Answer:
3) 16.2
Step-by-step explanation:
The supplement to the 115° angle on the right is 65°, the same as the angle at upper left. The vertical angles at C are the same measure, so this tells you that the two triangles FCB and ACD are similar by the AA similarity postulate. That being the case, corresponding sides are proportional:
CB/CD = CF/CA
CB = CD·CF/CA = 7.2·21.6/9.6
CB = 16.2
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When given two "point-to-point" triangles like this, quite often there is some sort of similarity relationship involved. First, you need to figure out what it is; then you need to make use of it as needed to answer the question being asked.
Answer:
We must add 400 ml of water.
Step-by-step explanation:
We can use the following equation:
Where:
- C(i) is the initial concentration of the solution (80%)
- C(f) is the final concentration of the solution (30%)
- V(i) is the initial volume (150 ml)
- V(f) is the final volume
Now, we just need to solve the equation for V(f).
Therefore, we must add 400 ml of water.
I hope it helps you!
In a throw of 2 fair dice, there are 6*6=36 equiprobability outcomes.
To get a sum of 5, there are 4 ways, (1,4),(2,3),(3,2),(4,1) with probability of 4/36=1/9
To get at least one 5, there are 6+6-1=11 outcomes (note (5,5) has been counted in both, so subtracted from sum). The probability is 11/36
Since the two events are mutually exclusive (once we have a five, the sum can no longer be 5), we can add the probabilities to get the probability of one event or the other.
P(sum of 5 OR at least one 5)=1/9+11/36=4/36+11/36=15/36=5/9
The length of the painting is 91 centimeters.
