Answer:
XZ > XY > YZ
Step-by-step explanation:
1. Approach
To solve this problem, one must find the value of (x), then the measure of every angle in the triangle. Remember, the sum of all angles in a triangle is equal to 180 degrees. Another property of a triangle is that the largest side of a triangle will be opposite the largest angle of the triangle, conversely, the smallest side of a triangle will be opposite the smallest angle in the triangle.
2. Find the value of (x)
The sum of all angles in a triangle is equal to 180 degrees. Using this theorem, one can state,
m<X + m<Y + m<Z = 180
Substitute,
(50) + (5x + 10) + (5x) = 180
Simplify,
10x + 60 = 180
Inverse operations,
10x + 60 = 180
-60 -60
10x = 120
/10 /10
x = 12
3. Find the measure of each angle
Now substitute the value of (x) into the expressions given to represent the value of each angle.
m<X = 50
m<Y = 5x + 10 = 5(12) + 10 = 60 + 10 = 70
m<Z = 5x = 5(12) = 60
4. Now apply this to find the comparative lengths of the sides
One property of a triangle is that the side opposite the largest angle in the triangle is the largest side. Moreover, the side opposite the smallest angle in a triangle is the smallest side. In this problem, it is impossible to find the exact lengths of the sides of the triangle, but one can find out which side is larger or smaller than the other side.
m<Y = 70
m<Z = 60
m< X = 50
<u>m<Y</u> > <u>m<Z</u> > <u>m<X</u>
Side XZ is opposite m<Y
Side XY is opposite m<Z
Side YZ is opposite m<X
This means,
XZ > XY > YZ
Answer:
c. 198 square feet
Step-by-step explanation:
Based on the picture I'm thinking the length of each line segment is 3ft, so each 'tile' on the surface of the figure is 9sqft.
Looking at the figure from the front and back you would see 4 tiles from each direction, same from the top and bottom (so far we have front + back + top + bottom = 4 + 4 + 4 + 4 = 16 tiles)
Looking directly from either side you would see 3 tiles each way, for 6 more tiles total, so the total number of tiles covering the figure is 16 + 6 = 22 tiles
Each tile is 9sqft, so total area is 22(9) = 198 sqft
Answer:
C.2
Step-by-step explanation:
(a) Plan b costs more by $10
(b) $275, Plan A will cost more
Answer:
1.6 meters per second.
Step-by-step explanation:
We have been given an position function and we are asked to find the speed of the rock after 1 second.
Derivative of this function will give us speed function.
Now let us find derivative when t=1,
Therefore, the speed of the rock after 1 second will be 1.6 meters per second.