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1 answer:
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The sum of the interior angles of a triangle is 180 degrees.
1.) Translating the problem into equation:
7:11:12 = 180 degrees
7x+11x+12x = 180 degrees; Where x = missing number
30x = 180
30x/30 = 180/30 divide both sides by 30
x = 6
2.) Substitute the values:
7x+11x+12x = 180
7(6)+11(6)+12(6) = 180
42+66+72 = 180
180 = 180
3.) Therefore, the angles should be 42 degrees, 66 degrees and 72 degrees.
4.) See attached drawing of triangle
1.) Translating the problem into equation:
7:11:12 = 180 degrees
7x+11x+12x = 180 degrees; Where x = missing number
30x = 180
30x/30 = 180/30 divide both sides by 30
x = 6
2.) Substitute the values:
7x+11x+12x = 180
7(6)+11(6)+12(6) = 180
42+66+72 = 180
180 = 180
3.) Therefore, the angles should be 42 degrees, 66 degrees and 72 degrees.
4.) See attached drawing of triangle
Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
=
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and = 345, thus
[ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = -
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10