Question
A ladder 20 m long rests against a vertical wall. If the foot of the ladder is 12 m away from the base of the wall, the height of the point on the wall where the top of the ladder reaches is ……..
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: the height of the point on the wall where the top of the ladder reaches is 16 m.
Here, Length of base(b) = 12 m
Length of hypotenuse(d) = 20 m
Let’s say that the height of the wall is given as h
Using Pythagoras theorem
d2 = h2 + b2
202 = h2 + 12
h2 = 202 - 122
d = 
= 16 m
Final Answer:
Hence, the height of the point on the wall where the top of the ladder reaches is 16 m.
= 16 mFinal Answer:
Hence, the height of the point on the wall where the top of the ladder reaches is 16 m.
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Solve 2x-3 > 5 or 3x-1 < 8 , graph the solution.
A compound inequality is a clause that consists of two inequality statements connected by the words "or" or "and." The conjunction "and" indicates that the compound sentence's two statements are true simultaneously. It is the point at which the solution sets for the various statements overlap or intersect.
¶A type of inequality with two or more parts is a compound inequality. These components may be "or" or "and" statements. If your inequality reads, "x is greater than 5 and less than 10," for instance, x could be any number between 5 and 10.
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Describe each solution as a set. Is one set a subset of the other? Explain your answer.
A compound inequality is a sentence that contains two inequality statements separated by the words "or" or "and." The term "and" indicates that both of the compound sentence's statements are true simultaneously. The intersection of the solutions of two inequalities joined by the word and the solution of a compound inequality. All of the solutions having the two inequalities in common are the solutions to a compound inequality, where the two graphs overlap, as we saw in the previous sections.
¶The graph of a compound inequality with a "and" denotes the intersection of the inequalities' graphs. If a number solves both inequalities, it solves the compound inequality. It can be written as x > -1 and x < 2 or as -1 < x < 2.
¶Graph the compound inequality x > 1 AND x ≤ 4.
Consider the solutions of the compound inequalities.
4 < x < 8 2 < x < 11
Describe each solution as a set. Is one set a subset of the other? Explain your answer.
A compound inequality is a sentence that contains two inequality statements separated by the words "or" or "and." The term "and" indicates that both of the compound sentence's statements are true simultaneously. The intersection of the solutions of two inequalities joined by the word and the solution of a compound inequality. All of the solutions having the two inequalities in common are the solutions to a compound inequality, where the two graphs overlap, as we saw in the previous sections.
¶The graph of a compound inequality with a "and" denotes the intersection of the inequalities' graphs. If a number solves both inequalities, it solves the compound inequality. It can be written as x > -1 and x < 2 or as -1 < x < 2.
¶Graph the compound inequality x > 1 AND x ≤ 4.
