Seven angles of an octagon measure 105, 139, 131, 115, 155, 138, and 145 degrees. What is the measure of the eighth angle?

The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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Answer:

63 grams

Step-by-step explanation:

42*4+Δ = 42+ 3*Δ

168 +Δ = 42 +3Δ subtract a triangle from both sides

168+Δ-Δ=42+3Δ-Δ

168 = 42 +2Δsubtract 42 from both sides

168-42 = 2Δ

126 = 2Δ divide both sides by 2

63 = Δ

Answer:

2 60in 56 going in the 60 two weeks 46ms

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer: $60  

Step-by-step explanation:beauce $50 of a 20% of a tip is $10. 20% tip equals $10.

The demand equation, by assuming it is linear. The equation expresses price p in terms of quantity q, q  =  -10000/3p + 52000

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

An album is downloaded 12000 times per week when its price is $12

It is downloaded 22000 times per week when the price drops to $9

The demand equation = ?

Suppose, price is expressed as p and quantity as q

Formula of linear relationship,

y = mx + c

So,

q  = mp + c

when,  p = 12 then q = 12000

12000 = 12m + c  _________(i)

when, p = 9 then q = 22000

22000 = 9m + c  _________ (ii)

Now by using elimination method solve equation i & ii

12m + c    =   12000

- 9m + (-c) =  -22000

3m  = -10000

m  = -10000/3

12m + c = 12000

c  = 12000 - 12 x (-10000/3)

c  =  12000 + 40000

c  =   52000

q  = -10000/3p + 52000

The equation is q  =  -10000/3p + 52000

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\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

We have two given terms :

Now, we have to find the breadth of his plot ~

that is :

\(\qquad \sf  \dashrightarrow \: area = length \times breadth\)

\(\qquad \sf  \dashrightarrow \: 800 = 32 \times b\)

\(\qquad \sf  \dashrightarrow \: b = 800 \div 32\)

\(\qquad \sf  \dashrightarrow \: b = 25 \: m\)

Therefore, breadth of the rectangular plot is 25 m

So, correct choice is C

Raju decided to purchase a rectangular plot with an area = 800 Square meters.

length of the plot = 32 m

Breadth of the plot = (b)

● Area = Length × Breadth

● 800 = 32 × Breadth

● \( \frac{800}{32} \) = Breadth

● 25 = Breadth

Breadth = 25

Therefore, Breadth of the rectangular plot is 25 m.

Answer:

x = 6

y = 4

Step-by-step explanation:

2(4x + 1) = 11x - 16

8x + 2 = 11x - 16

8x + 2 + 16 = 11x - 16 + 16

8x + 18 = 11x

8x + 18 - 8x = 11x - 8x

18 = 3x

6 = x

5y + 4 = 8(y - 1)

5y + 4 = 8y - 8

5y + 4 + 8 = 8y - 8 + 8

5y + 12 = 8y

5y + 12 - 5y = 8y - 5y

12 = 3y

4 = y

The product of rational numbers to represent the change in the submarine’s elevation after 3 hours is 1/120 × 180

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the submarine descends 1/120 mile every minute.

There are 60 minutes in 1 hour. Therefore, 3 hours will be:

= 3 × 60

= 180 minutes

The product will be:

= 1/120 × 180

= 3/2

= 1.5 miles

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Answer:

It's a, b, and e just to clarify with the multiple answers/comments.

Step-by-step explanation:

I just did it on edge

The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:

Branch of Santosh & Co. Chennai

For the year ended December 31, 2018

Sales revenue            $40,300

Cost of goods sold         4,200

Gross profit                 $36,100

Expenses:

Office expenses $36,000

Salaries                    3,600

Total expenses         $39,600

Loss                             $3,500

An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.

The profit or loss is the difference between the total revenue and the total expenses for the accounting period.

Credit sales at branch 40,000

Office expenses by Head office 36,000

Cash remittance to branch for petty cash 9,000

Goods sent to Branch 7,200

Salaries paid by head office 3,600

Debtors 31.12.2018 30,000

Petty cash on 31.12.2018 16,200

Cash sales at branch 300

Stock of 31.12.2018 3,000

Sales revenue   $40,300 ($40,000 + $300)

Cost of goods sold $4,200 ($7,200 - $3,000)

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The recursive formula for p(n) is; p(n) = p(n-2) + p(n-3) for n >= 3. Case 1: The last square is painted white. If the last square is painted white, then the second to last square must be painted gold.

There are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Case 2: The last square is painted gold. If the last square is painted gold, then the second to last square can be painted either white or gold. If the second to last square is painted white, then there are p(n-3) ways to paint the remaining n-3 squares of the checkerboard subject to the restriction.

If the second to last square is painted gold, then there are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Therefore, the recursive formula for p(n) is: p(n) = p(n-2) + p(n-3) for n >= 3

with initial conditions p(1) = 2 and p(2) = 3.

The base case for the recursion is p(1) = 2 and p(2) = 3, which are the number of ways to paint a 1 x 1 checkerboard and a 1 x 2 checkerboard subject to the restriction, respectively.

The recursive formula counts the number of ways to paint a 1 x n checkerboard subject to the restriction by considering the last column of the checkerboard.

