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Leno4ka [110]
3 years ago
7

What’s the difference quotient simplified

Mathematics
1 answer:
mihalych1998 [28]3 years ago
7 0

\text{Use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\f(x+h)\to\text{exchange x to x + h}\\\\f(x)=x^3+3x\\\\f(x+h)=(x+h)^3+3(x+h)\\\\f(x+h)=x^3+3x^2h+3xh^2+h^3+3x+3h\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-(x^3-3x)}{h}\\\\=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-x^3-3x}{h}\\\\=\dfrac{(x^3-x^3)+3x^2h+3xh^2+h^3+(3x-3x)+3h}{h}\\\\=\dfrac{3x^2h+3xh^2+h^3+3h}{h}\\\\=\dfrac{h(3x^2+3xh+h^2+3)}{h}\\\\=\boxed{3x^2+3xh+h^2+3}

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How to do polynomials ​
Travka [436]

Answer:

D

Step-by-step explanation:

12/6 is 2 and the the exponents when you are dividing you just subtract. so 9-3 = 6 which makes it x^6.

5 0
3 years ago
Which zero pair could be added to the function f(x)=x^2+12x+6 so that the function can be written in vertex form?
andrew11 [14]
<span>f(x) = x</span>² <span>+ 12x + 6  </span>→ y = x² + 12x + 6<span>

Let us convert the standard form into vertex form.

1) Complete the squares. Isolate x</span>² and x terms.
<span>y - 6 = x</span>² + 12x
<span>
2) Create the perfect square trinomial. Whatever number is added on one side must also be added on the other side. 

y - 6 + 36 = x</span>² + 12x + 36<span>
y + 30 = (x + 6)</span>²
<span>y = (x + 6)</span>² - 30  ← Vertex form
<span>
To check:

y = (x + 6) (x + 6) - 30
y = x</span>² + 6x + 6x + 36 - 30
<span>y = x</span>² + 12x + 6<span>

The zero that could be added to the given function is 36, -36</span>
4 0
3 years ago
A bench is 35 inches long and 19 inches wide. how many square inches does it cover?
vfiekz [6]
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4 0
3 years ago
How do you solve this equation? -5/4+(-7/9)= Thanks
Klio2033 [76]

Answer:

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Step-by-step explanation:

tik(tok) slapddaddy

8 0
3 years ago
He takes a random sample of 49 recent charterholders and computes a mean salary of $172,000 with a standard deviation of $35,000
uysha [10]

Answer:

the 90% of confidence intervals for the average salary of a CFA charter holder

 (1,63,775 , 1,80,000)

Step-by-step explanation:

<u>Explanation</u>:-

random sample of n = 49 recent charter holders

mean of sample (x⁻) =  $172,000

standard deviation of sample( S) = $35,000

Level of significance α= 1.645

<u> 90% confidence interval</u>

(x^{-} - Z_{\alpha } \frac{s}{\sqrt{n} } , x^{-} + Z_{\alpha } \frac{s}{\sqrt{n} })

(172000 - 1.645 \frac{35000}{\sqrt{49} } , 172000 +1.645 \frac{35000}{\sqrt{49} })

on calculation , we get

(1,63,775 , 1,80,000)

The mean value lies between the 90% of confidence intervals

(1,63,775 , 1,80,000)

4 0
3 years ago
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