If f(x)=3x-1 and g(x)=x+5, find (f o g)(x) and (g o f)(x)

(f o g)(x)=

(g o f)(x)

The resulting function is (f-g)(x) = 5 · x⁴ + 3 · x² + 10.

The resulting function is (f • g) (x) = 3 · (3 · x⁵ - 5 · x⁴ + 3 · x² - 15)⁵ + 6 · (3 · x⁵ - 5 · x⁴ + 3 · x² -15)² - 5.  

Let be [tex]f(x)[/tex] and [tex]g(x)[/tex] polynomial functions, the subtraction between between the two functions implies the subtraction of similar terms. If we know that [tex]f(x) = 3\cdot x^{5}+6\cdot x^{2}-5[/tex] and [tex]g(x) = 3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15[/tex], then the subtraction between the two functions:

[tex](f-g)(x) = (3\cdot x^{5}+6\cdot x^{2}-5)-(3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15)[/tex]

[tex](f-g)(x) = 5\cdot x^{4}+3\cdot x^{2}+10[/tex]

The resulting function is (f-g)(x) = 5 · x⁴ + 3 · x² + 10. [tex]\blacksquare[/tex]

The composition between two functions, the independent variable of the former function by the latter function. If we know that [tex]f(x) = 3\cdot x^{5}+6\cdot x^{2}-5[/tex] and [tex]g(x) = 3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15[/tex], then the composition between the two functions:

[tex]f\,\circ\,g\,(x) = 3\cdot (3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15)^{5}+6\cdot (3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15)^{2}-5[/tex]

(f • g) (x) = 3 · (3 · x⁵ - 5 · x⁴ + 3 · x² - 15)⁵ + 6 · (3 · x⁵ - 5 · x⁴ + 3 · x² -15)² - 5.  [tex]\blacksquare[/tex]

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Answer:

12x+4x-7y+45b+78a-44b+1a+1z+0d+1.1a+1.1a+2+2+2

Answer:

a) 13 m

b) 0.4 mm

Step-by-step explanation:

side length = x, area = x²

a) x² = 169, x = √169 = 13 m

b) x² = 0.16, x = √0.16 = 0.4 mm

Answer:

∠ EFA

Step-by-step explanation:

complementary angles sum to 90°

∠ EFA and ∠ EFA form a right angle ad sum to 90°

Veremos que la distancia total recorrida es de 20 metros, y el desplazamiento es de 0 metros.

Definimos el desplazamiento como la diferencia entre la posición final y la inicial. En este caso sabemos que la persona comienza en su casa, luego va al colmado, y luego regresa a su casa.

Entonces la posicion inicial y la final son la misma, por lo que concluimos que el desplazamiento es 0.

La distancia total recorrida será igual a dos veces la distancia entre la casa y el colmado.

Esta distancia es 10 metros, entonces la distancia recorrida es:

distancia = 2*10m = 20m

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1. When the bond is redeemed at maturity, the total return (profit) for Alejandro will be $600.00.

2. The total return on investment will be 12.5%.

The return on investment is a profitability measure that shows the rate of an investment's profit versus the cost.

The return on investment can be computed by subtracting the initial investment cost from the terminal value of the investment, then dividing the net return by the initial investment cost, then multiplying it by 100.

Face value of bond = $5,000

Price paid for bond = $4,800 ($5,000 x 96%)

Bond discount = $200 ($5,000 x 4%)

Maturity period = 2 years

Interest rate = 4%

Semi-annual interest receipts = $100 ($5,000 x 4% x 1.2)

Total interest receipts = $400 ($100 x 4)

Total return (profit) from the bond = $600 ($400 + $200)

Total return on investment = 12.5% ($600/$4,800 x 100)

Thus, the bond investment yields $600 at the end of the maturity period, which is 12.5% of the initial investment.

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Answer:

y=-3/2x-3

Step-by-step explanation:

For perpendicular lines,the product of their slopes is -1 this m1•m2=-1

For the given line 3y=7+2x

y=7/3+⅔x,the slope is ⅔

For the unknown line since the y-intercept is -3 then y=mx-3

compare the slopes of both lines

m•⅔=-1

m=-3/2

hence the the perpendicular line has the equation

y=-3/2x-3

Answer:

160

Step-by-step explanation:

The total number of girls in grade is = 120

the ratio of girls to boys is 6/8

Let the number of boys be x

[tex]\frac{6}{8} = \frac{120}{x}[/tex]

6 x = 120 x 8 = 960

x = 960/6

x = 160

Number of boys in grade = 160

Answer:

Sell, 10.80

Step-by-step explanation:

PLATO Users be like

Answer:

weight dog trhee monts ago is 28.i pounds

Step-by-step explanation:

Percentage:

20% × 36 =

Weight dog trhee months ago:

Answer:

7/10 is the fraction that Represents the shaded boxes.

I think it will help you.

