Mathematics, 09.10.2019 12:10 aspenwheeler6804

What is the simplest form of the expression? sqrt 20+ sqrt 45 - sqrt 5

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Before starting:

(√a)² = √a * √a = a

√(a²) = IaI

√(ab) = √a * √b

√(a/b) = (√a) / (√b)

√(a + b) ≠ √a + √b

= √20 + √45 - √5

= √(4 * 5) + √(9 * 5) - √5

= [(√4) * (√5)] + [(√9) * (√5)] - √5

= [(√2²) * (√5)] + [(√3²) * (√5)] - √5

= [2 * (√5)] + [3 * (√5)] - √5

= 2√5 + 3√5 - √5

= 5√5 - √5

= 4√5 → first answer

= 9^(1/3) * 81^(1/3) → you know that: 81 = 9² = 9 * 9 = 3² * 3² = 3^4

= (3^2)^(1/3) * (3^4)^(1/3) → you know that: (x^a)^b = x^(ab)

= 3^[2 * (1/3)] * 3^[4 * (1/3)]

= 3^(2/3) * 3^(4/3) → you know that: x^(a) * x^(b) = x^(a + b)

= 3^[(2/3) + (4/3)]

= 3^[(2 + 4)/3]

= 3^[6/3]

= 3^2

= 9 → second answer

Answer from: Quest

Ifound this on google “that means that the graph of a function with direct variation has these features: it is a straight line: because the slope is the ratio y/x = k. it passes through the origin (0,0): because y = kx = k (0) = 0.” i hope this you for what your looking for

Answer from: Quest

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

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