You are backpacking through Europe. You have 30 days until your flight home, but you have spent all
have found a hotel that is willing to accept one link per night for payment of room and board. However,
the manager
that they want one gold link in payment for every link they cut. How many links will you have when
you call home?

The equation of the tangent line to the curve at the given point is given by: y = x + 1.

Now,

Given:

To find: Equation of a tangent line through the given point.

Finding:

y = [tex]e^{x}[/tex] cos(x)

By product rule of differentiation, y' = [tex]e^{x} sin(x) +e^{x} cos(x)[/tex]

For x = 0, y' (0) = 1 (0) + 1( 1) = 1 = slope of the line

Now, we know: equation of a line is given by:

[tex](y-y_0)=m(x-x_0)[/tex]

For [tex]x_0 = 0 And y_0 = 1[/tex], The equation of the tangent line will be:

=> y - 1  = 1 (x - 0)

=> y - 1 = x

=> y = x + 1

Hence, The equation of the tangent line to the curve at the given point is given by: y = x + 1.

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Answer: 4^15

Step-by-step explanation:

(4^3)^5=

4^(3*5)=4^15

Answer:

Step-by-step explanation:

20 divided by 5x20+10=90

Answer:

90

Step-by-step explanation:

this is easiest if you know your order of operations PEMDAS so there are no parenthesis or exponents so next is multiplication and division. so 20/5= 4 then 4*20 is 80 and 80+10=90.

here's an easy way to remember PEMDAS

Please Excuse My Dear Aunt Sally

Answer:

The nearest whole number is 830.

We have a three digit -  829.9.

We have to convert it into nearest whole number.

Step-by-step explanation:

The expression that gives the distance, d, between the ships after t hours is d = 25t

From the question, we are to write an expression that gives the distance, d, between the ships after t hours

First, we will determine the distance the ships have traveled after t hours

Using the formula,

Distance = Speed × Time

Thus,

The first ship would have traveled

20 × t miles

= 20t miles

The second ship would have traveled

15 × t miles

= 15t miles

Using the Pythagorean theorem,

The distance, d, between the ships after t hours is

d² = (20t)² + (15t)²

d² = 400t² + 225t²

d² = 625t²

d = √(625t²)

d = 25t miles

Hence, the expression that gives the distance, d, between the ships after t hours is d = 25t

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The present ages of Ann and Julie are 12 years and 8 years, respectively.

Let x, y be the current ages of Ann and Julie, whose features are synthetized in the following linear equations:

Ann is 4 years older than Julie

x = y + 4

x - y = 4                                (1)

4 years ago, Ann was twice as old as Julie

x - 4 = 2 · (y - 4)

x - 4 = 2 · y - 8

x - 2 · y = - 4                         (2)

Now we proceed to determine the ages of Ann and Julie by solving the system of linear equations: (x, y) = (12, 8)

The present ages of Ann and Julie are 12 years and 8 years, respectively.

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Answer:

M/paws= (3x-3) and m/rqs

=(x+19).

the value of x is

Step-by-step explanation:

Answer:

64,100

Step-by-step explanation:

64,100are the values that are perfect square

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The two numbers by setting up a linear equation are 56 and 32

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

Let the two numbers be x and y

Where

y = 4 + 1/2x

So, we have

x + y = 88

Substitute y = 4 + 1/2x in x + y = 88

x + 4 + 1/2x = 88

Evaluate

1.5x = 84

Divide by 1.5

x = 56

Substitute x = 56 in y = 4 + 1/2x

y = 4 + 1/2 * 56

Evaluate

y = 32

Hence, the two numbers by setting up a linear equation are 56 and 32

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The correct answer for given question is 6.

If every element of a non-empty set X has only one image or range to a non-empty set Y, a relation 'f' is said to be a function.

Or

If 'f' is the function from X to Y and (x,y) f, then f(x) = y, where y is the image of x and x is the preimage of y under function f. It is written as;

f: X → Y.

