Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the function with its inverse.

Rewrite the limit as

[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5[/tex]

Then using the known limit,

[tex]\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1[/tex]

it follows that

[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}[/tex]

1. The mathematical expression that can be used to determine the total cost of mailing a package weighing p pounds is f(Tc) = 20 + 3p.

2. Since Betty spent $56 to mail her package, the weight in pounds of the mail must be 12 pounds.

A mathematical expression is a statement containing numbers, variables, and an arithmetic operation.

Flat (fixed) rate for mailing a package = $20

Variable mailing rate per pound = $3

Expression to model the total cost:

Let Tc = total cost

p = number of pounds

Tc = 20 + 3p

If Betty spent $56 to mail her package, the number of pounds, using the mathematical expression above:

Tc = 20 + 3p

56 = 20 + 3p

56 - 20 = 3p

36 = 3p

p = 12

Check:

Tc = 20 + 3p

56 = 20 + 3 (12)

56 = 20 + 36

56 = 56

Learn more about mathematical expressions at https://brainly.com/question/1852123

#SPJ1

y=-4x + 3

EXPLANATION

Given:

y = -4x + 5

To find the equation which represent a line that is parallel to the above, all we need to do is to oserve their slope.

Using a unique properties that states : slope of parallel lines are equal.

Observe that comparing the equation y =-4x + 5 with y=mx + b

slope = m= -4

From the option given, the only equation when compared with y=mx + b that has a slope of -4 is y=-4x + 3.

Therefore, the equation which represent a line that is parallel to y=-4x + 5 is y=-4x + 3

Answer:

If you have earned 20 points, this means you have passed 25 levels.

Step-by-step explanation:

25 =  5 (20/4)

Answer:

I hope this helps. Four is greater than six times a number t in inequality form is 4 › 6 * t

6 bottles are needed.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

given:

2 tablets 3 times per day

so, total tablets = 6 tablets

Total days = 14

so, total tablets in 14 days = 14 x 6 = 96

and, tablets per bottle= 15

Then, the number of bottles required = 96 /15 =6.4

Hence, 6 bottles are needed.

Learn more about unitary Method here:

https://brainly.com/question/22056199

#SPJ2

Let the Length of the rectangle be l and the width of the rectangle be w

The width of a rectangular field is 3 meters less than its length, this can be represented as

w = l - 3

Given the perimeter = 58meters

Perimeter of the rectangle = 2(l + w)

58 = 2(l + l-3)

58 = 2(2l - 3)

58 = 4l - 6

58 + 6 = 4l

64 = 4l

4l = 64

l = 64/4

l = 16

w = l - 3

w = 16 - 3

w = 13

Hence, the length of the rectangle is 16 meters while the width is 13 meters.

By substitute values in formula for volume of cuboid we get;

x² + 12x – 220 = 0

What is mean by Volume?

Volume of cuboid is defined as the amount of space occupied by the sides of cuboid in three-dimensional space.

Given that;

A cuboid with a volume of 924 cm' has dimensions,

4 cm, (x + 1) cm and (x + 11) cm.

Since, Volume of cuboid = Length x width x height

After substitute we get;

Volume of cuboid = 4 × (x + 1) × (x + 11)

924 = 4 (x² + 11x + x + 11)

924 = 4 (x² + 12x + 11)

Divide 4 both side;

231 = x² + 12x + 11

x² + 12x + 11 - 231 = 0

x² + 12x - 220 = 0

Thus, By the formula of volume of cuboid we get;

x² + 12x - 220 = 0

Learn more about the volume of cuboid visit:

https://brainly.com/question/22694657

#SPJ1

Given:

A passenger train traveled 35 miles in 50 minutes.

umber of miles that train can travel in one hour is 42 miles.

Answer:

261

Step-by-step explanation:

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.

Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .

                      Yes              No

Positive :          140            9

negative :         18              133

P = [tex]\frac{Someone get positive }{he not had the disease}[/tex]

= [tex]\frac{140}{142}[/tex]

=0.985

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

To learn more about probability visit:

brainly.com/question/12389726

#SPJ13

Given data:

The amount invested ( principal) is

The interest rate given is

The number of years is

The number of times compounded is quarterly

A quarterly event happens four times a year, at intervals of three months.

Concept:

The formula to calculate the amount compounded is given below as

By substituting the values above in the formula, we will have

By solving the equation above, we will have

Hence,

The final answer = $2,290.05

Answer: y= -2/5 + 36/5

Step-by-step explanation: when graphed, the slope is negative so it has to be -2/5x, and the y-intercept is positive so it has to be +36/5 (+7.2)

The number of payments to pay off the loan of $200,000 at 6.3% interest, compounded monthly is 315 monthly payments.

Using the compounding format for determining the monthly payments, the number of periods for the periodic payments can be computed.

In this situation, we used the online finance calculator to determine the number of payments.

Compounding accumulates the interest on a loan and adds it to the principal for computing subsequent interest.

