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Anettt [7]
3 years ago
10

F(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).

Mathematics
1 answer:
son4ous [18]3 years ago
5 0

Answer:

(f/g)(x) =  \frac{x + 5}{3x + 5}

Step-by-step explanation:

f(x) = 3x² + 10x - 25

g(x) = 9x² - 25

To find (f/g)(x) divide f(x) by g(x)

That's

(f/g)(x) =  \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 }

Factorize both the numerator and the denominator

<u>For the numerator</u>

3x² + 10x - 25

3x² + 15x - 5x - 25

3x ( x + 5) - 5( x + 5)

(3x - 5 ) ( x + 5)

<u>For the denominator</u>

9x² - 25

(3x)² - 5²

Using the formula

a² - b² = ( a + b)(a - b)

(3x)² - 5² = (3x + 5)(3x - 5)

So we have

(f/g)(x) =  \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)}

Simplify

We have the final answer as

(f/g)(x) =  \frac{x + 5}{3x + 5}

Hope this helps you

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What are the coordinates of the point on the directed line segment from (-8, -10)(−8,−10) to (6, -6)(6,−6) that partitions the s
frez [133]

Answer:

(2.5, -7)

Step-by-step explanation:

Given:

Two end points of a line segment are given as:

(-8, -10) and (6, -6)

The ratio of partition is 3 : 1.

Let the line segment be AB with A(-8, -10) and B(6, -6). Let point P(x,y) divide the line segment AB in the ratio 3 : 1.

In order to find the point P, we use section formula which is given as:

(x,y)=(\frac{nx_1+mx_2}{m+n},\frac{ny_1+my_2}{m+n})

Where, (x_1,y_1)\ and\ (x_2,y_2) are end points of line segment AB divided in the ratio m : n by the point (x, y).

Now, plug in the given values and solve for the coordinates of P. This gives,

P(x,y)=(\frac{1\times -8+3\times 6}{3+1},\frac{1\times -10+3\times -6}{3+1})\\\\P(x,y)=(\frac{-8+18}{4},\frac{-10-18}{4})\\\\P(x,y)=(\frac{10}{4},\frac{-28}{4})\\\\P(x,y)=(2.5,-7)

Therefore, the coordinates of the point on the directed line segment from (-8, -10) to (6,−6) that partitions the segment into a ratio of 3 to 1 is (2.5, -7).

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4 years ago
I WILL GIVE BRILLIANT
Katyanochek1 [597]

Answer:

The answer is 43.27, 27, and 10.58

Step-by-step explanation:

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3 years ago
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Hey there! 

Rotation
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If the P-value is 0.02, then means that the confidence interval is 2% 98% indeterminable. 95%
hoa [83]

Answer: 98%

Step-by-step explanation:

In statistics , the P-value gives the significance level of the population parameter in the population.

The significance level is denoted by \alpha.

Level of confidence is given by :-

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