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jonny [76]
3 years ago
14

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point)

Mathematics
2 answers:
madam [21]3 years ago
5 0

Answer:

f(x)= \frac{7}{x}+10 and g(x)=x^2 

Step-by-step explanation:

Given : Equation y=\frac{7}{x^2}+10.

To find : f(x) and g(x) so the function can be expressed as y = f(g(x)) ?

Solution :

Our aim is to express f as a function of g, where g is a function itself, of x.

In the expression,

y= \frac{7}{x^{2}}+10

We may notice two functions, the squaring x function, which may well be our g i.e. g(x)=x^2 

The function is re-written as, y= \frac{7}{g(x)}+10

and the "7 divided by x, +10" function is  f(x)= \frac{7}{x}+10

Therefore, f(x)= \frac{7}{x}+10 and g(x)=x^2.

Alla [95]3 years ago
3 0
Given y = 7/x² + 10

Let,

y = f(x)

f(x) = 7/x² + 10

And,

g(x) = x²

Hence, f(g(x))

Reason is;
You have to rewrite f(x) so that it can fit in g(x) into the equation

f(x) = 7/g(x) + 10
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In an isosceles triangle two sides are equal. The third side is two less than twice the length of the two equal sides. The perim
pogonyaev

Answer:

The equal sides' length = 10

Third side length = 18

Step-by-step explanation:

Let the two equal sides' length be "x"

Let the third side length be "y"

Third side (y) is 2 LESS THAN TWICE the equal side, so we can write:

y = 2x - 2

The perimeter is 38. The perimeters is the sum of all three sides. So we can write:

x + x + y = 38

Replacing y with 2nd equation, we have:

x + x + (2x - 2) = 38

Now, we can solve this for x first:

x + x + (2x - 2) = 38\\x+x+2x-2=38\\4x=38+2\\4x=40\\x=10

Now, y is:

y = 2x - 2

y = 2(10) - 2

y = 20 - 2

y = 18

The equal sides' length = 10

Third side length = 18

3 0
3 years ago
Choose the linear inequality that describes the graph. The gray area represents the shaded region.
jek_recluse [69]

Answer:

2x + 3y ≥ 5

Step-by-step explanation:

See the graph attached.

The bold straight line passes through the points (1,1) and (4,-1).

Therefore, the equation of the straight line will be  

\frac{y + 1}{- 1 - 1} = \frac{x - 4}{4 - 1}

⇒ 3(y + 1) = - 2(x - 4)

⇒ 3y + 3 = - 2x + 8

⇒ 2x + 3y = 5 ............. (1)

Now, the shaded region i.e. the solution to the inequality does not include the origin(0,0).

So, putting x = 0 and y = 0 in the equation (1) we get, 0 < 5

Therefore, the inequality equation is 2x + 3y ≥ 5 (Answer)

6 0
3 years ago
What is the ratio of 1/6:6 = what
frutty [35]
1/6=16.666666...

So it is 16.6666.... to 6(or 100)

5 0
2 years ago
2/3 + 1/2 <br> i just want to give some points away
goldfiish [28.3K]
Answer: 7/6, 1 and 1/6, or 1.16


Step by step explanation:

2/3 + 1/2

4+3/6

7/6
6 0
2 years ago
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A survey of 2500 subscribers to a certain news paper revealed that 2250 people subscribe to the daily morning edition and 1250 s
Aleks04 [339]

1500 people subscribed Sunday edition and 250 people subscribed only sunday edition.

<u>Solution:</u>

Given, A survey of 2500 subscribers to a certain news paper revealed that 2250 people subscribe to the daily morning edition  

And 1250 subscribe to both the daily and the sunday editions.  

We have to find how many subscribe to the Sunday edition? how many subscribe to the Sunday edition only?

Let x denote the number who subscribe to the Sunday edition.  

Then the addition rule with overlap tells us that  

Those who subscribe daily edition + those who subscribe sunday edition - those who subscribe both daily and sunday edition = total subscribers in survey

2250 + x – 1250 = 2500

1000 + x = 2500  

x = 1500  

so, 1500 subscribe to the Sunday edition and 1500 – 1250 = 250 subscribe to the Sunday edition only.

Hence, 1500 people subscribed Sunday edition and 250 people subscribed only sunday edition.

6 0
3 years ago
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