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xeze [42]
3 years ago
11

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

Mathematics
1 answer:
PtichkaEL [24]3 years ago
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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Answer:

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Step-by-step explanation:

We are given that:

(σ1)^2 = (σ2)^2 = Population variance = 0.25

So, E < 0.1

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n = n1 = n2

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So, Z (α /2) = 1.645

The margin of error E is given as;

E = Z (α /2)√[(σ1)^2)/n1] + [(σ2)^2)/n2]

= Z (α /2)√({(σ1)^2 + (σ2)^2}/n) < 0.1

Multiply both sides by √n to get;

Z (α /2)√(σ1)^2 + (σ2)^2} < 0.1√n

Divide both sides by 0.1;

{Z (α /2)√(σ1)^2 + (σ2)^2}}/0.1 <√n

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{Z (α /2)√(σ1)^2 + (σ2)^2}}/0.1} ^2 < n

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n > ( 1.645 x √{(0.25 + 0.25)/0.1}^2

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7 0
3 years ago
Find the area (in square feet) of a rectangle that measures 17" × 3'10".
Kitty [74]

Answer:

65 feet and 2 inches

Step-by-step explanation:

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6 0
2 years ago
The sum of the ages of Kristen and Ben is 32. Four years ago Kristen was twice as old as Ben. How old are they both now?
Elan Coil [88]

Let us say that:

K = age of Kristen

B = age of Ben

 

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K – 4) = 2 (B – 4)

 

Simplifying eqtn 2:

K – 4 = 2 B – 8

K = 2 B – 4

 

Plugging in this to eqtn 2:

(2 B – 4) + B = 32

3 B – 4 = 32

3 B = 36

B = 12

 

From eqtn 2:

K = 2 B – 4 = 2 (12) – 4 = 20

 

So Kristen is 20 while Ben is 12.

5 0
3 years ago
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Answer:

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Step-by-step explanation:

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