Answer:
Step-by-step explanation:
Let's start by using change of base property:
So, for 
Now, using change of base for 
You can express 
as:
Using reduction of power property:
Therefore:
As you can see the only difference between (1) and (2) is the coefficient 
:
So:
Well 24=4*6, and 35=7*5 not 6, so 4/7 doesn't = 24/35, so no
The only way 3 digits can have product 24 is
1 x 3 x 8 = 241 x 4 x 6 = 242 x 2 x 6 = 242 x 3 x 4 = 24
So the digits comprises of 1,3,8 or 1,4,6, or 2,2,6, or 2,3,4
To be divisible by 3 the sum of the digits must be divisible by 3.
1+ 3+ 8=12, 1+ 4+ 6= 11, 2 +2 + 6=10, 2 +3 + 4=9Of those sums of digits, only 12 and 9 are divisible by 3.
So we have ruled out all but integers whose digits consist of1,3,8, and 2,3,4.
Meanwhile they must be odd they either must end in 1 or 3.
The only ones which can end in 1 are 381 and 831.
The others must end in 3.
They must be greater than 152 which is 225. So the
First digit cannot be 1. So the only way its digits can contain of1,3,8 and close in 3 is to be 813.
The rest must contain of the digits 2,3,4, and the only way they can end in 3 is to be 243 or 423.
So there are precisely five such three-digit integers: 381, 831, 813, 243, and 423.
Step-by-step answer:
Given an enlargement from preimage (ABC) to image (A'B'C').
Need to find scale factor.
Solution:
Scale factor = linear size of image / linear size of preimage.
From the accompanying diagram, we see that
L(preimage) = AC = 4 units
L(image) = A'C' = 12 units
Therefore
Scale factor = L(image) / L(preimage) = 12 / 4 = 3
Answer:
Denote AH as height of triangle ABC, with H lies on BC.
Applying sine theorem:
AH/AC = sin 60
=> AH = AC x sin 60 = 47 x sqrt(3)/2 = 40.7
=> Area of triangle ABC is calculated by:
A = AH x BC x (1/2) = 40.7 x 30 x (1/2) = 610.5 = ~611
=> Option C is correct.
Hope this helps!
:)