In accordance with the conditions stated in the question:

f(x) = 3x^2 and g(x) = 4x^3 + 1

The composition of functions is defined as fog(x) = f(g(x)), where the input for the function f(x) is the actual expression of the function g(x) in terms of "x":

f(g(x)) = f(4x^3 + 1)

f(g(x)) = 3(4x^3 + 1)^2

f(g(x)) = 3(4x^3 + 1) (4x^3 + 1)

f(g(x)) = 3(16x^6 + 8x^3 + 1)

f(g(x)) = 48x^6 + 24x^3 + 3

Therefore, the degree of the given expression is 6 (the highest power of the variable ‘x’)

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Answer:

30 pieces

540 inches of ribbon in total

Step-by-step explanation:

1 foot = 12 inches

9 feet of ribbon = (9x12) 108 inches of ribbon (1 roll)

5 x 108 = 540 inches of ribbon (in total)

540 / 18 = 30

30 pieces of ribbon

The independent variable x ,represents minutes and dependent variable is the number of candies eating by Levi because the eating of candies depends on the minutes.

A function relating these variable is Z(x)=4x

So Z(7)=28 meaning In 7 minutes Levi ate 28 candies and number of candies left in the bag is 22.

As given,

Independent variable=x

Dependent variable=Z(x)

Function Z(x)=4x

So, Z(7)=4×7

            =28

Candies left in bag =50 -28

                              =22

Therefore, function relating independent variable x with Z(x)=4x  and Z(7)=28 represents number of candies ate by Levi in 7 minutes ,number of candies left in the bag is 22.

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Answer: f(x)=x^2+2x+1 and g(x)=-x^2+1 ==> 1st option

Step-by-step explanation:

Both are quadratic equations: -x^2 or x^2

Blue graph: x^2 since it's facing up

f(x)=(x-b)^2

Vertex: When x=-1, y=0 ==> 0=(-1+b)^2

0=-1+b

b=1

f(x)=(x+1)^2

f(x)=(x+1)(x+1)

f(x)=x^2+x+x+1

f(x)=x^2+2x+1

Red graph: -x^2 since it's facing down

g(x)=-x^2+b

Vertex: When x=0, y=1 ==> 1=(0)^2+b

1=0+b

b=1

g(x)=-x^2+1

f(x)=x^2+2x+1 and g(x)=-x^2+1 ==> 1st option

1/3 is the probability of rolling either a 5 or a 6 using a normal six-sided die.

Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event.

Given:

Six-sided dice rolled once

Let n be the number of outcomes

let x be the number of favorable outcomes

We know that,

[tex]Probability=\frac{x}{n}[/tex]

When the six-sided dice roll, The possible outcomes are,

[tex]\{1,\;2,\;3,\;4,\;5,\;6\}[/tex]

Therefore,

[tex]Number\;of\;outcomes,\;n=6[/tex]

[tex]Probability\;rolling\;5\;is\;\frac{1}{6}[/tex]

[tex]Probability\;rolling\;6\;is\;\frac{1}{6}[/tex]

Therefore, Probability of rolling either 5 or 6 is,

[tex]P(5\;or\;6)=\frac{1}{6} +\frac{1}{6}[/tex]

[tex]P(5\;or\;6)=\frac{2}{6}[/tex]

[tex]P(5\;or\;6)=\frac{1}{3}[/tex]

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By unitary method we can say that number of stacks of papers Lashona will pass back  from 140 if each stack conatins 28 papers is 5.

According to the given question.

Total number of papers Lashonna passed back = 140

And one stack is made up of 28 papers.

As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Therefore,

By unitary method number of stacks of papers would be made from 140 if each stack conatins 28 papers

= 140/28

= 5

Hence, by unitary method we can say that number of stacks of papers Lashona will pass back  from 140 if each stack conatins 28 papers is 5.

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The Associative property is not  displayed by any of the given equations.

The associative property of several binary operations in mathematics states that the outcome will not change if the parenthesis in an expression are rearranged.

The order in which the operations are carried out within an expression that has two or more instances of the same associative operator in a row doesn't matter as long as the order of the operands is left untouched.

Examples of associative property :

[tex]{\displaystyle {\begin{aligned}(7+8)+1&=7+(8+1)=9\,\\5\times (3\times 7)&=(5\times 3)\times 7=24.\end{aligned}}}[/tex]

The parentheses were rearranged on each line, but the expression values were left alone. It can be argued that "addition and multiplication of real numbers are associative operations" because this is true for addition and multiplication of all real numbers.

Here 8=8+0 displays additive identity property.

