (3x+5)/7

Swap every copy of x and y to get x = (3y+5)/7

Solve for y to get....
x = (3y+5)/7
7x = 7*(3y+5)/7
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3y/3 = (7x-5)/3
y = (7x-5)/3

So the inverse function is f^(-1)(x) = (7x-5)/3

Answer is choice A


5 0
3 years ago
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