5. Circle A has a radius of 9 units . Point R lies 5 units away from A. A chord drawn through R is partitioned by the diameter of A passing through R into two segments, one of which has a length of 7 units. Is the length of the other segment longer or shorter than 7 units ? Justify your answer.

The length of the other segment is longer than 7 units

Step-by-step explanation:

we know that

The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal

see the attached figure to better understand the problem

Remember that the diameter of the circle is two times the radius

Let

x ----> the length of the other segment

so

therefore

The length of the other segment is longer than 7 units

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: