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3 years ago

F(x)=2x+1 and g(x)=x^2-7, find (f g) (x)

Mathematics

1 answer:

hodyreva [135]3 years ago

5 0

The answer is (f o g)(x) = 2x^2 - 13

In order to find a composite function, you take the first letter (in this case f) and use that equation. You then remove the variable and put in the second letter (g).

f(x) = 2x + 1 ----> Remove variable.

f(x) = 2( ) + 1 ----> Insert g(x)

(f o g)(x) = 2(x^2 - 7) + 1 ----> Distribute

(f o g)(x) = 2x^2 - 14 + 1 ----> Simplify

(f o g)(x) = 2x^2 - 13

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The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5

Arada [10]

Answer:

Width = 15 inches Length = 20 inches

Step-by-step explanation:

The area of a rectangle is calculated using the following formula.

$A = Lx$ (1)

Where L is the length and x is the width of the rectangle

In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:

$L = x + 5$ (2)

Also The area of a rectangle can be represented by the equation $x^2 + 5x = 300$

so to find the width x we solve the equation

$x^2 + 5x -300=0$ (3)

For an equation of the form $ax ^ 2 + bx + c = 0$ the quadratic formula is:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case note that:

$a=1\\b=5\\c=-300$

Then:

$x=\frac{-5\±\sqrt{(5)^2-4(1)(-300)}}{2(1)}$

$x=\frac{-5\±\sqrt{25+1200}}{2}$

$x=\frac{-5\±\sqrt{1225}}{2}$

$x=\frac{-5\±35}{2}$

$x_1=\frac{-5+35}{2}$ → $x_1=15$

$x_2=\frac{-5-35}{2}$ → $x_2=-20$

We take the positive solution $x=15\ in$

Now we use equation (2) to find L

$L = x + 5$

$L = 15 + 5$

$L = 20\ in$

8 0

3 years ago

Please help......

rosijanka [135]

1. using 2 dots that are on the blue line (0,72) and (6,69)
find the slope:

slope = change in Y over change in x = 69 - 72 / 6-0 = -3 / 6 = -1/2
equation would be y = -1/2x + 72

2. y = -1/2x+72 = -1/2(30) +72 = -15 +72 = 57 beats per minute

3. replaced x in the equation with 30 to find the beats per minute for exercising 30 minutes

5 0

3 years ago

How do you figure P added 6

r-ruslan [8.4K]

Answer:

huh

Step-by-step explanation:

4 0

2 years ago

I don’t need to know how to solve it I’m going to ask my teacher how to tomorrow but for now I need help on these

Mars2501 [29]

1) slope=3 and y-int.=-5
2) slope=2 and y-int.=-6
3) slope=-6 and y-int.=1/2
4) slope=-7 and y-int.=5/2
5) slope=1/2 and y-int.=7
6) slope=3/4 and y-int.=8
7) slope=-2/3 and y-int.=-1/3
8) slope=-1/8 and y-int.=-3/8
9) slope=2/3 and y-int.=5
10) slope=-2/7 and y-int.=-1
11) slope=-3 and y-int.=6
12) slope=4 and y-int.=7
Hope this helps!

4 0

3 years ago

Ten times the difference of a number x and 8

AleksAgata [21]

Answer:

Expression will be 10(x - 6).

Step-by-step explanation:

Let the given number is x.

Difference of this number and 6 will be represented by

(x - 6)

Then ten times the difference of this number and 6 will be represented by

10(x - 6)

Therefore, the statement " ten times the difference of a number and six " will be represented by the expression 10(x - 6)

4 0

2 years ago