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Crazy boy [7]
3 years ago
13

PLZZ HELPPP!!

Mathematics
1 answer:
MAXImum [283]3 years ago
4 0
We need to find 2 digit numbers (10-99) each of which has 
a) 8 divisors
b) 9 divisors
 
Here's what I found:
For 8 divisors, the number must have
    a. 3 distinct prime factors, or
    b. of the form {p^3, q}
    which are:
2^3*3=24 (1,2,3,4,6,8,12,24)
2*3*5=30 (1,2,3,5,6,10,15,30)
2^3*5=40 (1,2,4,5,8,10,20,40)
2*3*7=42 (1,2,3,6,7,14,21,42)
2*3^3=54 (1,2,3,6,9,18,27,54)
2^3*7=56 (1,2,4,7,8,14,28,56)
2*3*11=66 (1,2,3,6,11,22,33,66)
2^3*11=88 (1,2,4,8,11,22,44,88)
2*3*13=78 (1,2,3,6,13,26,39,78)
2*5*7=70 (1,2,5,7,10,14,35,70)

For 9 divisors, it is necessary that the 2-digit number be a perfect square, and the square-root is composite.
For this, we can list only
(2*3)^2=36  (1,2,3,4,6,9,12,18,36)

So there are 10 2-digit numbers with 8 factors, and 1 with 9 factors.

Note: looks like 72 has 12, the most factors in two digit numbers:
72 (1,2,3,4,6.8,9,12,18,24,36,72)
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andrew-mc [135]
B. The equation is 4x = -48. Ben’s point total is -12.
6 0
2 years ago
A rectangle has a height of w^2+3w+9 and a width of w^2+2 express the area of the entire rectangle
lara31 [8.8K]

Answer:

w⁴ + 3w³ + 11w² + 6w + 18

Step-by-step explanation:

Rectanle area = height * width

area = (w²+3w+9)(w² + 2)

        = w²*w² + w²*2 + 3w*w² + 3w*2 + 9*w² + 9*2

        = w⁴ + 2w² + 3w³ + 6w + 9w² + 18

        = w⁴+ 3w³ + (9w²+2w²) + 6w + 18

        = w⁴ + 3w³ + 11w² + 6w + 18

6 0
3 years ago
Read 2 more answers
How much is (2^2)<<1
Musya8 [376]
It's 2.
<< is bit operation to move one left, so it's similiar to divide by 2,
2*2/2 = 2
6 0
3 years ago
What is the answer to this?
Vsevolod [243]

Answer:

option (3) y≥7

Step-by-step explanation:

|x-1|≥0

|x-1| +7≥0+7

y≥7

5 0
3 years ago
PLEASEE HELP AND SHOW WORK​
taurus [48]

Answer:

x = 44°

Step-by-step explanation:

2x - 6 = 82

2x = 82 +6

2x = 88

divide through by 2

x = 44°

similar triangle

7 0
2 years ago
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