f(x)=4x+1 and g(x)=2x2+1, find (f∘g)(x) and (g∘f)(x)

The inverse equation of x = y is y = x

Inverse equations are the opposite of an original equation

The equation is given as

x = y

Swap the positions of x and y in the above equation

y = x

This means that the inverse equation of x = y is y = x

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The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units

As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.

Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).

Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)

Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).

Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).

This is the coordinates for A'.

Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.

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Answer:

376.99112cm²

Step-by-step explanation:

A=2 pi rh + 2 pi r²

A=(2 x pi x 5 x 7) + (2 x pi 5²)

pi 22/7

Answer:

c

Step-by-step explanation:

The measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line AT at C, and R respectively such that the angle ∠DCR is 77 degrees.

We know that the angle ∠DCR & ∠SRT and ∠DCR & ∠SRT are corresponding angles. Then they are equal to each other.

∠DCR = ∠SRT = 77°

∠CRQ = ∠CRS

We know that the angle ∠CRQ and ∠CRS are supplementary angles. Then we have

∠CRQ + ∠SRT = 180°

∠CRQ + 77° = 180°

∠CRQ = 103°

Then the measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.

The diagram is given below.

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a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

The future value can be determined using an online finance calculator.

Data and Calculations:

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

Result:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

Using the formula A = Pert

Principal (P):  $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years):   8 years

Result:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50,  the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

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[tex]g(x)=f(4x)=(4x)^2 = 16x^2[/tex]

The graph is shown in the attached image.

Answer:

Slope: [tex]-\frac{1}{5}[/tex]   Y-intercept: (0,0)

Step-by-step explanation:

By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].

Answer:

k ≈ 50.77

Step-by-step explanation:

using the cosine ratio in the right triangle

cos19° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{48}{k}[/tex] ( multiply both sides by k )

k × cos19° = 48 ( divide both sides by cos19° )

k = [tex]\frac{48}{cos19}[/tex] ≈ 50.77 ( to 2 dec. places )

Hi :)

            We'll use sohcahtoa to solve this problem

[tex]\Large\boxed{\begin{tabular}{c|1} \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~\div \text{hyp}\\\sf{Cah} & Adj \div \text{hyp}\\\sf{Toa} & Opp \div \text{adj} \end{tabular}}[/tex]

Looking at our triangle, we can clearly see that we have :

Set up the ratio

[tex]\longrightarrow\darkblue\sf{cos(19)=\dfrac{48}{k}}[/tex]

solve for k

[tex]\longrightarrow\darkblue\sf{k\cos(19)=48}[/tex] > multiply both sides by k to clear the fraction

[tex]\longrightarrow\darkblue\sf{k=\dfrac{48}{\cos(19)}}[/tex]  > divide both sides by cos (19)

[tex]\star\longrightarrow\darkblue\sf{k\approx50.77}\star[/tex]

[tex]\tt{Learn~More ; Work\ Harder}[/tex]

:)

The value of the probability P(A and B) is 0.20

The given parameters about the probability are

P(A or B) = 0.9

P(A) = 0.5

P(B) = 0.6

To calculate the probability P(A and B), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

P(A and B) = 0.5 + 0.6 - 0.9

Evaluate the expression

P(A and B) = 0.2

Hence, the value of the probability P(A and B) is 0.20

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hope this helps

by

aman10we

The value of x after solving this equation is 2

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, the equation as : (4x - 5)^4 = 81.​

(4x - 5)^4 = 3⁴.​

4x - 5    = 3

      x     = 2

Hence, the value of x is equal to 2

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The solution to the original equation is 1, 1/6

Equations are expressions separated by mathematical operations.

Given the equation below

x/x − 1 = 6x + 1/x − 1

From the given expression, the least common denominator is x -1

Multiply both sides by x-1 to have;

x = 6x(x-1) +1

Expand

x = 6x^2-6x + 1

Equate to zero

6x^2-6x-x + 1 = 0

6x^2-7x +1= 0

The resulting quadratic equation in general form is 6x^2-7x +1 = 0

Factorize

6x^2 -6x-x + 1 = 0

Group the result

6x(x-1)-1(x-1) = 0

(6x-1)(x-1) = 0

6x - 1 = 0 and x -1 = 0

x = 1 and 1/6

Hence the solution to the original equation is 1, 1/6

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By solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.

Given two equations x+2y=5 and 4x-12y=-20.

We are required to solve the equations through elimination and substitution method.

Firstly we will solve the equations through elimination method.

x+2y=5-------------1

4x-12y=-20--------2

Multiply the equation 1 by 4 and then subtract the equation 2 from equation 1.

