geno3141

You can simplify the subtraction of logs by tuning the problem into a division problem.

log₃(x) - log₃(4)  =  log₃(x/4)

log₃(x/4) - log₃(12)  =  log₃(x /4 ÷ 12)  =  log₃(x/48)

Since 405 ends in 5, it is divisible by 5 --

405  =  5 x 81

Since 81 = 9 x  9 --

405  =  5 x 9 x 9

Since 9 = 3 x 3 --

405  =  5 x 3 x 3 x 3 x 3

Since those factors can't be reduced:

405  =  3⁴ x 5

The side opposite the 30° angle (the short side) is 1/2 the hypotenuse.

The side opposite the 60° can be found by multiplying the short side by √3.

Since they are all independent choices, multiply the possible choices together:  4 x 9 x 3 x 10  =  1080 possible combinations.

(5x²y) / (2x)

The x in the denominator cancels one of the x's in the numerator:  5xy/2

Find the amount of discount:  $125.00 - $90.00  =  $35.00

Divide by the original price:  $35.00 / $125.00  =  0.28

Turn into a percentage:  0.28  =  28%

The parts of SSA may not determine a triangle.

For instance, if you are given an angle (A), the side adjacent to the angle (S₁), and the side opposite to the angle (S₂), S₂ must be at least as large as S₁·sin(A).

if A = 30°, S₁ = 12, and S₂ = 5, there won't be a triangle, S₂ is too short!

 S₁·sin(A) = 12·sin(30) = 6 --->  means that there won't be a triangle because S₂ is too short (it's only 5).

If S₂ <  S₁·sin(A)    --->  there won't be a triangle.

If S₂ =  S₁·sin(A)    --->  the triangle is a right triangle.

If S₂ >  S₁·sin(A) and S₂ < S1   --->  there will be two possible triangles.

If S₂ >  S₁·sin(A) and S₂ ≥ S1   --->  there will be one triangle.

There are 4 choices for the first digit, 4 choices for the second digit, 4 choices for the third digit, and 4 choices for the last digit; thus, there will by 4 x 4 x 4 x 4 choices.

To determine the number of palindromes: there are 4 choices for the first digit and 4 choices for the second digit, however, there is only 1 choice for the third digit (it must match the second digit), and there is only 1 choice for the last digit (it must match the first digit). Thus, there will be 4 x 4 x 1 x 1 choices.

If the hypotenuse is 16, then the shorter side leg will be 8 and the longer leg will be 8√3.

Since it's a right triangle, the area will be ½·8·8√3  =  32√3  = 55.43 (approx)

I agree with you!

The number of ways that you can have 8 heads out of 10 flips, without caring about order is:  ₁₀C₈.

The number of ways that you can have 9 heads out of 10 flips, without caring about order is:  ₁₀C₉.

The number of ways tht you can have 10 heads out of 10 flips, without caring about order is:  ₁₀C₁₀.

To find the number of ways to have at least 8 out of 10, add those three answers together.