Count the number of positive integers less than 100 that do not contain any perfect square factors greater than 1.
Possible perfect squares are the squares of integers 2-9.
In fact, only squares of primes need be considered, since for example, 6^2=36 actually contains factors 2^2 and 3^2.
Tabulate the number (in [ ])of integers containing factors of
2^2=4: 4,8,12,16,...96 [24]
3^2=9: 9,18,....99 [11]
5^2=25: 25,50,75 [3]
7^2=49: 49,98 [2]
So the total number of integers from 1 to 99
N=24+11+3+2=40
=>
Number of positive square-free integers below 100 = 99-40 = 59
Answer:
B)60m^2
Step-by-step explanation:
The area of the rectangle is 40m^2 and the area of the triangle is 20m^2. So 40+20 is 60.
Answer:
3) B) 90°
4) A) 75°
Step-by-step explanation:
3) interior angles of a triangle =180°
So
40+50+?=180
? =180- 90
? =90
4) same rule
40+65+?=180
? =180 - 105
? = 75
Multiply2 * x/15 to 2x/15
multiply both sides by 30 which is the LCM of 10, 5, 3, and 15
expand it
simplify 18 - 15x - 12x - 6 + 10x to 12 - 17x
add 17x to both sides
add 4x + 17x to = 21x
divide both sides by 21
simplify 12/21 to 4/7
now simplify
Answer: x = 4/7.
Answer:
Step-by-step explanation:
The slope of line 2=
=0
