Jaime knows that 30² is 900. He wonders if knowing that 30² can help him finds 29x31. Raquel knows what 25² equals. How can she use the knowledge to find 24x26?

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  Jaime: yes: 29·31 = 900 -1 = 899

  Raquel: 24·26 = 25^2 -1 = 624

Step-by-step explanation:

The difference of squares factors as the product of the sum and difference of the roots:

  a^2 -b^2 = (a -b)(a +b)

Jaime

  29·31 = (30 -1)(30 +1) = 30^2 -1^2 = 900 -1 = 899

  Jaime can subtract 1 from 30^2 to find 29·31

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Raquel

  24·26 = (25 -1)(25 +1) = 25^2 -1^2 = 625 -1 = 624

  Raquel can subtract 1^2 from 25^2 to find 24·26.

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

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: