Answer:
13 cms
Step-by-step explanation:
By Pythagoras:-
x^2 = 12^2 + 5^2
x^2 = 144 + 25
x^2 = 169
x = √169
= 13
The nearest thousand is 547,000
Answer:
yes
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem, so the triangle is a right triangle.
7.5² +10² = 12.5²
56.25 +100 = 156.25
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You may recognize that the ratios of side lengths are ...
7.5 : 10 : 12.5 = 3 : 4 : 5
A 3-4-5 triangle is a well-known right triangle, as this is the smallest set of integers that satisfy the Pythagorean theorem. They also happen to be consecutive integers, so form an arithmetic sequence. Any arithmetic sequence that satisfies the Pythagorean theorem will have these ratios.
_____
If you're familiar with trigonometry, you know the law of cosines tells you ...
c² = a² + b² - 2ab·cos(θ) . . . . where θ is the angle between sides a and b. This reduces to the Pythagorean theorem when θ=90°, which makes cos(θ)=0. If the sides do not satisfy the Pythagorean theorem, cos(θ)≠0 and the triangle is not a right triangle.
Answer:
a₆ ≈ 25.284
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
8 ÷ 6 = 
÷ 8 = 
This indicates the sequence is geometric with nth term
= a₁ 
where a₁ is the first term and r the common ratio
Here a₁ = 6 and r = , then
a₆ = 6 × 
= 6 × 
= 
≈ 25.284 ( to the nearest thousandth )
The correct answer is two thirds
