Step-by-step explanation:
3cm on map = 45 km
1 cm on map = Xkm
Xkm = 45 / 3
Xkm = 15km
Therefore scale = 1:15000
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:
decreasing
Step-by-step explanation:
"Increasing" means the graph is going up from left to right.
"Decreasing" means the graph is going down from left to right.
"Constant" means the graph is "flat" (this is not a technical term) it is keeping the same y value, neither going up nor going down.
What can be super confusing is the
(2.2, 5) mentioned in the question. THIS IS NOT A POINT. It is an interval and points and intervals unfortunately have the same notation sometimes.
An "interval" is a section of the graph, here: FROM 2.2 not including 2.2, TO 5 not including 5. These are like the address on the x-axis. If you look at your graph at 2.2 on the x-axis, it is a peak(relative maximum) and it goes down to the right to where x is 5 where it bottoms out (relative minimum) So on that interval, from 2.2 to 5, the graph is DECREASING.
S^2 + s^2 = 9^2 => 2s^2 = 81 => s^2 = 81/2 => side length s = 9(sqrt(2))/2 = 6.37 cm.
Answer:
Step-by-step explanation:
Hello There!
Once again we need to isolate the variable using inverse operations
to get rid of the -8.2 we add 8.2 to each side
-8.2+8.2 cancels out
-9.7+8.2=-1.5
now we have
-1.2z>-1.5
now we wan to get rid of the -1.2
to do so we want to divide each side by -1.2
Remember we have to flip the inequality sign because we're dividing by a negative number
we're left with
z<1.25
