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goblinko [34]
3 years ago
8

Given the functions: f(x) = x^2-9 and g(x) = 3 what is (f/g)(x)? A. x-3 B. x-9 C. x+3 D. x+9

Mathematics
1 answer:
uysha [10]3 years ago
3 0

Answer:

f + g)(x) = f (x) + g(x)

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(

g

f

)(x)=

g(x)

f(x)

= \small{\dfrac{3x+2}{4-5x}}=

4−5x

3x+2

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}

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A bottle weighs 1.2 kg when it is 1/4 full of water. It weighs 2.4 kg when it is full. What is the weight of the empty bottle?
sweet [91]

Answer:

Weight of empty bottle = 0.8 kg

Weight of water = 1.6 kg

Step-by-step explanation:

As given , A bottle weighs 1.2 kg when it is 1/4 full of water. It weighs 2.4 kg when it is full.

Let us assume

Weight of empty bottle = x

Weight of water = y

Now,

when the bottle is 1/4 full of water

then,

weight of water = \frac{1}{4}×y

As given , Bottle weight = 1.2 , when it is 1/4 full of water

⇒ Weight of water + weight of bottle = 1.2

⇒ \frac{1}{4}×y + x = 1.2

⇒ y + 4x = 4.8      .......(1)

Also given, A bottle weight = 2.4 , when it is full of water

⇒ Weight of water + weight of bottle = 2.4

⇒ y + x = 2.4        ......(2)

Subtract equation (2) from equation (1) , we get

y + 4x - ( y+ x) = 4.8 - 2.4

⇒ y + 4x - y - x = 2.4

⇒3x = 2.4

⇒x = \frac{2.4}{3} = 0.8 kg

and y = 2.4 - x = 2.4 - 0.8 = 1.6 kg

∴ we get

Weight of empty bottle = x = 0.8 kg

Weight of water = y = 1.6 kg

4 0
3 years ago
Use the graph to find the limit (if it exists). If the limit does not exist, explain why.
Mandarinka [93]

Answer:

  the limit does not exist

Step-by-step explanation:

As x approaches π/2 from below, tan(x) approaches +∞. A x approaches π/2 from above, tan(x) approaches -∞. These two limits are not the same, so the limit is said not to exist.

___

For a limit to exist, it must be the same regardless of the direction of approach.

6 0
3 years ago
Plez halp with question bc im smol brain
Studentka2010 [4]

Answer:

B. y= 2x–15

Step-by-step explanation:

The equation that represents the line that passes through the points (8, 1) and (10,5) is y= 2x–15

"x" is found on the left hand side of the bracket and "y" is found on the right hand side of the bracket :)

(8, 1) and (10, 5)

x in the first bracket is 8 and x in the second bracket is 10.

y in the first bracket is 1 and y in the second bracket is 5.

When this equation is applied to find the value for y we get:

y= 2x-15

y= 2(8)-15

y= 16-15

y= 1

y= 2x-15

y= 2(10)-15

y= 20-15

y= 5

We got back the values of y and this means that the equation was correctly chosen and the answer is correct :)

6 0
3 years ago
When inscribing a square in a circle, which of these should have equal lengths? A) a radius of the circle and a diagonal of the
koban [17]
Hope this helps you.

5 0
3 years ago
Read 2 more answers
A 16,000 ft<br>B 8000 ft<br>C 4000 ft<br>D 150 ft​
Cloud [144]

Answer:

A

Step-by-step explanation:

If all of the dimensions of the tank are doubled, since we live in three dimensions, the volume of the new tank will be 2^3=8 times as large. 8\cdot 2000=16000 feet, or answer choice A. Hope this helps!

3 0
2 years ago
Read 2 more answers
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