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pychu [463]
4 years ago
11

Help me solve for z, step by step if you can

Mathematics
1 answer:
zheka24 [161]4 years ago
5 0

Answer:

z=6

Step-by-step explanation:

z/3 + 1/2 = 5/2

Subtract 1/2 from each side

z/3 + 1/2-1/2 = 5/2-1/2

z/3 = 4/2

z/3 =2

Multiply each side by 3

z/3*3 = 2*3

z = 6


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If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.
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There's no if about it, 

f(x)=x^3+3x^2-x-3


has a zero f(1)=0 so x-1 is a factor.   That's the special case of the Remainder Theorem; since f(1)=0 we'll get a remainder of zero when we divide f(x) by x-1.

At this point we can just divide or we can try more little numbers in the function.  It doesn't take too long to discover f(-1)=0 too, so  x+1 is a factor too by the remainder theorem.  I can find the third zero as well; but let's say that's out of range for most folks.

So far we have 

x^3+3x^2-x-3 = (x-1)(x+1)(x-r)

where r is the zero we haven't guessed yet.  Again we could divide f(x) by (x-1)(x+1)=x^2-1 but just looking at the constant term we must have

-3 = -1 (1)(-r) = r

so

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We check f(-3)=(-3)^3+3(-3)^2 -(-3)-3 = 0 \quad\checkmark

We usually talk about the zeros of a function and the roots of an equation; here we have a function f(x) whose zeros are

x=1, x=-1, x=-3

8 0
3 years ago
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Suppose 123 people voted for Danny. If 55 of the votes were from girls what would be the ratio of voted from girls to votes from
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Step-by-step explanation:

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Murljashka [212]

Answer:

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7 0
3 years ago
Use (pemdas) what is 3 x 7 - 25 / 5 write 3 steps
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Answer:

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