Determine the 5th term in the sequence defined by g subscript n equals 9 times open parentheses 1 third close parentheses to the power of n minus 1 end exponent.

Answer:

(1, 1) , (5, 2), (6, 4), (4, 7) and (2, 3)

Step-by-step explanation:

When a point is rotated 180° about the origin(either clockwise or anticlockwise), the transformed coordinates are the negatives of the original coordinates.

Thus when a point (x, y) is rotated about the origin, its new coordinates become (-x, -y)

Given the original 5 vertices of the pentagon, the vertices of the rotated pentagon are transformed as follows

Original Vertex    ==>     Transformed Vertex

(-1, -1)                      ==>          (1, 1)
(-5, -2)                    ==>          (5, 2)
(-6, -4)                    ==>          (6, 4)
(-4, -7)                    ==>          (4, 7)
(-2, -3)                    ==>          (2, 3)

Answer:

A. (0, 4), (4, ∞)

B. (-∞, -4), (4, ∞)

C. (-∞, 0), (0, ∞)

Step-by-step explanation:

1

p(x) = -------- ; m(x) = x² - 16

√x

a.

p(x)

-------

m(x)

1 1

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

√x √x

------------------------------ = ---------------------

x² - 16 (x + 4)(x - 4)

Domain: (0, 4), (4, ∞)

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

B.

P(m(x))

1 1 1

------- = ----------------- = ----------------------

√x √(x² - 16) √(x - 4)(x + 4)

Domain: (-∞, -4), (4, ∞)

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

C.

M(p(x))

x² - 16

1 1

( ------- )² - 16 = ------- - 16

√x x

Domain: (-∞, 0), (0, ∞)

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

I hope this helps!

Answer:

Step-by-step explanation:

The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n) (nt)

where

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

here

we have to found semianually

P= 2000

r= 11% =0.11

n=2   .... for semiannual

t =5

A = 2000( 1 +0.11 /2 )(2*5)

 = 2000(1 +0.055)10

= 2000(1.055)10

= 2000(1.708)

=3416

The function y = (x + 3)² is the result of translating the function y = x² 3 units in the -x direction.

In this question we have a function of the form y = f(x), which is modified by transformation rules. The statement defines the original function as y = x² and we see that the resulting expression is y = (x + 3)². By direct observation, we that the latter function is the consequence of using an horizontal translation of the form:

g(x) = f(x - k), where k < 0.

This transformation rule indicates a horizontal translation in the - x direction. To be specific, a horizontal translation 3 units in the -x direction. Graphically specific, the graph of f(x) is moved 3 units in the - x direction.

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The equation can be expressed in Logarithmic form as log₃ 81 = 4

logarithmic form is a method to write equations when solving for a variable in an exponent.

Any exponential equation can be written as a logarithm. The logarithmic form is used to calculate an exponent of an equation.

The logarithmic form is a rearrangement of the exponential form. Exponential form: aᵇ = c

Logarithmic form: logₐ c = b

Comparing this with our equation, a=x, b=4, c=y

Therefore, we get the logarithmic form as log₃ 81 = 4

Hence, the Conversion from exponential form to logarithmic form gives the final answer as log₃ 81 = 4

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Answer: 1.7

Step-by-step explanation:

The simplification of the given logarithmic functions ln (2x-1)² = 7 is 17.055.

The logarithm of a number is the exponent by which a fixed value referred as the base should always be raised to generate a certain number. For instance, because 1000 is 10 to the third power, a log of 1000 to base 10 is 3.

Some properties of the logarithmic functions are defined as-

As, for the stated log or ln function ln (2 x-1)²=7

Use the power rule on the left side of the equation.

2 ln (2 x-1) = 7

Simplifying the equation.

ln (2 x-1) = 7/2

ln (2 x-1) = 3.5

Using the exponential property of the log.

e∧[ln (2 x-1)] = e∧3.5

2x-1 = 33.11

2x = 33.11 + 1

2x = 34.11

x = 34.11/2

x = 17.055

Therefore, the value of the x for the stated logarithmic functions ln (2x-1)² = 7 is calculated as 17.055.

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The area of a rectangular cement walkway of width x meters around a 50m by 25m pool is 4x²+150x sq. meters.

Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A rectangle is a form of a quadrilateral, a two-dimensional object with four sides and four vertices. The four angles of the rectangle are all perfectly right angles or 90 degrees. The opposing sides of the rectangle are equal and parallel.

Area of Rectangle = Length × Breadth

In the given question,

The width of the walkway is x meters.

Width of the pool= 25+2x meters

and the Length= 50+2x.

So the area of the walkway with the pool is

= (25+2x)+(50+2x)

= 1250+100x+50x+4x²

= 4x²+150x+1250 sq. m

Area of the pool= 50x25

= 1250 sq. m

Area of the walkway= 4x²+150x+1250-1250

= 4x²+150x sq. meters.

