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andrew11 [14]
2 years ago
10

Consider these functions:

Mathematics
2 answers:
IgorLugansk [536]2 years ago
8 0

Answer:

The value of f(g(-2)) is 12.

Step-by-step explanation:

We'll start by solving g(-2):

g(-2)\\= (-2)^2 + 2\\= 4 + 2\\= 6

Now we can take that value and plug it into function f:

f(6)\\= \frac{-1}{2}6^2 + 5 * 6\\= -36/2 + 30\\= -18 + 30\\= 12

Alternatively, you can work out a new single function that in itself describes f(g())

f(g(x)) = -\frac{1}{2}g(x)^2 + 5g(x)\\= -\frac{1}{2}(x^2 + 2)^2 + 5(x^2 + 2)\\= -\frac{1}{2}(x^4 + 4x^2 + 4) + 5x^2 + 10\\= -\frac{1}{2}x^4 - 2x^2 - 2 + 5x^2 + 10\\= -\frac{x^4}{2} + 3x^2 + 8

and try plugging -2 into the new function

= - \frac{-2^4}{2} + 3(-2)^2 + 8\\= -16 / 2 + 3 * 4 + 8\\= -8 + 12 + 8\\= 12

rusak2 [61]2 years ago
8 0

Answer:

The answer is 12

Step-by-step explanation:

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A line with slope 3 passes through the point (0,10). What is the y-coordinate of the point on the line with x-coordinate 2?
lana [24]
Hello!

So to find the y-coordinate we need an equation for the line. The equation we can use is

y = mx + b

In this we already know m(the slope which is 3) and we can find b by plugging in the points that are given.

10 = 3(0) + b
10 = 0 + b
10 = b

So now that we've found b, we can use this in our equation

y = 4x + b

So now we can plug in the x-coordinate that we know (2) and find the y - coordinate.

y = 4(2) + 10
y = 8 + 10
y = 18

18 is your y-coordinate 
4 0
3 years ago
What is the average rate of change for the function f(x)=3x^2 -5 on the interval −3 ≤ x ≤ −1 ?
Anestetic [448]

Answer:

-12

Step-by-step explanation:

Let b = -1 and a = -3

The average rate of change = \frac{f(b) - f(a)}{b - a}

f(b) = f(-1) = 3(-1)^2 - 5 = 3 - 5 = -2

f(a) = f(-3) = 3(-3)^2 - 5 =27 - 5 = 22

f(b) - f(a) = -2 - 22 = -24

b - a = -1 + 3 = 2

\frac{f(b) - f(a)}{b - a} = -24/2 = -12

4 0
3 years ago
A field has a length of 12 m and a diagonal of 13 m what is the width?
kvv77 [185]
Do Pythagorean Theorem because a rectangle divided in diagonals form right triangles
A^2+b^2=C^2
Plug in the correct numbers and solve
A and B can be switched around but C is always the longest diagonal side which is called the hypotenuse not the Adjacent sides that form a right angle
So with correct solving you should get 5.
7 0
3 years ago
Hi help me with this pls ​
Rudiy27

\huge \underline{ \pink{Answer}}

Refer to the attachments

Attachment (1)

B (1)

Attachment 2

B(2)

3 0
2 years ago
There is a hot market at school for used graduation gowns, in fact the price is growing exponentially! Last week I could have go
Daniel [21]

Answer:

$100

Step-by-step explanation:

the equation to solve this is:

y=12.5x+25

y=12.5x+25\\ =(12.5*6)+25\\ =75+25\\ =100

(Assuming, of course, that this is a homework assignment and not you actually buying it cuz' in real life the numbers would be different from month to month)

4 0
2 years ago
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