Question 1)
2 answers:
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Answer:
∠B ≅ ∠Y △ABC ~ △ZYX by the SAS similarity theorem.
Step-by-step explanation:
1. units
units
units
units, then
2. and
are right angles - given
3. two right angles are always congruent.
4. by SAS similarity theorem.
SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
(a) The probability that there is no open route from A to B is (0.2)^3 = 0.008.
Therefore the probability that at least one route is open from A to B is given by: 1 - 0.008 = 0.992.
The probability that there is no open route from B to C is (0.2)^2 = 0.04.
Therefore the probability that at least one route is open from B to C is given by:
1 - 0.04 = 0.96.
The probability that at least one route is open from A to C is:
(b)
α The probability that at least one route is open from A to B would become 0.9984. The probability in (a) will become:
β The probability that at least one route is open from B to C would become 0.992. The probability in (a) will become:
Gamma: The probability that a highway between A and C will not be blocked in rush hour is 0.8. We need to find the probability that there is at least one route open from A to C using either a route A to B to C, or the route A to C direct. This is found by using the formula:
Therefore building a highway direct from A to C gives the highest probability that there is at least one route open from A to C.
Therefore the probability that at least one route is open from A to B is given by: 1 - 0.008 = 0.992.
The probability that there is no open route from B to C is (0.2)^2 = 0.04.
Therefore the probability that at least one route is open from B to C is given by:
1 - 0.04 = 0.96.
The probability that at least one route is open from A to C is:
(b)
α The probability that at least one route is open from A to B would become 0.9984. The probability in (a) will become:
β The probability that at least one route is open from B to C would become 0.992. The probability in (a) will become:
Gamma: The probability that a highway between A and C will not be blocked in rush hour is 0.8. We need to find the probability that there is at least one route open from A to C using either a route A to B to C, or the route A to C direct. This is found by using the formula:
Therefore building a highway direct from A to C gives the highest probability that there is at least one route open from A to C.
Answer:
The value of k is 3.
Step-by-step explanation:
The function f(x) passes through the points (0,4) and (-6,-2)
So the equation of the function is
⇒ y = x + 4 ....... (1)
Again the function g(x) passes through the points (0,4) and (-2,-2).
Therefore, the equation of g(x) will be
⇒ y = 3x + 4
Therefore, g(x) = 3x + 4 = f(3x) {from equation (1).
So, the value of k is 3. (Answer)