10×1=10 displays multiplicative identity

5+0=5 displays displays additive identity property.

[tex]5\times \frac{1}{5}=1[/tex]  displays multiplicative inverse property.

[tex]3+\frac{3}{4} =3+\frac{3}{4}[/tex]  displays reflexive property.

Hence no equation displays associative property.

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Answer:

1. 5h

2. 4h

3. h

4. ht

5. hx (x + 1)

Step-by-step explanation:

1/3 is equal to 0.3333333...

1/10 is equal to 0.1

If you subtract the two you will get a fraction equal to 0.23333333...

[tex]\frac{1}{3} - \frac{1}{10} \\\\[/tex]

Get a common denominator

[tex]= \frac{10}{30} - \frac{3}{30}[/tex]

Then combine them

[tex]= \frac{10-3}{30}\\\\= \frac{7}{30}[/tex]

Your answer is [tex]\frac{7}{30}[/tex]

[tex]Answer:\ -55.102^0F\leq t^0\leq 595.958^0F[/tex]

Step-by-step explanation:

[tex]\displaystyle\\C^0=\frac{5}{9} (F^0-32^0)\\[/tex]

Let's multiply both parts of the equation by 9/5:

[tex]\displaystyle\\\frac{9}{5} C^0=F^0-32^0\\\\\frac{9}{5} C^0+32^0=F^0-32^0+32^0\\\\\frac{9}{5} C^0+32^0=F^0\\\\Thus,\\\\F^0=1.8C^0+32^0[/tex]

[tex]t=-48.39^0C\\Hence,\\t^0(F)=1.8(-48.39^0)+32^0\\t^0(F)=-87.102^0+32^0\\t^0(F)=-55.102^0[/tex]

[tex]t=313,31^0C\\Hence,\\t^0(F)=1.8(313,31^0)+32^0\\t^0(F)=563.958^0+32^0\\t^0(F)=595.958^0[/tex]

[tex]Thus,\\-55.102^0F\leq t^0\leq 595.958^0F[/tex]

Answer:

16

Step-by-step explanation:

Given that the total number of seats in an auditorium is modeled by the following equation:where x represents the number of rows of seats.We are to find the number of rows are there in the auditorium with a total of 416 seats.So, we are to find the value of x if f(x) = 416.

Since the number of rows cannot be negative, so the required number of rows in the auditorium is 16.Thus, the number f rows is 16.

Answer:

122 degrees

Step-by-step explanation:

43 + 15 = 58 - 180 = 122

Answer:

F(x) = -6x - 3

F(x) = -6(-8) - 3

F(x) = 48 - 3

F(x) = 45

7.86 liters  of purple paint in each container.

volume of red paint is 8.54 liters.

volume of blue paint is 8.31 liters.

Number of container taken is 2 container.

Paint left after equally poured in 2 container.

and we have to find how many liters of paint are in each container.

Volume of RED Paint + Volume of BLUE Paint =  Volume of PURPLE Paint

8.54 liters + 8.31 liters = 16.85 liters.

(16.85/2) - (1.13/2) = 15.72/2

                            =7.86 liters

7.86 liters of purple paint in each container.

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Answer: 31 times

Step-by-step explanation:

Answer:

$31.6666667

Step-by-step explanation:

$64 - $16.50 =$47.5

$47.5÷$1.50 =$31.6666667

i used a calculator

The expression for m from the given equation is m = E/o^2

The subject of formula is a way of representing a variable with another variable

Given the equation

E = mo^2

We are to make m the subject of the formula. To do that, we will divide both sides of the equation by o^2 to have:

E/o^2 = mo^2/o^2

E/o^2 = m

Swap

m = E/o^2

Hence the expression for m from the given equation is m = E/o^2

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The tax on the product will be $1.964.

It should be noted that from the information, the sales tax is 6% and the price of the product is $32.74.

Therefore, the value of the tax will be:.

Tax percentage × Price

= 6% × $32.74

= 0.06 × $32.74

= $1.9643

Therefore, the tax on the product will be $1.964.

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Answer:

ssdf

Step-by-step explanation:

dbd beddbees sveveusbs wie eje edidjebebe djebejdjebe ejd s

Answer:

1.6

Step-by-step explanation:

| -1.6 | = 1.6