The factors of 33 are <u>1</u>, 3, <u>11</u>, and 33 .
The factors of 55 are <u>1</u>, 5, <u>11</u>, and 55 .
The <u>common</u> factors of 33 and 55 are 1 and 11 .
The<u> greatest</u> one is <em>11</em> .
Yes and no. A negative number and it's opposite are 'integers.' Yes, a negative and a negative multiplied together give you a positive. The two negative signs cancel out making it positive. But no, a positive and a positive multiplied together do not give you a negative. When you subtract positive numbers you can get a negative, but not when multiplying. If you were to do a positive times a negative it would be negative because the positive can't cancel it out. Example: -3 · -3 = 9. [] 3 · 3 = 9. [] -3 · 3 = -9. Other than the positive number part, the statement is true about the negatives. I hope that helped!
Step-by-step explanation:
the introduction of a fraction tells us that we are dealing with multiplications, and therefore a geometric sequence (where every new term is created by multiplying the previous term by a constant factor, the ratio r).
I think your teacher made a mistake, or you made one when typing the question in here.
there is no factor r that creates
15×r = 9
and
9×r = 5/27
it would mean that
15 × r² = 5/27
r² = 5/27 / 15 = 5/27 × 1/15 = 5/405 = 1/81
r = 1/9
but 15 × 1/9 = 5 × 1/3 = 5/3 is NOT 9
and 9 × 1/9 = 9/9 = 1 is NOT 5/27
so, this can't be right.
on the other hand
15 × r = 9
r = 9/15 = 3/5
and then
9 × 3/5 = 27/5
so, either the sequence should have been
15, 5/3, 5/27
or (and I suspect this to be true)
15, 9, 27/5
under that assumption we have
s1 = 15
r = 3/5
sn = sn-1 × r = s1 × r^(n-1) = 15 × (3/5)^(n-1)
s10 = 15 × (3/5)⁹ = 15 × 19683/1953125 =
= 3 × 19683/390625 = 59049/390625 =
= 0.15116544 ≈ 0.151
There is 2 midpoints on a line segment.
Therefore, the answer is b < 7.