At the end of the period, the balance is made up of the principal and compounded interest.

I/Y (Interest per year) = 6.3%

PV (Present Value) = $200,000

PMT (Periodic Payment) = $-1300

FV (Future Value) = $0

Results:

N (# of periods) = 314.854

Sum of all periodic payments = $-409,309.97

Total Interest $209,309.97

Thus, you are likely to make 315 monthly payments to settle the loan.

Learn more about periodic payments at https://brainly.com/question/13031679

#SPJ1

The finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes in Rocket Run 5k.

The formula for calculating the z-score is;

z = (x - μ)/σ

x = sample size

μ = mean of the sample

σ = standard deviation of the sample

The given values are-

μ =  57 minutes

σ = 8 minutes

Probability = 20% = 0.20

Find the z-score from the negative z table for 0.20

z score = -0.84

Put the values in z formula and find x.

z = (x - μ)/σ

-0.84 = (x - 57)/8

Simplifying;

x = -6.72 + 57

x = 50.28 minutes

Thus, finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes Rocket Run 5k.

To know more about the z-score, here

brainly.com/question/24213960

#SPJ13

1.4 repeating as a simple fraction is 13/9

Simple fraction is a fraction with whole number as the numerator and denominator. The top term is called numerator and the bottom term is called denominator.

Decimal number is a number that consist of one whole number and a fractional part and those are  separated by a decimal point

The repeating decimal = 1.4444

Consider the value x = 1.4444

Then multiply 10 on both side of the equation

We get

10x = 14.444

Subtract x from the 10x

10x-x = 14.444-1.4444

Subtract the like terms in the equation

9x = 13

Move 9 to the right hand side

x = 13/9

Hence, 1.4 repeating as a simple fraction is 13/9

The complete question is

1.4 repeating as a fraction in simplest form

Learn more about simple fraction here

brainly.com/question/2115640

#SPJ1

The measure of the vertically opposite angle ∠A = 136°

From the given question;

∠A and ∠B are vertical angles.

Thus, ∠A = ∠B

The values are given as;

∠A = (2x +26)°

∠B = (3x − 29)°

Equating both;

(2x +26)°  =  (3x − 29)°

Simplyfying;

2x + 26 = 3x − 29

3x - 2x = 26 + 29

x = 55

Put the value of x in ∠A = (2x +26)°

∠A = (2x +26)° = 2x55 +26

∠A = 136°

Thus, the measure of the vertical angle ∠A = 136°.

To know more about the vertically opposite angle, here

https://brainly.com/question/68367

#SPJ13

Ek, this is the solution:

Step 1: Let's review the information provided to us to answer the problem correctly.

Sales of the new toy = 2,000 per day

Price of the toy when sales are 2,000 per day = $ 6

Ther

The graph of the linear equation:

y = -3x + 4

Can be seen in the image at the end.

To draw a line, we just need to find two points that belong to the line, graph them, and then connect them with a  line.

Here we know that we have the line:

y = k*x + 4

Where k = -3, then:

y = -3*x + 4

By evaluating this in a value of x, for example, x = 0, we will get:

y = -3*0 + 4 = 4

Then we also have the point (0, 4) (and the given one, (2, -2))

So we can draw these two points and then connect them with a line (just use a ruler and draw a line that passes through both points).

Learn more about lines:

https://brainly.com/question/24644930

#SPJ1

Question 14

[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]

Question 15

[tex]\binom{15}{6}=\frac{15!}{9!6!}=5005[/tex]

The equivalent value to 2.76 is C. two and nineteen twenty-fifths.

An equivalent value is an amount or numerical expression possessing the same value as the other.

Equivalent values are expressed as equations, using the equation symbol (=).

Equations are a class of the properties of mathematical expressions, including numbers and variables.

Two and nineteen twenty-fifths = 2¹⁹/₂₅.

When expressed as a decimal, 2¹⁹/₂₅ = 2.76.

Thus, 2.76%, 27.6%, or twenty-five over nineteen are not equivalent values of 2.76 but 2¹⁹/₂₅.

Learn more about equivalent values at https://brainly.com/question/843074

#SPJ1

The table representing the exact values of y from the function is attached below.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The sets X and Y are referred to as the function's domain and codomain, respectively.

The given function is of the form y = 2x .

Now let us find the respective values of y for the given values of x.

At x = -2

y = 2x = 2 × (-2) = -4

At x = -1

y = 2x = 2 × (-1) = -2

At x = 0

y = 2x = 2 × (0) = 0

At x = 1

y = 2x = 2 × (1) = 2

At x = -2

y = 2x = 2 × (2) = 4

Therefore the table to represent this y-values of the function is [tex]\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}[/tex][tex]\begin{table}[]\begin{tabular}{ll} & \\ & \\ & \\ & \\ & \end{tabular}\end{table}[/tex]attached below.

To learn more about function visit:

https://brainly.com/question/12431044

#SPJ1

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.

