Find the inverse of each of the given functions.
f(x) = 4x-12
ƒ¹(x) =

When converting a measurement from one unit to another, the conversion factor is a ratio of equal measurements.

In this instance, we are determining the corresponding lengths in centimetres, metres, and inches.

We must locate the conversion factors and use them in order to finish the table of equivalent measurements. We multiply by 100 to convert Metres to centimetres.

We multiply by 0.01 to change from centimetres to metres.

We can write 2.54cm to represent the number of centimetres needed to equal one inch. One centimetre is equal to 0.39 inches in terms of inches.

We can convert 3 inches to centimetres by using the conversion factor from issue 4. 7.62 centimetres are equal to 3 inches times 2.54 centimetres per inch.

In issue number four, the conversion factors are inches to centimetres and centimetres to inches.

The conversion factor for centimetres to inches is 0.39 and for inches to centimetres is 2.54.

We can convert 10 centimetres to inches by using the conversion factor from issue 4. 3.9 inches are equal to 10 centimetres times the unit's 0.39 inch.

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So, the constant of proportionality from the original figure to the scaled copy is indeed 5/3.

To find the constant of proportionality from the original figure to the scaled copy, we need to find the ratio of the corresponding side lengths. Let's take the first pair of corresponding side lengths, 6 and 10, from the table.

To get from 6 to 10, we multiply by a constant factor. Let's call this constant factor "k". Then:

[tex]6 * k = 10[/tex]

Solving for k, we get:

[tex]k = 10/6 = 5/3[/tex]

So, the constant of proportionality from the original figure to the scaled copy is 5/3.

We can check this for the other pairs of corresponding side lengths in the table as well. For example, taking the second pair of corresponding side lengths, 12 and 39:

[tex]12 *k = 39[/tex]

Solving for k, we get:

[tex]k = 39/12 = 13/4[/tex]

We can see that this also satisfies the other pair of corresponding side lengths:

[tex]6 * (13/4) = 39[/tex]

and

[tex]10 * (13/4) = 65[/tex]

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Square Area = side x side = 3x3 = 9

Rectangle Area = side x side= 7x3= 21

9 + 21 = 30 square inches

Answer:

30 square inches

Step-by-step explanation:

   [tex]\boxed{\text{\bf Area of rectangle = length *width}}[/tex]

Rectangle1:

     Area = 6 * 3

              = 18 square inches

Rectangle2:

Area = 4 * 3

          = 12 square inches

Area of the figure = area of rectangle1 + area of rectangle2

                             = 18 + 12

                             = 30 square inches

Answer:

Volume = 30 cm³

Step-by-step explanation:

The formula for the volume of a box is:

V = width x length x height

Plug in the values given:

V = 2 x 5 x 3

V = 30

Answer:

30 cm

Step-by-step explanation:

Area= length x width x height

5 x 2 x 3

10 x 3 = 30

Graph 1 shows the solution to the system of linear inequalities.

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two.

When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Several types of linear inequalities can be represented in a number of different ways.

For the given system of linear equalities, the solution of the inequality A is the shaded area above the dashed line .

Also, the solution of the inequality B is the shaded area below the dashed line.

Plotting the graph we see that, the graph is as follows:

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The complete question is:

the can in the case of cat food will be 12.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

There are 12 cans of cat food in total.

Since there are 2 layers and each layer has 6 cans, you can calculate the total number of cans by multiplying the number of cans in one layer by the number of layers:

6 cans/layer x 2 layers = 12 cans.

Hence the can in the case of cat food will be 12.

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there were 240 pages in the printing task.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Now we can use the last two equations to solve for "p". First, substitute "r" into the equation for Printer A's printing rate:

r + 4 = (p / t)

(p / 40) + 4 = (p / 24)

Multiplying both sides by 120 (the least common multiple of 40 and 24) to eliminate the fractions, we get:

3p + 480 = 5p

480 = 2p

p = 240

Therefore, there were 240 pages in the printing task.

