The line with equation 5y - 4x = k , where k is a constant , does not intersect the circle with equation (x - 3) ^ 2 + (y + 2) ^ 2 = 41. Find the range of possible values of k .

The function g(x) is the inverse function of the function g(x).

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The functions are given below.

\(\rm \\f(x ) = \dfrac{3^{(1/2)x + 4} - 1}{5}\)

g(x) = 2 log₃ (5x + 1) - 8

Replace 'x' with 'y' and f(x) with 'x' in first function, then we have

\(\rm x = \dfrac{3^{(1/2)x + 4} - 1}{5}\)

Simplify the function, then we have

\(\rm x = \dfrac{3^{(1/2)y + 4} - 1}{5}\\\\5x = 3^{(1/2)y + 4} - 1\\\\5x + 1 = 3^{(1/2)y + 4}\)

Take log with base 3 on both sides, then the equation is rewritten as,

(1/2)y + 4 = log₃ (5x + 1)

(1/2)y = log₃ (5x + 1) - 4

y = 2log₃ (5x + 1) - 8

Replace 'y' with g(x),

g(x) = 2log₃ (5x + 1) - 8

The function g(x) is the inverse function of the function g(x).

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Answer:

  (g∘f)(x) = x

Step-by-step explanation:

You want to show that f(x) = (3^(x/2+4) -1)/5 and g(x)=2log₃(5x+1)-8 are inverses using composition.

Functions f(x) and g(x) will be inverses of each other if and only if ...

  (f∘g)(x) ≡ x

The composition in the other order will also be true:

  (g∘f)(x) ≡ x

Here, we judge it easier to evaluate (g∘f)(x) = g(f(x)), so we'll do that.

  \((g\circ f)(x)=2\log_3(5\dfrac{3^{\frac{1}{2}x+4}-1}{5}+1)-8=2\log_3(3^{\frac{1}{2}x+4}-1}+1)-8\\\\=2\log_3(3^{\frac{1}{2}x+4})-8=2(\frac{1}{2}x+4)-8=x+8-8\\\\\boxed{(g\circ f)(x)=x}\)

__

Additional comment

The attached graph shows the functions are reflections of each other in the line y=x, as inverse functions will be. The green lines and the intersection coordinates are shown because the graph resolution is not sufficient to show the functions are mirrors of each other near the axes for negative input values.

Answer: 7 3/4 x 3 5/7 is 28 11/14

Step-by-step explanation:

7 3/4 x 3 5/7

31/4 x 26/7

806/28

403/14 or 28 11/14

Answer:

44 2/7

Step-by-step explanation:

Turn into improper fractions

31/4*40/7

Cross Multiply (4 and 40)

31/1*10/7

Now multiply

310/7

Simplify

44 2/7

Hope this helps!!!

Have a great day!!!!

Answer:

f ≥ 5

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

2(f - 4) ≥ 2

Opening the bracket, we have;

2f - 8 ≥ 2

Rearranging the equation, we have;

2f ≥ 2 + 8

2f ≥ 10

Dividing both sides by 2, we have;

f ≥ 5

Therefore, the possible values for Felipe’s age is 5, 6, 7, 8, 10 till infinity.

Answer: 4m

Step-by-step explanation:

Note : midpoints divide a line into two equal parts.

To calculate the length of SA;

We can consider the large triangle QRS with

Two midpoints :

A on the line QS, QA = 4m ;

and B on the line RS with RB = 3m

Fron the definition of midpoint :

QS = QA + AS

where QA = AS

QS = 2QA = 2AS

Therefore,

QA = QS

4m = 4m

Answer:

4m

Step-by-step explanation:

Popeyes chicken sandwich bussin

Answer:

D

Step-by-step explanation:

I would have to assume its D since the starting point is (-7, 5) and the slope is 1/2, since it is a positive slope it would reach (13, 9)

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

D

Step-by-step explanation:

Answer:

1.875 pounds of tomatoes were used to make sauce

Step-by-step explanation:

Answer:

The standard deviation of the given data set

 σ =  2.135

Step-by-step explanation:

Step(i):-

Given numbers are 4 2 8 5 7

Mean of the numbers

 \(= \frac{4+2+8+5+7}{5}\)

= 5.2

The mean of the numbers (μ) = 5.2

Step(ii):-

x        :    4         2       8        5         7

x-μ     :   -1.2   -3.2     2.8    -0.2     1.8

(x-μ)² :   1.44    10.24  7.84  0.04    3.24

The standard deviation of the given data

            σ = √Σ( x-μ)² / N

           σ  = \(\sqrt{ \frac{1.44+10.24+7.84+0.04+3.24}{5}}\)

            σ =  2.135

The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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The Taylor polynomial of degree 5 about a = 0 of f is P₅(x) = 1 - x²/2! + x⁴/4!

