A digit is written to the right of the units digit of 757. If the resulting four-digit number is divisible by 3, how many possibilities are there for the digit that was written?

3

Step-by-step explanation:

It is a well known trick that when you add together the digits of a number, if they are a multiple of 3 then the number is divisible by 3. Let's go through the options and check them:

7+5+7+0=19 not a multiple of 3

7+5+7+1=20 not a multiple of 3

7+5+7+2=21 multiple of 3

7+5+7+3=22 not a multiple of 3

7+5+7+4=23 not a multiple of 3

7+5+7+5=24 multiple of 3

7+5+7+6=25 not a multiple of 3

7+5+7+7=26 not a multiple of 3

7+5+7+8=27 multiple of 3

7+5+7+9=28 not a multiple of 3

As you can see, only 3 of these were possibilities that satisified the conditions. Hope this helps!

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or  

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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