4x+8y-4x+12y=20+20

20y=40

y=2

Use the value of y in 1

x=5-2*2

x=5-4

x=1

From substitution method.

First find the value of x from first equation in terms of y.

x=5-2y-----4

Now put this value in second equation to get the value of y.

4(5-2y)-12y=-20

20-8y-12y=-20

20-20y=-20

-20y=-40

y=2

Put the value of y in equation 4.

x=5-2y

x=5-2*2

x=5-4

x=1

Hence by solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.

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Answer:

For example, 8f + 4g is one of the most used expression

Another example is 4 (2f + g), is correct too

Answer:

2

Step-by-step explanation:

The linear function whose points are given is f(x)=[tex]x/5 +1[/tex]

Given the points of the function f(-10)=-1,f(0)=1,f(10)=3.

We are required to find the function whose points are given.

Function is relationship between two or more variables that are expressed in equal to form. In function each value of x must have a corresponding y value.

x value is known as domain and y value if known as codomain of the function.

Take two points (-10,-1) and (0,1) and we can form one equation as under:

y+1=(1+1/0+10) * (x+10)

y+1=2/10 (x+10)

y+1=x/5 +10/5

y+1=x/5+2

y=x/5+2-1

y=x/5+1

Hence the linear function whose points are given is [tex]f(x) = x/5 +1[/tex]

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Answer:

Step-by-step explanation:

12 + 2x + 24 = 27 + x

2x + 36 = 27 + x

x + 36 = 27

x = -9

2(-9) + 24 = -18 + 24 = 6

12 + 6 = 18

27 + (-9) = 18

Answer:

mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Answer:

a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).

a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).

b.i) The Hare runs 31,680 inches per minute (1,900,800/60).

b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).

c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).

In this exercise, the following equivalent values are used for computing the distance and speed:

Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)

Speed of Hare = 30mph

30 miles = 52,800 yards (30 x 1,760)

52,800 yards = 1,900,800 inches (52,800 x 36)

= 880 yards per minute (52,800/60)

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Answer:

=====================================

We know that diagonals of rhombus are perpendicular to each other.

Hence its area is half the product of diagonals.

The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.

Let's find the length of diagonals, using the difference of coordinates:

Now find the area:

Answer:

[tex]-3(x-2)^2+5[/tex]

Step-by-step explanation:

First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].

Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].

In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].

What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]

Finally, plugging  [tex]b = -2[/tex]  that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get  [tex](x^2 - 4x + 4) = (x-2)^2[/tex].

So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].

In summary, the procedure is

[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]

The expression that represents the perimeter of the rectangle is 30h - 2

The dimensions of the rectangle are given as:

Length = 7h + 3

Width = 8h - 4

The perimeter of the rectangle is given as:

P = 2 * (Length + Width)

Substitute the known values in the above equation

P =2 * (7h + 3 + 8h - 4)

Evaluate the like terms

P = 2 * (15h - 1)

Evaluate the product

P = 30h - 2

Hence, the expression that represents the perimeter of the rectangle is 30h - 2

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[tex]f(x) = \sqrt[3]{11x} \\ y = \sqrt[3]{11x} \\ x = \sqrt[3]{11y} \\ x {}^{3} = 11y \\ y = \frac{x {}^{3} }{11} [/tex]

[tex]f(x) = \frac{x}{7} + 10 \\ y = \frac{x}{7} + 10 \\ x = \frac{y}{7} + 10 \\ x - 10 = \frac{y}{7} \\ y = \frac{x - 10}{7} [/tex]

[tex]f(x) = \frac{7}{x} - 2 \\ y = \frac{7}{x} - 2 \\ x = \frac{7}{y} + 2 \\ x - 2 = \frac{7}{y} \\ y = \frac{7}{x - 2} [/tex]

[tex]f(x) = 9x - 6 \\ y = 9x - 6 \\ x = 9y - 6 \\ x + 6 = 9y \\ y = \frac{x + 6}{9} = g(x)[/tex]

So, the equation is sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)

The question has to to with trigonometric identities?

Trigonometric identities are equations that show the relationship between the trigonometric ratios.

Given the equation sin(x + y)/sin(x - y)

Using the trigonometric identities.

So, sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/(sinxcosy + cosxsiny)

Dividing the rnumerator and denominator of ight hand side by sinx, we have

sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/sinx/(sinxcosy + cosxsiny)/sinx

sin(x + y)/sin(x - y) = (sinxcosy/sinx + cosxsiny/sinx)/(sinxcosy/sinx + cosxsiny/sinx)

= (cosy + cotxsiny)/(cosy + cotxsiny) (since cosx/sinx = cotx)

Dividing the numerator and denominator of the right hand side by cosy, we have

= (cosy + cotxsiny)/cosy/(cosy + cotxsiny)/cosy

= (cosy/cosy + cotxsiny/cosy)/(cosy/cosy + cotxsiny/cosy)

= (1 + cotxstany)/(1 + cotxtany)   [since siny/cosy = tany]

So,  sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)

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[tex] \frac{3a}{4} > - 16 \\ 3a > - 64 \\ a > \frac{ - 64}{3} \\ a > 21 \frac{1}{3} [/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]

[tex]\mathsf{\dfrac{3}{4}a > - \dfrac{16}{1}}[/tex]

[tex]\huge\textbf{Divide \boxed{\dfrac{4}{3}} to both sides:}[/tex]

[tex]\mathsf{\dfrac{4}{3}\times\dfrac{3}{4}a > -16\times\dfrac{4}{3}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{a > \dfrac{4}{3}\times -16}[/tex]

[tex]\mathsf{a > - \dfrac{16}{1} \times\dfrac{4}{3}}[/tex]

[tex]\mathsf{a > \dfrac{-16\times4}{1\times3}}[/tex]

[tex]\mathsf{a > \dfrac{-64}{3}}[/tex]

[tex]\mathsf{a > -\dfrac{64}{3}}[/tex]

[tex]\mathsf{a > -21 \dfrac{1}{3}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{- \frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

$15666.83 (2dp)

Step-by-step explanation:

Mean = Total of all values / Number of Values

= [tex]\frac{17484+14978+13521+14500+18540+14978}{6}[/tex]

=[tex]\frac{94001}{6}[/tex]

= $15666.83 (2dp)

The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.

The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.

If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).

Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:

(0, -6) = (x1, y1)

(2, 0) = (x2, y2)

Plug in the values into the slope formula to find the slope:

Slope (m) = (0 - (-6)) / (2 - 0)

Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]

Slope (m) = (6) / (2)

Slope (m) = 3

Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.

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Answer:

[tex]2x+5y=41[/tex]

Step-by-step explanation:

Median of a triangle:  A line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Vertex:  The point where any two sides of a triangle meet.

Given vertices of a triangle:

Find the midpoint of BC (Point D) by using the Midpoint formula.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

Substitute the defined endpoints into the formula:

[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]

Therefore, D = (-27, 19).

Find the slope of the median (line AD) using the Slope formula.

Define the points:

Substitute the defined points into the Slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]

Therefore, the slope of the median is -²/₅.

Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]

Simplify and rearrange the equation so it is in standard form Ax+By=C:

[tex]\implies 5(y-9)=-2(x+2)[/tex]

[tex]\implies 5y-45=-2x-4[/tex]

[tex]\implies 2x+5y-45=-4[/tex]

[tex]\implies 2x+5y=41[/tex]

Therefore, the equation of the median is:  

2x + 5y = 41

Answer:

the price of one pound of trail mix is $3

the price of one pound of jelly beans is $2.5

Step-by-step explanation :

let t be the price of one pound of trail mix.

and b be the price of one pound of jelly beans.

This statement:

“For 3 pounds of trail mix and 8 pounds of jelly beans,

the total cost is $29”

Can be translated mathematically like this :

3t + 8b = 29

This statement:

“For 5 pounds of trail mix and 2 pounds of jelly beans,

the total cost is $20”

Can be translated mathematically like this :

5t + 2b = 20

We obtain a system of two equations :

3t + 8b = 29

5t + 2b = 20

Solving the system:

3t + 8b = 29  (equation 1)

5t + 2b = 20. (equation 2)

3t + 8b = 29

20t + 8b = 80   [4×(equation 2)]

3t + 8b = 29

17t = 51  [4×(equation 2) - equation 1]

3t + 8b = 29

t = 51/17 = 3

9 + 8b = 29

t = 3

8b = 20

t = 3

b = 20/8 = 5/2

t = 3

b = 5/2

t = 3

Therefore ,the solution to our system is (3 , 2.5)

Answer:

480

Step-by-step explanation:

1/5 of 400 =   1/5 * 400 = 80

  increase 400 by 80   = 480

Answer:

4,928 rounded to the nearest hundred = 4,900

Step-by-step explanation:

Greetings!

Hope it helps!

Answer:

The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).

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I hope help you :)

Kind regards, Antonio.