The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
Answer:
x=-27, y=-15
Step-by-step explanation:
In the attached file
Answer:
The number of children's tickets sold was 27
Step-by-step explanation:
Let
x ----> the number of children's tickets sold
y ----> the number of adult's tickets sold
we know that
----> equation A
----> equation B
Solve the system by substitution
Substitute equation B in equation A
solve for x
therefore
The number of children's tickets sold was 27
Answer:
B. 5 rolls
Step-by-step explanation:
The areas of the room, not including the ceiling, are discriminated as follows:
Longer walls: 
(6 inches equals one foot)
Shorter walls: 
(6 inches equals one foot)
Window area: 
Door area: 
Area that will be effectively covered:
Total area to wallpaper: 
Amount of paper needed: 
That is, the area of a roll of paper is 
Number of rolls needed:
rolls
Answer:
x=8
Step-by-step explanation:
9x - 8 = 64 (being vertically opposite angles)
9x = 64 + 8
x=72/9
x=8
9x -8
9*8 -8
72-8
64