Hence, the answer is 4x²+150x sq. meters.

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The sum of (-3) + (-1) is -4.

The addition expression (-3) + (-1) on a number line is : (-4).

Here, we have,

To represent the addition expression (-3) + (-1) on a number line,

we would start at -3 and move to the left by 1 unit.

Here's how we can explain it step by step:

Start at -3 on the number line.

Since we have a negative sign in front of both numbers, we will move to the left (in the negative direction) on the number line.

The first number, -3, indicates that we will start at -3 on the number line.

The second number, -1, indicates that we will move to the left by 1 unit from -3.

When we move to the left from -3 by 1 unit, we will reach -4 on the number line.

So, (-3) + (-1) represented on the number line means starting at -3 and moving to the left by 1 unit, resulting in -4.

The sum of (-3) + (-1) is -4.

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If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.

Given data or information:

Feet away=40 feet away

Feet high=1,000 feet high

Now let find or determine  the angle of inclination rom Lily's location to the top of the waterfall

Hence,

tanФ=1,000/40

Ф=tan^-1 (1,000/40)

Ф=87.70°

Therefore If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.

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[tex]{\huge\color{yellow}{\boxed{\fcolorbox{blue}{black}{꧁ANSWER ꧂}}}} \\ \\ \frac{3}{4} + ( - \frac{1}{4} ) \\ \\ = \frac{9 - 3}{12} = \frac{6}{12} = \frac{2}{4} \\ \\ \frac{3}{8} + ( - \frac{3}{8}) = 0(cancel \: \: out)[/tex]

Answer:

3/4 + (-1/4)

-1/4 = -0.25

3/4 = 0.75

3/8 + (-3/8)

-3/8 = -0.375

3/8 = 0.375

The least sum of money can be made up of an exact number of 25 pieces or 50  pieces is 50.

So, the least sum:

Therefore, the least sum of money can be made up of an exact number of 25 pieces or 50 pieces is 50.

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The value of the stock after 2 years was 0.6497xx.

What is Mathematical expression?

The combination of number and variable by using addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

Christopher bought stock in a company two years ago that was worth xx dollars.

In the first year that he owned the stock, then it decreased by 11%.

In the second year the value of the stock decreased by 27%.

Now,

The multiplier of value for the first year was (1 - 11%) = 0.89

The multiplier of value for the second year was (1 - 27%) = 0.73

Then the multiplier of value for the two years was = 0.89 * 0.73

                                                                             = 0.6497

Hence, The value of the stock after 2 years was 0.6497xx.

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Answer: 100 million or 100,000,000

Step-by-step explanation:

Do the exponent in the brackets. Then the one outside of the brackets.

10 to the power of 4=10000(which is 10 x 10 x 10 x10)

Then figure out 10000 the the power of 2.

10000 x 10000 = 100,000,000

Therefore the value of this is 100 million.

Answer:

5x+40-7<23

5x+33<23

5x<-10

x<-2

Answer: 8c + 40

Step-by-step explanation: i did this on OW

Answer:

Step-by-step explanation:

w(t)  =  F(t) - D(t) = water into (or out of the pool)

        =  t^2 + 8t+9      -   (t^2 +11t+4)

 w(t)        = -3t + 5       <===== shows all of the water will leak out after 5/3 hr

the two functions intersect at 5/3 hr    this is where water in = water out = dry pool

Answer:

In the first image, the triangles are congruent because each side measures equally to the other. The circles are not because they are not the same size. The big circle is 4 by 4 squaes and the small circle is 2 by 2.

In the second image the first image is congruent, and in the second image the figures are not congruent because the image to the right is thinner than the left.

Step-by-step explanation:

Hope it helps! =D

Answer: Ok for the first screen shot (the one with the triangles) its yes then the circles no

the upside down L 's yes

and the quadrilaterals no

Step-by-step explanation: congruent means the same or identical.

Hope it helped :D

The answer to the present question is: log(a²b³/c⁴) = 2log(a) + 3log(b) - 4log(c)

For solving this kind of question, we are going to use these three identities:

log(x*y) = log(x) + log(y)   ....(1)

log(x/y) = log(x) - log(y)    ....(2)

log(xⁿ) = nlog(x)                ....(3)

So, using (2), log(a²b³/c⁴) may be written as: log(a²b³) - log(c⁴)  ....(4)

Again, using (1), log(a²b³) are often written as: log(a²) + log(b³)  ....(5)

Now, Putting equation (4) in equation (3), we get:

log(a²) + log(b³) - log(c⁴)   ....(5)

Now, using (3), expanding all the terms, we get:

log(a²) = 2log(a)log(b³) = 3log(b)log(c⁴) = 4log(c)

Putting of these in equation 5, we get:

2log(a) + 3log(b) - 4log(c)

Therefore,  log(a²b³/c⁴) = 2log(a) +3log(b) - 4log(c)

