Answer:
The answer is given below
Step-by-step explanation:
From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.
The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠BYZ and ∠DZY are interior angles.
∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)
∠BYZ/2 + ∠DZY/2 = 180/2
∠BYZ/2 + ∠DZY/2 = 90°
In ΔOYZ:
∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).
But ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180
90 + ∠YOZ = 180
∠YOZ = 180 - 90
∠YOZ = 90°
Therefore Angle bisectors of the same side interior angles are perpendicular.
Basic Pay = $40
Commission for 1 pair of shoes = $4.50
Let x be the number of shoes he needs to sell.
40 + 4.5x ≥ 112
4.5x ≥ 72
x ≥ 16
Answer: He must sell at least 16 pairs of shoes.
Answer:
<em>h = 8.54 units</em>
Step-by-step explanation:
<u>The Law of Cosines
</u>
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
Since we know the values of all three side lengths, we solve the equation for x:
For the triangle ABC in the image, a=10, b=15, c=13, thus:
Thus, A = 58.67°
For the right triangle of height h and hypotenuse 10, we use the sine ratio:
Solving for h:
h = 8.54 units
Answer:
Please see below :)
Step-by-step explanation:
Integers - Whole numbers (no fractions or decimals!)
11 to 111
12, 14, 16, 18, 20
22, 24, 26, 28, 30
32, 34, 36, 38, 40
42, 44, 46, 48, 50
52, 54, 56, 58, 60
62, 64, 66, 68, 70
72, 74, 76, 78, 80
82, 84, 86, 88, 90
92, 94, 96, 98, 100
102, 104, 106, 108, 110
Hope this helped!
Answer:
If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).
Step-by-step explanation:
We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.
The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:
Then, we can express one side in function of the other as:
Then, if we define b, we get the value of a that satisfies the equation.
A graph of values of a and b is attached.
If both side a and b are integers, we can see in the graph that are only two solutions: (b=4, a=6) and (a=4, b=6).