Answer:

7/10

Step-by-step explanation:

Apply law of cosines

[tex]\\ \rm\longmapsto c^2=a^2+b^2-2abcos\gamma[/tex]

[tex]\\ \rm\longmapsto c^2=150^2+35^2-2(150)(35)cos110[/tex]

[tex]\\ \rm\longmapsto c^2=22500+1225-10500(-0.34)[/tex]

[tex]\\ \rm\longmapsto c^2=23725+3570[/tex]

[tex]\\ \rm\longmapsto c^2=27295[/tex]

[tex]\\ \rm\longmapsto c=165.2yd[/tex]

Answer:

165 yd (nearest yard)

Step-by-step explanation:

To calculate the distance from the ball to the center of the green, we need to use the cosine rule:

[tex]c^2=a^2+b^2-2ab \cos (C)[/tex]

where:

Therefore, for this triangle:

Substituting these values into the cosine rule formula:

[tex]\implies c^2=35^2+150^2-2(35)(150) \cos (110\textdegree)[/tex]

[tex]\implies c^2=23725-10500\cos(110\textdegree)[/tex]

[tex]\implies c=\sqrt{23725-10500 \cos(110\textdegree)}[/tex]

[tex]\implies c=165.2761674...[/tex]

[tex]\implies c = 165 \textsf{ yd (nearest yard)}[/tex]

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

The y - intercept of the shown line on the graph is -4

Y - intercept is the " y - coordinate of the point on line when it cuts the y - axis "

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &201000\\ r=rate\to 0.5\%\to \frac{0.5}{100}\dotfill &0.005\\ t=\textit{elapsed time}\dotfill &1\\ \end{cases} \\\\\\ A=201000(1 + 0.005)^{1}\implies A=201000(1.005)\implies A=202005[/tex]

Step-by-step explanation:

all points on the x axis have a y value of 0.

so, we need to find all points (x, 0) with a distance of 16 to (4, -8).

the distance to a point is the Hypotenuse of the right-angled triangle with the coordinate differences as legs.

and so Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

so, in our case we have

16² = (4-x)² + (-8 - 0)²

256 = 16 - 8x + x² + 64 = x² - 8x + 80

x² - 8x - 176 = 0

if we have no other idea of factorization the general solution of such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -8

c = -176

x = (8 ± sqrt((-8)² - 4×1×-176))/(2×1) =

= (8 ± sqrt(64 + 704))/2 = (8 ± sqrt(768))/2 =

= (8 ± sqrt(256×3))/2 = (8 ± 16×sqrt(3))/2 =

= 4 ± 8×sqrt(3)

x1 = 4 + 8×sqrt(3) = 17.85640646...

x2 = 4 - 8×sqrt(3) = -9.856406461...

so, the points on the x axis that are 16 units apart from (4, -8) are

(x1, 0) and (x2, 0)

I am not sure in what format you need the answer.

please fill in for x1 and x2 from above what you need.

Answer:

Maggie = 15 hours

Ryan = 30 hours

Step-by-step explanation:

let x - time it takes Ryan to do the job alone.

x-15 - time it takes Maggie to do the job alone

[tex] \frac{10}{x} + \frac{10}{x - 15} = 1 \\ \\ \frac{10(x - 5) + 10x}{x(x - 15)} = 1[/tex]

[tex]10x - 150 + 10x = x {}^{2} - 15x \\ \\ 20x - 150 = x {}^{2} - 15x \\ \\ x {}^{2} - 15x - 20x + 150 = 0 \\ \\ x {}^{2} - 35x + 150 = 0 \\ \\ (x - 30)(x - 5) = 0 \\ \\ x = 30 \: and \: x - 15 = 15[/tex]

x = 5 --> not valid because x-15 will be NEGATIVE

Therfore,

Maggie can do the job in 15 hours.

Ryan can do the job in 30 hours.

Answer:

A=102 and B=0

Step-by-step explanation:

Sub values for X and Y into equation, put into your calculator and you will get the correct answer.

Answer:

a) 102

b) 0

Step-by-step explanation:

A:

B:

Answer:

-12(y-4x)

Step-by-step explanation:

-12y+48x=-12(y-4x)

Answer:

  3/2

Step-by-step explanation:

The composition of transformations has you dilate the line by a factor of 1/2, then by a factor of 3. Then the line is rotated about the origin.

The scale factor of the result will be the product of the dilation factors:

  (3)(1/2) = 3/2

The scale factor of the transformation is 3/2.

Answer:

3/2

Step-by-step explanation:

The composition of transformations has you dilate the line by a factor of 1/2, then by a factor of 3. Then the line is rotated about the origin.

The scale factor of the result will be the product of the dilation factors:

 (3)(1/2) = 3/2

The scale factor of the transformation is 3/2.

Step-by-step explanation:

a.

(ax + b)² = 0

√( (ax + b)²  )= √0

ax + b = 0

dont know the rest

Answer:

90-24=76°

Step-by-step explanation:

____________________

Step-by-step explanation:

The first one is [tex]6 \frac{1}{2} [/tex]

2nd is [tex]6 \frac{5}{8} [/tex]

3rd is [tex]6 \frac{3}{4} [/tex]

Answer:

44% is shaded

Step-by-step explanation:

Having carefully counted, I find 44 of the squares shaded. I'm sure of it.

Answer:

Yes, the other is correct. The answer is 44%

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{6a}{a^2-6a+9}}+\frac{9}{a^2-2a-3)}\\\\=\frac{6a}{(a-3)^2}+\frac{9}{(a-3)(a+1)}\\\\\\[/tex]

[tex]=\frac{6a(a+1)+9(a-3)}{(a-3)^2(a+1)}\\\\=\frac{6a^2+6a+9a-27}{(a-3)^2(a+1)}\\[/tex]

[tex]=\frac{6a^2+15a-27}{(a-3)^2(a+1)}\\\\=\frac{3(2a^2+5a-9)}{(a-3)^2(a+1)}[/tex]

Answer:

  E, F, A, ED, BC, EF, ABC, EDF

Step-by-step explanation:

The angle and side markings show which segments and angles are congruent.

We can make a table of corresponding pairs based on the number of marks:

marks, angle, side

__

This can help us fill in the question numbers:

Answer:

5 packages of Takis

Step-by-step explanation:

The total number packages that were placed on the shelf were 16 packages. The total number of packages of Flamas that were placed on the shelf were 9 packages. So to identify the number of packages of Takis the clerk put on the shelf, we simply do

16-9=5