The algebraic expression n<span>/10, where </span>n<span> is the number of boards, represents the number of times he gets 2 free boxes of nails. So 2(</span>n<span>/10), or </span>n/5, is the number of boxes, and 100(n/5), or 20n<span>, is the number of nails. Substituting 90 in for </span>n<span>, Peter will get 1,800 nails.</span>
<u>Explanation</u><u>:</u><u>-</u>
We have given measure of angles of the triangle are in ratio 4 : 7 : 9 and here we need to find the measure of largest angle of a ∆.
Let, the three angles of a triangle be 4x, 7x, 9x.
We know that, Sum of all angles of a triangle is 180°.
4x + 7x + 9x = 180°
⇛20x = 180°
⇛x = 180°:20
⇛x = 9°
Now, finding largest angle by putting the value of “x”
- 4x = 4(9) = 36°
- 7x = 7(9) = 63°
- 9x = 9(9) = 81°
Hence ,the measure of largest angle is 81°.
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Answer:
x = 4 sqrt(5)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
8^2 + x^2 = 12^2
64+ x^2 =144
Subtract 64 from each side
x^2 = 144-64
x^2 =80
Take the square root of each side
sqrt(x^2) = sqrt(80)
x = sqrt(16*5)
x = 4 sqrt(5)
Let us prove that angle 1 is complementary to angle 3 step by step.
1. We have been given that angle 1 is complementary to angle 2.
2. Since we know that complementary angles add up to 90 degrees, therefore, by the definition of complementary
.
3. We have been also given that line segment BD bisects
.
4. By the definition of bisect
.
5. Angles are congruent if their measures, in degrees, are equal, therefore, by angle congruence postulate
.
6. 
Upon substituting
in above equation we will get,
Therefore, by substitution property of equality
.
Hence, proven that angle 1 is complementary to angle 3.