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Answer:

C

Step-by-step explanation:

7.55 x 35 =

264.25

Hope this helped

Answer:

D

Step-by-step explanation:

The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.

We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

α = (1 - 0.90)/2 = 0.05.

Now, we have to find z in the Ztable as such z has a p-value of 1 - α.

So it is z with a pvalue of  1 - 0.05 = 0.95 = 1.96.

Now, find the margin of error M as such,

M = z×(sigma/√n).

5 = 1.96×(16/√n).

5√n = 31.36.

n = 39.9.

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Answer:

A would be your answer.

Step-by-step explanation:

An irrational number shows that it's never ending, and that it doesn't repeat. Therefore, A would be correct.

Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

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The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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Answer:

The 1st one

Step-by-step explanation:

Linear relates to a graph that depicts a straight line when the values are plugged in and plotted. Here the only graph with a straight line is graph a.

Graph A- Linear ✅

Graph B- A quadratic functions graph( the shape of a parabola or like the letter U)

Graph C- A quadratic functions graph( the shape of a parabola or like the letter U)

Graph D- A square root function's graph.

Answer:

11/12

Step-by-step explanation:

We compute

1 2/3 - 3/4 =

5/3 - 3/4 =

20/12 - 9/12 =

11/12 Cups

Answer:

Step-by-step explanation:

To find the vertex from the given table look when the values of x or y start to switch the pattern. For example look at y value they get lower and lower 15,8,3,0,-1 then they get greater and greater 0, 3,8,15,24,...

So the he vertex is at (-2, -1) because here is where the pattern changed.

Y-intercept of the parabola is where the parabola intersects the y-axis so the x must be 0 there. Look in the table where is x=0 and see is at y=3.

Y-intercept point is at (0, 3)

X-intercept of the parabola is where the parabola intersects the x-axis so the y must be 0 there. Look in the table where is y = 0 and see is at x= -1 and also at x= -3.

X-intercept points are at (-1, 0) and (-3, 0)

Equation of the parabola in factored form is in general

y= (x- x intercept1)(x- x intercept 2), and for our problem is:

y = (x +1)(x +3)

The equation for the axis of symmetry is x = -2 because we have a vertical parabola (since x is squared in the equation) and the vertex is as we said previously at (-2, -1).

Answer:

Step-by-step explanation:

Domain of the function will be,

{x ∈ R | x ≠ -2}

Range of the function is,

{y ∈ R | y ≠ -4}

Intercepts of the function,

Their are no intercepts of the given rational function.

Horizontal asymptotes:

Horizontal line parallel to x-axis representing discontinuity.

y = -4

Vertical asymptotes:

Vertical line parallel to y-axis representing discontinuity.

x = -2

No oblique asymptotes.

A function assigns the value of each element of one set to the other. There are no oblique asymptotes of the given rational function.

A function assigns the value of each element of one set to the other specific element of another set.

The domain of the function

1. The Domain of the function will be {x ∈ R | x ≠ -2}

2.The Range of the function is {y ∈ R | y ≠ -4}

3. As the given function is a rational function, therefore, there are no intercepts of the given function.

4. The Horizontal line parallel to the x-axis represents the discontinuity of the horizontal asymptotes. Therefore, the horizontal asymptotes of the function will lie at y = - 4.

5. The Vertical line parallel to the y-axis represents the discontinuity of the vertical asymptotes. Therefore, the vertical asymptotes of the function will lie at x = -2.

6. There are no oblique asymptotes of the given rational function.

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Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

They may bake 20 additional bags of cookies. The problem is represented by the inequality x < 80.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, A bakery wants to bag at most 100 cookies into cookie packs. Each cookie pack has 4 cookies. They have already bagged 20 cookies.

Since each cookie pack can hold 4 cookies

Thus, 100 cookies will require = 100/4 packs

100 cookies will required = 25 packs

Since They have already bagged 20 cookies.

Thus,

The total pack they used = 20/4

The total pack they used = 5

Inequality:

let "x" be the number of cookies they can make

80 > x

Therefore, 20 more bags of cookies they could make. the inequality that represents the situation is x< 80.

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AB = CD = √8 ≈ 2.8 units

BC = AD = √2 ≈ 1.4 units

Area of the rectangle ABCD = 3.92 units²

Perimeter of the rectangle ABCD = 8.4 units

Given the coordinates of vertices of rectangle ABCD as:

To find the area and perimeter, use the distance formula to find the distance between A and B, and B and C.

Using the distance formula, we have the following:

AB = √[(2−0)² + (4−2)²]

AB = √[(2)² + (2)²]

AB = √8 ≈ 2.8 units

CD = √8 ≈ 2.8 units

BC = √[(2−3)² + (4−3)²]

BC = √[(−1)² + (1)²]

BC = √2 ≈ 1.4 units

AD = √2 ≈ 1.4 units

Area of the rectangle ABCD = (AB)(BC) = (2.8)(1.4) = 3.92 units²

Perimeter of the rectangle ABCD = 2(AB + BC) = 2(2.8 + 1.4) = 8.4 units

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Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

Answer:

\(y=x+1\)

Step-by-step explanation:

I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.

\(f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})]\)

Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for \(x=1\):

\(f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1\)

We're almost done. We got the point, we have the slope, we can rewrite the tangent line as

\(y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1\)