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After expanding logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_7(\sqrt{r} )+9}{s^2t^\frac{1}{3} }[/tex]

as, log (√x) = 1/2 log (x), equation becomes

[tex]= \frac{\frac{1}{2} log_7(r) + 9}{s^2t^\frac{1}{3} } \\[/tex]

now, after rationalize this equation

[tex]= \frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

Thus, after expanding the logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

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[tex] \large \bf \implies{(x - 6)^{2}(x + 1) }[/tex]

[tex] \sf \longrightarrow\frac{1}{ {x}^{2} - 5x - 6} \: and \: \frac{1}{ {x}^{2} - 12 + 36 } \\ [/tex]

[tex] \sf \longrightarrow \frac{1}{ {x}^{2} - 5x - 6 } = \frac{1}{(x - 6)(x + 1)} \\ \\ \sf \: and \\ \\ \sf \longrightarrow \frac{1}{ {x}^{2} - 12x + 36 } = \frac{1}{(x - 6)(x - 6)} [/tex]

Step 1) : First of all notice that term is in standard form.

For eg :- 6x + 2x² + 5 = 2x² + 7x + 5

Step 2) : Multiply with first and last term.

2 × 5 = 10

Step 3) : Next we have multiply got the answer 10 and subtract or add we have got the answer 7.

Now, we have got the term. We have multiply 2 and 5 got the answer 10 and we have add got the answer 7.

Step 4) : Attach the factor into the removal of 7x

2x² + 5x + 2x + 5

Step 5) : Simplify it

Step 6) : We have got the answer

[tex]\sf \longrightarrow(2x + 5)(x + 1)[/tex]

We need to know about logarithm to solve this problem. The exponential form of the logarithm is [tex]2^{7} =128[/tex].

Logarithm is the exponent that is raised to a base to get a certain number.There are a few rules of logarithm, log a+ log b can be written as log ab, log a -log b can be written as log a/log b, when the number whose logarithm is being calculated is raised to a power, then the power can be multiplied to the log itself. Logarithm when written as log without base mentioned, the base is 10, the log of a number that is same as the base is always 1, the log of 1 is always 0 because a nonzero number raised to 0 is always 1. To write a logarithm in exponential form we have to raise the value of the logarithm to the base which is equal to the number whose logarithm we found.

[tex]log_{2} 128=7[/tex] can be written as [tex]2^{7} =128[/tex]

Therefore we found the exponential form of the logarithm to be [tex]2^{7} =128[/tex]

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Answer:

a

Step-by-step explanation:

the complement of R is 90 - R , then

R = 5(90 - R) - 6

R = 450 - 5R - 6

R = 444 - 5R ( add 5R to both sides )

6R = 444 ( divide both sides by 6 )

R = 74°

complement = 90° - 74° = 16°

Option(a) 16 is correct option, the measure of the complement of R is 16

Two angles are complementary if their sum is 90°.

Let x be an angle and y be its complement of x then x + y = 90°.

Let the measure of the complement of R be x

Given that the measure of angle R is 6 less than 5 times its complement

Then 5 times the complement of R = 5x

And 6 less than 5 times the complement of R  = 5x-6

Thus, R = 5x -6

∴ R + complement of R = 90°

⇒5x-6 + x = 90

⇒6x = 96

⇒x = 96/6 = 16

Therefore, the measure of the complement of angle R is 16 and option (a) is correct option.

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The decimal number will be 0.248.

So, decimal number less than 1:

Therefore, the decimal number will be 0.248.

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Answer:Student A

Step-by-step explanation:

1. -(3)

2.-19

20

When Todd says that he used 718 feathers to make the cat toys, it does not sound right.

To solve this problem, we have to state the equations using the information of the problem

Information about the problem:

Calculating how many feathers Todd should use to made 198 cat toys:

Total feathers = No. of toys * No. feather per toy

Total feathers = 198 toys  * 6 feather/ toy

Total feathers = 1188 feathers

With the calculate we can confirm that Todd's calculate is not right because:

Total feathers > Todd's calculated

1188 feathers > 718 feathers

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

[tex]\mathrm{88 + v}[/tex]

Darla can spend the greatest total cost of groceries in order to spend as close to $15 as possible is approximately $14.20.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let the cost of the groceries be represented as "c", then we have;

Cost price + VAT = c + (5% of c)

In order to get the cost, c, that make him spend as close to $15. Since the tax is 5% of the cost price, then the cost price will be close to $15.

Let c = $14.20, then;

So that,

c + (5% of c) = 14.20 + (5% of 14.20)

                   = 14.20 + 0.71

                   = $14.91

Therefore, the greatest total cost of groceries she can spend in order to spend as close to $15 as possible is approximately $14.20.

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Answer:

-85

Step-by-step explanation:

(-60) + (-25) = (-85)

Answer:

Step-by-step explanation:

the fish is 85 feet bellow the surface

explanation 60+25 is 85 so therefor -60-25 would be -85