Mathematics

Solve: log2 (x) + log2 (x + 1) = 1

log2 (x) + log2 (x + 1) = 1 log2 [(x)(x+1)] = 1 log2 (x^2 + x) = 1 x^2 + x = 2^1 x^2 + x = 2 x^2 + x - 2 = 0 (x + 2) ( x -1) = 0 x = -2or x = 1-x = 1

Trig Problem solving in terms of pi

Interval of [0,2pi) terms of pi 5tan^2-15=0 tan^2x=3 tanx=sqt3 This is as far as ive got please help-tan^2x=3 => tanx = +/- sqrt(3) x = pi/3, 2pi/3, 4pi/3, 5pi/3

How to factor x^2 -8x +17 with imaginary i (more) how to... please

16x^4 -81 x^4-10x^2 + 25 i need to find the zeros, this kind of factoring includes imaginary number i-x^2 -8x +17 = (x^2 -8x +16) + 17-16 = (x-4)^2 + 1 = (x-4)^2 - i^2 = (x -4 -i) (x -4 +i) so x = 4

Word Problems Questions help

1. The length of a rectangular boat storage shed must be 4 meters more than the width, and the perimeter must be at least 120 meters. What is the range of values for the width? a. at least28 meters

How do you factor 2t^2 - 5t = 3

Algebra. (:-Bring the 3 over -> 2t^2-5t-3=0 Now factor: (2t+1)(t-3)->if you times it back out it turns to be:2t^2-6t+t-3->2t^2-5t-3=0 t=(-1/2) and 3-2t^2 - 5t = 3 2t^2 -5t -3 = 0 (2t +1)(t -3) = 0

The exact value of sin 5π / 12 is

5π/12 = π/6 + π/4 (another way to write it) Use the angle addition formula for sine: sin (a + b) = sin a * cosb + cos a * sin b Substituting in a = π/6 and b = π/4 sin (π/6 + π/4)= sin π/6 * cos

Solve Each Equation by using Square Root Property (10 POINTS!)

Write All Radicals in Simplest Form 1. x² = 81 2. r² + 36 = 0 3. y² - 250 = 0 4. (x-9)² = 49 5. (m+12)² = -9 6. (2x+9)² -4 = 0 7. (3r - 2)² - 28 = 0-√(ab) = √a * √b x² = 81 x = +/- √81 x = 9,-

Subtract and simplify if possible. 76 11/18 - 60 PLEASE explain if possible tx.

16) Subtract and simplify if possible. 76 11/18 - 60PLEASE explain if possible tx.-76 11/18 - 60 = 16 11/18-Given: 76 11/18 - 60 We need to first make the improper fraction into a proper fraction.

Solve for x. Give exact answer. log(x + 4) - log x = 1

The logarithm base 10 of x is the exponent of 10 needed to produce x. log10x = c means that where 10^c = x where x > 0 Logarithms base 10 are called common logarithms and log10x is written as log x.

Simplify: [ 6x^(-1/2) y^(2/3) / 18x^(-1) ] [ 2y^(1/4) / x^(1/3) ]

I trust you know the basic rules of multiplying fractions, and the rules of exponents. [ 6x^(-1/2) y^(2/3) / 18x^(-1) ] [ 2y^(1/4) / x^(1/3) ] = [12 x^(-1/2) y^(2/3 + 1/4)] / [18 x^(1/3 - 1)] = [2 x^(

Simplify √15(-2√5 + 4√6) ? (10 points guaranteed for the help)

I think the square root over the 15 is over the whole equation (i think). ANSWER: -10√3 + 12√10 I dont know how they got the answer. Can someone please show me the answer?-1√15(-2√5 + 4√6) 1√15(-2√

Trig Identities help

sin^2x / 1 - cosx = 1 + cosx Have no idea how to get the other side and tried multiple things! I am confused!-sin^2/(1 - cos) = 1 + cos (1 + cos)sin^2/((1 + cos)(s - cos)) = 1 + cos sin^2(1 + cos)/

Solve for x. (√3)^x+1=9^3x-1

to solve ignore the sqrt and focus on sqrt(3) and 9. since sqrt(3)*sqrt(3)*3 = 9 then sqrt(3)^4 = 9 (hope you follow my logic) and so: sqrt(3)^(x+1) = sqrt(3)^4^(3x-1) so x+1 = 4(3x-1)-->PEMDAS x

Convergent or divergent series

Is the following geometric sequence 0.005+ 0.05+ 0.5+ ... converent, divergent, both or neither.How would you figure this out?-It is divergent since the common ratio is 10 which is >1 in absolute valu

Find all prime ideals and all maximal ideals of Z2 * Z4

Ideals of Z₂ x Z₄ must have order dividing 8. Since (Z₂ x Z₄) / (Z₂ x Z₄) ≅ {0}, there is no maximal/prime ideal of order 8. Order 4: {0} x Z₄: Note that (Z₂ x Z₄) / ({0} x Z₄) ≅ Z₂ is a field/integ