“if it is a regular hexagon, then it has exactly 6 congruent sides.”
“it is a hexagon” being your hypothesis (p)
“it has exactly 6 congruent sides” being your conclusion (q).
hope this helps :)
Answer:
22 2/9
Step-by-step explanation:
When z "varies jointly" with x and y, it can be described by the formula
z = kxy
Here, we have bags of mulch (n) varying jointly with area (a) and depth (d), both in feet. The given information can let us find the value of k.
n = kad
10 = k·(120)(1/4)
10/30 = k = 1/3 . . . . . divide by the coefficient of k
Now, we can fill in the other values of interest.
n = (1/3)·(200)·(1/3) = 200/9
n = 22 2/9
You need 22 2/9 bags of mulch to cover 200 ft² to a depth of 4 inches.
_____
<em>Comment on the problem</em>
This problem requires the formula be written with both area and depth expressed in feet, yet it gives depth in inches. The formula can also be written using depth in inches. In that case, k = 1/36.
(-6)(-0.4)(-0.5) = (-1)6⋅4⋅5⋅10⁻² = -1.2
(3 cos x-4 sin x)+(3sin x+4 cos x)=5
(3cos x+4cos x)+(-4sin x+3 sin x)=5
7 cos x-sin x=5
7cos x=5+sin x
(7 cos x)²=(5+sinx)²
49 cos²x=25+10 sinx+sin²x
49(1-sin²x)=25+10 sinx+sin²x
49-49sin²x=25+10sinx+sin²x
50 sin² x+10sinx-24=0
Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100
We have two possible solutions:
sinx =(-10-70)/100=-0.8
x=sin⁻¹ (-0.8)=-53.13º (360º-53.13º=306.87)
sinx=(-10+70)/100=0.6
x=sin⁻¹ 0.6=36.87º
The solutions when 0≤x≤360º are: 36.87º and 306.87º.
