Answer:B
Step-by-step explanation: x is the total .she has only 1/2 hours and she need to complete 6 different stretches so you multiply 1/2 by 6 .Which gives you choice B (x= 1/2 times 6) in total.
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The following integer values of x satisfy the given inequality,
4, 5, 6, 7, 8
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made using inequality.
Solving the Inequality
The given inequality is,
5x + 4 > 19
5x > 19 - 4
5x > 15
x > 15/5
x > 3
So, the required values of x must be greater than 3 in the given interval, [2,8]
Thus, the integer values of x in the the interval [2,8] that satisfy the given inequality are 4, 5, 6, 7 and 8 (∵ Square brackets of an interval denote inclusion of the terminal values).
Learn more about inequality here:
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Diagram for part A and part C is attached herewith.
Solving for part B:-
Given is the circle O. We start with drawing two radii OA and OC, then we join two points A and C to make a chord AC of the circle. Now The radius of the circle intersects the chord AC at point B such that it bisects AC into two equal parts AB and BC. Now we have two triangles ΔOBA and ΔOBC. In these two triangles, we have OA=OC (radii of circle), OB=OB (reflexive property), and BA=BC (given in the question). Using SSS congruency of triangles we can say ΔOBA≡ΔOBC and using CPCTC, we can conclude ∡OBA=∡OBC (=90°). Hence OB⊥AC i.e. OB is perpendicular to AC.
Solving for part D:-
Given is the circle O. We start with drawing two radii OA and OC, then we join two points A and C to make a chord AC of the circle. Now The radius of the circle intersects the chord AC at point B such that AB is perpendicular to AC i.e. ∡B=90°. Now we have two Right triangles ΔOBA and ΔOBC. In these two triangles, we have OA=OC (radii of circle), OB=OB (reflexive property). Using HL congruency of right triangles we can say ΔOBA≡ΔOBC and using CPCTC, we can conclude BA=BC. Hence OB bisects AC into AB=BC.
Answer: 164 students passed and 41 students failed.
Step-by-step explanation:
Let the number of students be x
x students failed, but 4 times the failed students passed.
So 4x students passed and x students failed.
4x + x = 205
5x = 205
x = 205/5
x = 41
41 times 4 is 164 and 41 times 1 is 41.
So 164 students passed and 41 students failed