Part A)<span>In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
we know that
</span>cos 45°=√2/2
[he length of the hypotenuse]=11/cos 45-----------> 11/(√2/2)----> (11*2)/√2
=22/√2-------> 11√2 in
the answer Part A) is 11√2 in
Part B) <span>What is the exact value of sin 45° ?
</span>
we know that
sin 45°=11/(11√2)-------> 1/√2---------> (1/√2)*(√2/√2)-----> √2/2
the answer part b) is √2/2
Part C)
<span>What is the area of a regular hexagon with a side length of 4 m?
we know that
</span>In case of a regular hexagon <span> each of the six triangles that are formed by connecting its center with all six vertices is an equilateral triangle with a side equaled to 4 m.
The area of this hexagon is six times greater than the area of such a triangle
</span>
In an equilateral triangle with a side d<span>
the altitude </span>h can be calculate from the Pythagorean Theorem as
h²=d²−(d/2)²=(3/4)d²
<span>Therefore,
</span><span>h=d<span>√3/2
</span></span><span>Area of such a triangle is
</span>A=d*h/2------------> d²*√3/4
From this the area of the regular hexagon with a side d<span> is
</span>S=6*A----------> d²3√3/2
for d=4 m
S=4²3√3/2------> 24√3 m²------------> 41.57 m²
the answer Part C) is 41.57 m²
Part D) <span>In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
</span>[he length of the hypotenuse]=5/sin 30--------> 5/(1/2)---------> 10 cm
the answer part D) is 10 cm
Answer:
X=1/2
Step-by-step explanation:
-2x1/2=-1
-2x1=-2
-1+-2=-3
5 is a prime number because there's no number that can go into 5 but 1 and 5
- -5 is always smaller than -4. So, x might be -4. So, A is an option you should select.
- 2 is greater than -4. So, x might be -4. So, B is an option you should select.
- If we place -4 in x, we get 3(-4)+4, i.e., -12 + 4 = -8. So, 3x + 4 = -8. Therefore, you cannot select C because it cannot be greater than, it should be always equal to.
- 5(-4) = -20, 2(-4) - 3 = -8 -3 = -11. -11 is greater than -20 but they are never equal. So, you cannot select D.
- 4 - 2(-4) = 4 + 8 = 12. 12 is greater than -6. Therefore, you should select E.
<u>Answer</u>
<u>A,</u><u> </u><u>B,</u><u> </u><u>E.</u>
Hope you could get an idea from here.
Doubt clarification - use comment section.