From the question, we have the following parameters that can be used in our computation:

f(x) = cos(x).

The Taylor polynomial is calculated as

\(P_n(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)\²/2! + f'''(a)(x - a)\³/3! + ...\)

Recall that

f(x) = cos(x).

Differentiating the function f(x), the equation becomes

\(P_5(x) = cos(a) - sin(a)(x - a) - cos(a)(x - a)\²/2! + sin(a)(x - a)\³/3! + cos(a)(x - a)^4/4! - sin(a)(x - a)^5/5!\)

The value of a is 0

So, we have

\(P_5(x) = cos(0) - sin(0)(x - a) - cos(0)(x - a)\²/2! + sin(0)(x - a)\³/3! + cos(0)(x - a)^4/4! - sin(0)(x - a)^5/5!\)

This gives

P₅(x) = 1 - 0 - 1(x - 0)²/2! + 0 + 1(x - 0)⁴/4!  - 0

Evaluate

P₅(x) = 1 - x²/2! + x⁴/4!

Hence, the Taylor polynomial of degree 5 about a = 0 of f is P₅(x) = 1 - x²/2! + x⁴/4!

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The value of x is 77 cm which will make the triangles similar by SSS similarity theorem

Given length of the three sides of one triangle are  35 , 20 and 20

and length of the three sides of another triangle are  x, 44,44

We need to find the values of x by using SSS Similarity theorem

We know that triangles are are similar by side - side - side similarity creation and hence the sides are in the same ratio

As both the triangles are isosceles triangles

Therefore ,

x/35 = 44/20=44/20 (Using ratio)

Solving the equation we get

x=44*35/20

x= 77

Hence the value of x is 77cm

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Answer:

-1 or -1/1

Step-by-step explanation:

Looked it up, found an answer that said

"X+Y = 6

change into slope intercept form y=mx+b

y= -x +6

the number infront of X is the slope...so....-1/1 would be your slope

Parallel lines have the same slope, so the answer is -1 or -1/1"

Hope this is correct, and good luck

Answer: 0.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Michael is 33 years old and Brandon is 21 years old.

To find the current age of Michael and Brandon, we can use the information given in the problem to set up and solve a system of equations.

Let x be Brandon's current age, and y be Michael's current age.

From the problem, we know the following:

Michael is 12 years older than Brandon: y = x + 12

Seventeen years ago, Michael was 4 times as old as Brandon: y - 17 = 4(x - 17)

We can substitute the first equation into the second equation to eliminate y:

y - 17 = 4(x - 17)

x + 12 - 17 = 4(x - 17)

x - 5 = 4x - 68

3x = 63

x = 21

So, Brandon's current age is 21 years old.

We can use this information to find Michael's current age:

y = x + 12

y = 21 + 12

y = 33

So, Michael's current age is 33 years old.

Simultaneous equations are a set of two or more equations that contain the same variables. These equations must be solved together, or "simultaneously," in order to find the values of the variables. Solving simultaneous equations involves finding values for the variables that will make all the equations true at the same time.

The goal of solving a system of simultaneous equations is to find the values of the variables that satisfy all the equations in the system. The solution of the system of equations is the set of values that satisfy all the equations in the system.

In short, simultaneous equations are a set of two or more equations that contain the same variables. Solving simultaneous equations is to find the values of the variables that satisfy all the equations in the system. There are different methods to solve simultaneous equations such as substitution, elimination, and graphing.

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Answer:

D. -3, -7

Step-by-step explanation:

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

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Convergent series:A series is said to be convergent when the limits of the series converge to the finite possible value for the series.

Consider a series

Sn=a1+a2+a3+a4+........+an

this form a new series as ,

Sn(n=1 to infinity)=

=s.

It is important that the partial sum of series, there should be a limit existed and that is finite in nature then only the series converges.

The geometric series gives a proper idea of how the limit decides the convergent and divergent nature.

A series in which the individual term, approaches zero then series is convergent in nature but not for all time.

The series,

A convergent series is a series for which limits exist.

If the sequence of the partial sum is a convergent sequence.

G(r,c)=  r+c

where r≠1 then series converges.

Divergent series:

A series is an infinite series that does not converge at  any point,

had an infinite sequence of partial sums with no finite limit.

A series where the individual sum does not approaches zero diverges.

For e.g.

This series diverges.

Or harmonic series which diverges.

Where is limit tends to infinity, eventually series added up to infinity means no exact answer will be there.

For summing the divergent series  there method is:

FT

extrapolation methods.

Abelian theorems

Regularity, linearity, and stability test for the series.

If this test is checked then we will get to know which series diverges and converges.

