Two numbers are in the ratio 7:5 and their difference is 22.Find the numbers

Let x and y be the two numbers. Then

yx=57  and x−y=20

Cross multiplying the proportion

5x=7y  or y=75x

So, x−y=20

x−75x=20⇒77x−5x=72x=20

⇒x=2140=70

y=75x=75×70=50

So smaller number is 50.

Check :yx=5070=57 and 70−50=20

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! : )

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