A forest covers 77,000 acres. A survey finds that 0.7% of the forest is old-growth trees. How many acres of old-growth trees
2 answers:
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Answer:
The height of the larger traffic signs is 51.96 inches
Step-by-step explanation:
Given that initially, A company makes traffic signs of an equilateral triangle with the perimeter of 144 inches
Now, A company makes similar traffic signs of perimeter 1.25 of original
New perimeter will be 1.25x144=180 inches
Let triangle ABC be a larger triangle with 180inches of the perimeter.
It is given that the triangle is an equilateral triangle,
Therefore, Side AB=BC=AC
The perimeter of a triangle ABC is
AB+BC+AC=180
3AB=180
AB=60 inches
Figure show that triangle ABC and AD is the height of the triangle.
Since, the triangle ABC is an equilateral triangle,
AD is the perpendicular bisector of BC
so that,
BD=DC and Angle ADB=90
In right triangle ADB,
Angle D =90 and Angle B =60
Side BD=60/2=30 inches and AB=60 inches
Using Pythagoras theorem,
AD=51.96 inches
Thus, The height of the larger traffic signs is 51.96 inches
Answer:
Step-by-step explanation:
As 2 and 7 are the only prime divisors of both and
we know that both can be written as:
Where is the set of all natural numbers adding the zero (careful because this part is important as I'll explain next).
We also know that 14 divides both numbers and that is actually the greatest common divisor between them. So we can rewrite a and b as follows:
Why do I write them like this? Because this way is easier to observe that if and
were both greater than zero, then 28 would divide both hence 14 wouldn't be their g.c.d.. Likewise, if
and
were both greater than zero, then 98 would divide both and once again, 14 wouldn't be their g.c.d.
So either of them has to be equal to zero. And then we have that
All we have left to do is find the possible values for and
so that
and that only happens if
and