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madam [21]
2 years ago
5

Find (f/g) (x) for the functions provided: ƒ(x) = x3 − 27, g(x) = 3x − 9

Mathematics
1 answer:
AnnZ [28]2 years ago
5 0

Answer:

(\frac{f}{g})(x)=\frac{1}{3}(x^2+3x+9)

Step-by-step explanation:

We have been given that

f(x)=x^3-27,g(x)=3x-9

We can use the formula for difference of cubes to simplify the function f(x)

difference of cubes -  a^3-b^3=(a-b)(a^2+ab+b^2)

f(x)=x^3-27\\\\=x^3-3^3\\\\=(x-3)(x^2+3x+9)

And g(x) can be written as

g(x)=3x-9\\=3(x-3)

Thus, we have

(\frac{f}{g})(x)=\frac{(x-3)(x^2+3x+9)}{3(x-3}

On cancelling the common factors, we get

(\frac{f}{g})(x)=\frac{1}{3}(x^2+3x+9)

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What is the initial value in the function 2x + 3y = 6?
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<h2>Explanation:</h2><h2></h2>

The initial value of this function is the y-intercept. We know that the slope-intercept form of the equation of a line is given by:

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Writing our equation in slope intercept form:

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3 years ago
Find the product of 2 1/3 × 3/5
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Step-by-step explanation:

8 0
2 years ago
The low temperature on Monday was 16°F. On Tuesday, the low was 18°F cooler. On Wednesday, the low temperature was –4 times Tues
drek231 [11]

Answer:

-4(16-18), [16 + (-18)](-4)

Step-by-step explanation:

Given: The low temperature on Monday was 16°F. The low temperature on Tuesday was 18°F cooler. The low temperature on Wednesday was –4 times Tuesday’s temperature.

To find: expression that can be used to describe the low temperature on Wednesday

Solution:

Temperature on Monday = 16°F

So,

Temperature on Tuesday = (16-18)\°F

Temperature on Wednesday = -4(16-18)\°F

So, expression -4(16-18)=(16-18)(-4) can be used to describe the low temperature on Wednesday.

Also,

(16-18)(-4)=[16 + (-18)](-4)\,\,\left \{\because  (a-b)=\left [ a+(-b) \right ] \right \}

So, expression [16 + (-18)](-4) also represent temperature on Wednesday.

3 0
3 years ago
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max2010maxim [7]
1/2 is less than 3/4. So 1/2 < 3/4
3 0
3 years ago
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