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3 years ago

Given: f(x) = x2 and g(x) = 2x +1, find f(g(x)]. 4x² + 4x + 1 4x² + 1 2x²+1

Mathematics

2 answers:

aleksklad [387]3 years ago

8 0

Answer:

$\huge\boxed{f\bigg(g(x)\bigg)=4x^2+4x+1}$

Step-by-step explanation:

$f(x)=x^2;\ g(x)=2x+1\\\\f\bigg(g(x)\bigg)-\text{instead of}\ x\ \text{in}\ f(x)\ \text{put the expression}\ 2x + 1\\\\f\bigg(g(x)\bigg)=f(2x+1)=(2x+1)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\f\bigg(g(x)\bigg)=(2x)^2+2(2x)(1)+1^2=4x^2+4x+1$

kenny6666 [7]3 years ago

3 0

Answer:

4x^2 + 4x + 1 = f(g(x))

Step-by-step explanation:

To create the function f(g(x)), expand (2x + 1)^2:

We get 4x^2 + 4x + 1 = f(g(x))

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You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

$Width=10.5\ ft$

$Area=110.25\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

$P=2(x+y)$

we have

$P=42\ ft$

$42=2(x+y)$

simplify

$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

$x=10.5\ ft$

Find the value of y

$y=21-10.5=10.5\ ft$

The garden is a square

the area is equal to

$A=(10.5)(10.5)=110.25\ ft^{2}$ ----> is equal to the y-coordinate of the vertex is correct

6 0

3 years ago

Write as many equivalent expressions to 3/4(4x-8)+1/4(4x-8)

Deffense [45]

Answer:

4x-8

Step-by-step explanation:

3/4(4x-8)+1/4(4x-8)

12/4x-24/4+4/4x-8/4

3x-6+x-2

3x+x-6-2

4x-8

8 0

3 years ago

Read 2 more answers

For y = x^2 + 10x + 24, write the axis of symmetry, the vertex, and whether the

mylen [45]

Answer:

x= - 2

Step-by-step explanation:

hello :

note : the equation of the axis symmetry for the parabola : y =ax²+bx+c

when : a≠ 0 is : x=- b/2a

in this exercice : a=1 and b=10

so : x= -10/2 = -5

7 0

4 years ago

Two investments totallng $47,500 produce an annual income of $3000. One investment ylelds 9% per year, while the other yields 6%

enot [183]

Answer:

The correct answer is "$5000".

Step-by-step explanation:

The given values are:

Two investments totaling,

= $47,500

Annual income,

= $3000

One investment yields per year,

= 9%

Other yield,

= 6%

Let,

The amount invested in 9% will be "x".
The amount invested in 6% will be " $47,500-x$ ".

Now,

⇒ $0.09x+0.06(47,500-x)=3000$

⇒ $0.09x+2850-0.06x=3000$

⇒ $0.03x+2850=3000$

⇒ $0.03x=150$

⇒ $x=\frac{150}{0.03}$

⇒ $x=5000$

5 0

3 years ago

A spider must eat 3 flies a day to survive. After he has taken his three he quits for the day. For any fly that crosses his path

attashe74 [19]

The answer is 0.75.
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7 0

3 years ago