Each pair of polygons is similar. Find the value of x.
1 answer:
Answer:
The value of x is 1.5
Step-by-step explanation:
<em>In similar figures, corresponding sides have the same ratio</em>
In the given figure
∵ There are 2 similar polygons
∴ We must write their names with corresponding angles
∵ ∠A = ∠L, ∠B = ∠M, ∠C = ∠N, ∠D = ∠P
∴ Their names are ABCD and LMNP
→ By using the rule above
∴ Their corresponding sides have the same ratio
∴ =
∵ AB = 14 and LM = x + 9
∵ BC = 10 and MN = x + 6
→ Substitute them in the ratio up
∴ =
→ By using the cross multiplication
∵ 14 × (x + 6) = 10 × (x + 9)
∴ 14(x) + 14(6) = 10(x) + 10(9)
∴ 14x + 84 = 10x + 90
→ Subtract 10x from both sides
∵ 14x - 10x + 84 = 10x - 10x + 90
∴ 4x + 84 = 90
→ Subtract both sides by 84
∵ 4x + 84 - 84 = 90 - 84
∴ 4x = 6
→ Divide both sides by 4 to find x
∴ x = 1.5
∴ The value of x is 1.5
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Answer:
Probability = 0.190
Step-by-step explanation:
Given:
Number of questions, 'n' = 20
Each question has four choices.
Let event of choosing correct answer be success and its probability be represented by 'p'.
Therefore, event of choosing wrong answer is failure and its probability be represented by 'q'.
Now, probability of success is choosing one correct answer out of 4 options. So,
Now, 'p' and 'q' are complements of each other. Therefore,
Now, we need 4 successes. Therefore,
Using Bernoulli's theorem to find 'x' successes from 'n' questions, we get:
Plug in 4 for 'x', 20 for 'n', 0.25 for 'p' and 0.75 for 'q'. Solve.
Therefore, the probability of getting 4 correct answers out of 20 questions is 0.190.