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3 years ago

Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.

1 answer:

8 0

Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250.

According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a).
In this case,
f(x)=x^3-75x+250
(x+a)=(x+10)
Therefore, the remainder f(-a)=f(-10)

=x^3-75x+250
=(-10)^3-(75*-10)+250
=-1000+750+250
=1000-1000
=0.
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.

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Please help me with these two math problems that I do not quite understand. This is urgent!

g100num [7]

Answer:

1) $a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19$

2) $a_{10}=4+8(10-1)\Rightarrow a_{10}=76$

Step-by-step explanation:

1) To write an Arithmetic Sequence, as an Explicit Term, is to write a general formula to find any term for this sequence following this pattern:

$a_{n}=a_{1}+d(n-1)\Rightarrow \left\{\begin{matrix}a_{n}=n^{th}\: term\\a_1=1st \: term \\d=\: difference\\n=n^{th}\, term\end{matrix}\right.$

<em>"Write an explicit formula for each explicit formula A(n)=-1+(n-1)(-2)"</em>

This isn't quite clear. So, assuming you meant

Write an explicit formula for each term of this sequence A(n)=-1+(n-1)(-2)

As this A(n)=-1+(n-1)(-2) is already an Explicit Formula, since it is given the first term $a_{1}=-1$ the common difference $d=-2$ let's find some terms of this Sequence through this Explicit Formula:

$a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19$

2) $(4,12,20,28, ..)$ In this Arithmetic Sequence the common difference is 8, the first term value is 4.

Then, just plug in the first term and the common difference into the explicit formula:

$a_{10}=4+8(10-1)\Rightarrow a_{10}=76$

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3 years ago

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marishachu [46]

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2 years ago

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If f(x) = -3x + 4 and g(x) = 2, solve for the value of x for<br> which f(x) = g(x) is true.

creativ13 [48]

Answer:

the lines meet at (2/3, 2)

Step-by-step explanation:

f(x) = g(x)

plug equations for f(x) and G(x)

-3x+4 = 2

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x = 2/3

since both equations meet at x = 2/3, it doesn't matter which equation you plug x = 2/3 into to find the y-coordinate

for simplicity purposes since g(x) is easier to solve, I am going to plug x = 2/3 into g(x), but plugging it into f(x) will give you same answer

g(x) = 2

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the lines meet at (2/3, 2)

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2 years ago

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