Any two ordered pairs can be used to create a solution set on a graph by connecting them with a straight line. Thus, any point along this graphed line would be included in the solution set.

There is only one solution that holds true for both equations if the equations' graphs cross. There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel).

The answer for this graph is -4.

To learn more about Graph solution refer to:

https://brainly.com/question/19040584

#SPJ13

The value of  [tex]f^{-1}(-7)[/tex] is given by -57/8.

Given that:-

f(x) = (x + 1)/(x + 8)

We have to find the value of [tex]f^{-1}(-7)[/tex].

Let f(x) = y

Hence,

[tex]f^{-1}(y) = x[/tex]

Now, we will find the inverse of the given function.

Hence, we can write,

y = (x + 1)/(x + 8)

We can rewrite it as:-

y = (x + 8 - 7)/(x + 8) = (x + 8)/(x + 8) - 7/(x + 8) = 1 - 7/(x + 8).

1 - y = 7/(x + 8)

x + 8 = 7/(1 - y)

x = 7/(1 - y) - 8

x = 7/(1 - y) - 8(1 - y)/(1 - y)

x = (7 - 8(1 - y))/(1 - y)

x = (7 - 8 + 8y)/(1 - y)

[tex]f^{-1}(y) = \frac{(8y - 1)}{( 1 - y)}[/tex]

Replacing y with x in the above equation, we can write,

[tex]f^{-1}(x) = \frac{(8x - 1)}{( 1 - x)}[/tex]

The above equation is the inverse of the function.

Putting x = -7 in the above equation, we get,

[tex]f^{-1}(-7) = \frac{(8(-7) - 1)}{( 1 - (-7))}[/tex]

= (-56 - 1)/ (1 + 7) = - 57/8

To learn more about inverse of the function, here:-

https://brainly.com/question/2541698

#SPJ1

Using multiplication of matrices, it is found that the values of a and b are given as follows:

To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix.

Hence, the element of the row 1 and column 1 of the product matrix is given by the multiplication of the row 1 of the first matrix by the column 1 of the second matrix, then:

3(-1) -2(2) + a(3) = 5

-3 - 4 + 3a = 5

3a = 12

a = 4.

The element of the row 2 and column 2 of the product matrix is given by the multiplication of the row 2 of the first matrix by the column 2 of the second matrix, then:

4(3) - 1(b) + 2(-2) = 2

12 - b - 4 = 2

8 - b = 2

b = 8 - 2

b = 6.

More can be learned about multiplication of matrices at https://brainly.com/question/24274686

#SPJ1

The value of x is 1 , -5 and y is 3 , -3

A[tex]x^{2}[/tex] + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilized in a wide variety of situations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. Additionally, a quadratic equation is useful in many fields, including physics, engineering, astronomy, etc.

Given that : the linear-quadratic system of equations is y = [tex]x^{2}[/tex] +5x - 3 and y -x=2 .

y = [tex]x^{2}[/tex] +5x - 3 .....(i)

y = 2+ x.....(ii)

put the value of y in equation i

2 + x = [tex]x^{2}[/tex] +5x - 3

[tex]x^{2}[/tex] +4x - 5 = 0

[tex]x^{2}[/tex] +(5-1)x - 5 = 0

x(x + 5) -1(x + 5) = 0

(x -1)(x + 5)=0

x=1

x=-5

now put value of x in equation ii

y = 2+ x.....(ii)

y = 3 (when x = 1)

y = -3(when x = -5)

The value of x is 1 , -5 and y is 3 , -3

To learn more about quadratic equation visit :

brainly.com/question/17177510

#SPJ13

Answer:

16

Step-by-step explanation:

112/7=16, 16x4=64, 16x3=48, 64-48=16

The vertex form of a parabola is expressed as

y = a(x - h)^2 + k

where

a is the leading coefficient

h and k are the horizontal and vertical coordinates of the vertex.

Recall, the general expression for a quadratic equation is

y = ax^2 + bx + c

By comparing with the given equation,

a = - 2, b = 36, c = - 171

The formula for the x coordinate of the vertex is

x = - b/2a

x = - 36/(2 * - 2) = - 36/- 4 = 9

Substituting x = 9 into the equation, we have

y = - 2(9)^2 + 36(9) - 171

y =

Answer:

[tex]x = \frac{20}{91}[/tex]

Step-by-step explanation:

Since this is a proportion, first you need to cross multiply.

[tex]\frac{20}{7}[/tex] × [tex]\frac{2}{25}[/tex] = [tex]\frac{40}{175}[/tex]

[tex]\frac{26}{25} x = \frac{40}{175}[/tex]

Now multiply both sides by the reciprocal of 26/25 which is 25/26.

[tex]\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\[/tex]

Cancel on the right side, 25 and 175, by 25.  Then cancel 40 and 26 by 2.

[tex]x = \frac{20}{7} (\frac{1}{13} )[/tex]

[tex]x = \frac{20}{91}[/tex]