Alex’s printer can print 8 photos in 12 minutes.

Mathematics

1 answer:

Gre4nikov [31]3 years ago

7 0

Answer:

$120\ minutes$

Step-by-step explanation:

step 1

Alex’s printer

we know that

print 8 photos in 12 minutes

by proportion

Find how long will it take the printer to print 120 photos

$\frac{12}{8}=\frac{x}{120}\\ \\x=120*12/8\\ \\x=180\ minutes$

step 2

Khalil’s printer

we know that

print 24 photos in 1 hour (60 minutes)

by proportion

Find how long will it take the printer to print 120 photos

$\frac{60}{24}=\frac{x}{120}\\ \\x=120*60/24\\ \\x=300\ minutes$

step 3

Find the difference

$300\ minutes-180\ minutes=120\ minutes$

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Step-by-step explanation:

Each vertical asymptote corresponds to a zero in the denominator. When the function does not change sign from one side of the asymptote to the other, the factor has even degree. The vertical asymptote at x=-4 corresponds to a denominator factor of (x+4). The one at x=2 corresponds to a denominator factor of (x-2)², because the function does not change sign there.

Each zero corresponds to a numerator factor that is zero at that point. Again, if the sign doesn't change either side of that zero, then the factor has even multiplicity. The zero at x=1 corresponds to a numerator factor of (x-1)².

Each "hole" in the function corresponds to numerator and denominator factors that are equal and both zero at that point. The hole at x=-3 corresponds to numerator and denominator factors of (x-3).

Taken altogether, these factors give us the function ...

$\boxed{f(x)=\dfrac{(x+3)(x-1)^2}{(x+4)(x+3)(x-2)^2}}$