Answer:
The answer is C
Step-by-step explanation:
it just makes sence,and all the numbers are compatible with each other
Hoped it helped^^
Answer:
Answer: Yes, the diagonals could be 6 and 7 in. In a parallelogram, only the opposite sides of the parallelogram are congruent.
Step-by-step explanation:
Given =
∠lkm = 7x - 5
∠nkm = 3x +9
find = value of∠ lkm.
To proof - let us assume that we takeapoint say n and draw a line nk.
nk is angle bisector it divided angle in two equal parts.
( as shown in the diagram given below)
thus we have
∠lkm = ∠lkn + ∠nkm
7x-5 = 3x+9 +3x +9
x = 23
thus the value of∠ lkm
∠lkm = 7x-5
(put the value of x)
thus
∠lkm = 7×23 - 5
∠lkm = 156°
Answer:
7 )
x = ![\frac{3\sqrt{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Csqrt%7B2%7D%20%7D%7B2%7D)
![y= 3](https://tex.z-dn.net/?f=y%3D%203)
8 )
![x=6\sqrt{6}](https://tex.z-dn.net/?f=x%3D6%5Csqrt%7B6%7D)
![y= 9\sqrt{2}](https://tex.z-dn.net/?f=y%3D%209%5Csqrt%7B2%7D)
Step-by-step explanation:
7 ) 8)
In Δ ABC In Δ XYZ
∠ C = 45° ∠ X = 60°
∠ A = 90° ∠ Y = 90°
![XY= 3\sqrt{6}](https://tex.z-dn.net/?f=XY%3D%203%5Csqrt%7B6%7D)
To Find :
x = ?
y = ?
Solution:
We Know
In Δ ABC
∠ C = 45°
∠ A = 90°
∴ ∠ B = 45° ......Angle sum property of a triangle i.e 180°
∴ Δ ABC is an Isosceles Triangle
∴ AC = AB = x = ![\frac{3\sqrt{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Csqrt%7B2%7D%20%7D%7B2%7D)
Now appplying Trignometry identity we get
![\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2} }{2}\\\\y= 3](https://tex.z-dn.net/?f=%5Csin%20C%20%3D%20%5Cfrac%7B%5Ctextrm%7Bside%20opposite%20to%20angle%20C%7D%7D%7BHypotenuse%7D%5C%5C%5C%5C%5Csin%2045%20%3D%20%5Cfrac%7BAC%7D%7BBC%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20%3D%5Cfrac%7B%5Cfrac%7B3%5Csqrt%7B2%7D%20%7D%7B2%7D%7D%7By%7D%5C%5C%5C%5Cy%3D%5Cfrac%7B3%5Ctimes%20%5Csqrt%7B2%7D%5Ctimes%20%5Csqrt%7B2%7D%20%20%7D%7B2%7D%5C%5C%5C%5Cy%3D%203)
Now In Δ XYZ
∠ X = 60°
∠ Y = 90°
∴∠ Z = 30° . .....Angle sum property of a triangle i.e 180°
Now appplying Trignometry identity we get
![\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}](https://tex.z-dn.net/?f=%5Ctan%20X%20%3D%20%5Cfrac%7B%5Ctextrm%7Bside%20opposite%20to%20angle%20X%7D%7D%7B%5Ctextrm%7Bside%20adjacent%20to%20angle%20X%7D%7D)
![\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\ y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}](https://tex.z-dn.net/?f=%5Ctan%2060%20%3D%20%5Cfrac%7BYZ%7D%7BXY%7D%5C%5C%5C%5C%5Csqrt%7B3%7D%20%3D%5Cfrac%7By%7D%7B3%5Csqrt%7B6%7D%20%7D%5C%5C%20%20y%3D%203%5Csqrt%7B3%7D%20%5Csqrt%7B6%7D%20%5C%5Cy%3D%209%5Csqrt%7B2%7D)
Now,
![\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}](https://tex.z-dn.net/?f=%5Csin%20X%20%3D%20%5Cfrac%7B%5Ctextrm%7Bside%20opposite%20to%20angle%20C%7D%7D%7BHypotenuse%7D%5C%5C%5C%5C%5C%5C%5Csin%2060%20%3D%20%5Cfrac%7BYZ%7D%7BXZ%7D%5C%5C%20%5C%5C%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%3D%5Cfrac%7B9%5Csqrt%7B2%7D%20%7D%7Bx%7D%20%5C%5C%5C%5Cx%3D%5Cfrac%7B18%5Csqrt%7B2%7D%20%7D%7B%5Csqrt%7B3%7D%20%7D%20%5C%5C%5Ctextrm%7Bafter%20fationalizing%20the%20denominator%20root%203%20we%20get%7D%5C%5C%5C%5Cx%3D6%5Csqrt%7B6%7D)
Answer: 0.3413
Step-by-step explanation:
Given: an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds.
Let
.
Let x be the random variable that denotes the amount of newspaper for garbage generated by each household each month.
If the data conforms to a normal distribution and a household is selected at random, the probability of its generating between 28 and 30 pounds per month is about
![P(28](https://tex.z-dn.net/?f=P%2828%3Cx%3C30%29%3DP%28%5Cdfrac%7B28-28%7D%7B2%7D%3C%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3C%5Cdfrac%7B30-28%7D%7B2%7D%29%5C%5C%5C%5C%3DP%280%3Cz%3C1%29%5C%20%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%5C%5C%20%3DP%28z%3C1%29-P%28z%3C0%29%5C%5C%5C%5C%3D0.8413-0.5%3D0.3413)
Hence, the required probability is 0.3413.