It is not possible to determine whether a series converges or diverges based on its sum alone. The sum of a series can be finite, infinite, or undefined, but it does not provide information on whether the series converges or diverges. Other mathematical tests, such as the ratio test or the integral test, are used to determine whether a series converges or diverges.

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Answer:

40 degreses

Step-by-step explanation:

there is a right angle and that means it is 90 degreese then it gives you 50 degreese so you add them up and get 140 then you subtract that 140 from 180 and get 40 degreese.

Answer:

c

Step-by-step explanation:

cause it is

Number of metal sheets in the inventory are available for the mechanic's repair needs is 80, in the given arithmetic question.

Mathematical arithmetic is the study of the properties of whole and fractional numbers, both counting and not counting, as well as the fundamental operations performed on these numbers. In reality, the word isn't often used as a noun in the sense described above.

Math is a common designation for the subject in the early grades when numbers are the primary subject of study. Up until much later, when paradoxically it becomes Algebra I, the term "mathematics" is still used. In the latter, letters are frequently used as stand-ins for abstract or unknowable numbers.

If thickness of metal sheet is 0.155+0.235/ 2

= 39/2

= 0.195

80 metal sheets are available.

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Answer:

x = 19683 or x = 0

Step-by-step explanation:

Solve for x:

2 x = 54 x^(2/3)

Hint: | Isolate the radical to the left hand side by reversing the equality.

2 x = 54 x^(2/3) is equivalent to 54 x^(2/3) = 2 x:

54 x^(2/3) = 2 x

Hint: | Eliminate the power on the left hand side.

Raise both sides to the power of three:

157464 x^2 = 8 x^3

Hint: | Move everything to the left hand side.

Subtract 8 x^3 from both sides:

157464 x^2 - 8 x^3 = 0

Hint: | Factor the left hand side.

Factor x^2 and constant terms from the left hand side:

-8 x^2 (x - 19683) = 0

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by -8:

x^2 (x - 19683) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x - 19683 = 0 or x^2 = 0

Hint: | Look at the first equation: Solve for x.

Add 19683 to both sides:

x = 19683 or x^2 = 0

Hint: | Look at the second equation: Eliminate the exponent.

Take the square root of both sides:

Answer: x = 19683 or x = 0

Answer: 0.045%

Step-by-step explanation:

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

(i) a1/a2 =/ b1/b2

(ii) a1/a2=b1/b2 =/ c1/c2

(iii) a1/a2=b1/b2=c1/c2

Step-by-step explanation:

=/ means not equal to.

graphical repesentation of

1.intersecting lines

2.coincident lines

3.parallel lines

a1/a2 and next two slots is basically dividing the coefficents if each equation.

for eg. 1. a1/a2= 2/4=1/2 and so on.

parallel lines are inconsistent whereas intersecting and coincident lines are consistent.

Answer:

the standard form of y=5x+0.5 is B=-5x+y=0.5

Answer:

the answer is 5x - y= -0.5

Answer:

adassdasdsa c c c c cc c c c c c c c cc c c c

Step-by-step explanation:

win / total = 6 /9

For 15 games:

x / 15

Where x is the number of wins in 15 games.

Cross multiply:

Divide both sides by 9

They will win 10 games.

Answer:

To solve for x in 2a we need to set up an equation.

Since there are two equations with x that form a straight angle(180) we can make an equation by adding the given equations to making it equal 180.

(21x - 3) + (5x + 1) = 180

combine like terms

26x - 2 = 180

inverse property of subtraction is addition:

+2            +2

26x = 182

inverse property of multiplication is division:

/26     /26

X = 7

Now to solve for y in 2a:

Same concept, both equations that contain the variable y will be a striaght angle(180) so we form the equation by adding the given equations with the variable y to equal 180(straight angle).

(4y) + (17y - 9) = 180

combine like terms

21y - 9 = 180

inverse operation of adding is subtracting

+9             +9

21y = 189

Inverse property of multiplying is dividing

/21    /21

y = 9

*I'm sorry I can only help you with 2a*

for 2b use the same idea as I did with 2a or seek help from guardian members

Rolling-circle replication of plasmids proceeds in one direction from a single fixed origin

Explanation:

Rolling-circle replication of plasmids is a replication mechanism in which the replication process moves in one direction from a single fixed origin. Rolling-circle replication is a process that is often seen in circular plasmid DNA. It is a process that begins with an initiator protein, which is responsible for the nicking of a single DNA strand.The initiation point allows the helix to begin unwinding in one direction.

             As the DNA helix unwinds, replication is carried out in a continuous manner, and the helix is wound up behind it. During the replication process, a new strand is synthesized that is attached to the parent strand's 3' end.

                     Rolling-circle replication, on the other hand, is utilized to produce new plasmids that have a single strand, which can then be employed in other cells for the production of proteins or for research purposes.

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