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Answer: 2.8831036e+17

Step-by-step explanation:

Answer:

5,767,911,845,985,421,000

Step-by-step explanation:

20023555 X 119994 = 2,402,794,503,470T

To square this number, we can multiply it by itself:

2,402,794,503,470^2 =

5,767,911,845,985,421,000

Therefore, the result of 20023555 X 119994 squared is 5,767,911,845,985,421,000.

Let's assume that the farmer counted 5x chickens and 8x pigs, where x is a positive integer.

The ratio of chickens to pigs is 5:8, which means that the total number of animals counted is 5x + 8x = 13x.

To find the percentage of animals that are pigs, we need to divide the number of pigs by the total number of animals and then multiply by 100:

(Number of pigs / Total number of animals) x 100

Substituting 8x for the number of pigs and 13x for the total number of animals, we get:

(8x / 13x) x 100 = (8/13) x 100

Simplifying, we get:

(8/13) x 100 ≈ 61.5%

Therefore, approximately 61.5% of the animals counted are pigs.

Brainliest? This took a long time :)

The weight below which one can find the lightest 90% of all navel oranges is approximately 4.83 ounces.

Standard deviation is a statistical measure that represents the amount of variability or dispersion in a set of data. It measures how spread out the data is from the mean or average value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

In the given question,

We can use Excel's NORM.INV function to find the weight below which we can find the lightest 90% of all navel oranges, given the mean and standard deviation of the weight distribution.

The NORM.INV function takes three arguments: the probability value (in this case, 0.9 for the lightest 90%), the mean value (μ), and the standard deviation value (σ). The function returns the corresponding z-score, which can be multiplied by the standard deviation and added to the mean to get the weight value.

Using Excel, the formula to find the weight below which we can find the lightest 90% of all navel oranges is:

=6 - 0.8 * NORM.INV(0.9,0,1)

This gives us a result of 4.83 ounces (rounded to two decimal places).

Therefore, the weight below which one can find the lightest 90% of all navel oranges is approximately 4.83 ounces.

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Answer:

102.19 cubic inches

Step-by-step explanation:volume =cross-section area * Length

cross-section area= (5.1 *4.6)+((13.6-4.6)*2.8)= 23.46 + 25.2= 48.66 square inches.

Length we take 2.1 in

volume = 46.66 * 2.1in = 102.19 cubic inches

Answer:

x = - 1

Step-by-step explanation:

Just by looking, we can tell that the axis of symmetry in this graph is going to be a vertical line. to make vertical lines, we start with:

x = ____

For a quadratic, the vertical line always hits the vertex. The x value of the vertex is - 1.

Therfore, the equation of the axis of symmetry is x = - 1

Answer:

First, we need to calculate the total cost of car insurance for six months:

Mr. Jones' insurance = $160

Mrs. Jones' insurance = $290

Total insurance cost for six months = $160 + $290 = $450

To find the monthly cost, we divide the total cost by 6:

$450 ÷ 6 = $75

Therefore, the answer is A. $75. They should budget $75 per month for car insurance.

Here, x-2y=-8 is an equation of the linear function.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the equation of a linear function given its x-intercept and y-intercept, we can use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the x-intercept is -8, which means that the point (-8, 0) is on the line. We are also given that the y-intercept is 4, which means that the point (0, 4) is on the line. Using these two points, we can find the slope of the line:

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 0) / (0 - (-8))

m = 4 ÷ 8

m = 1/2

Now that we know the slope is 1/2 and the y-intercept is 4, we can write the equation of the line in point slope form:

y - y₁ = m(x - x₁)

y - 4 = 1/2(x - 0)

y - 4 = 1/2(x - 0)

y = 1/2(x - 0) + 4

y = 1/2x + 4

Multiply all by -2

y = 1/2x + 4

-2y = -x -8

x -2y = -8

Therefore, The other equations do not have the same slope and/or y-intercept as the linear function except x -2y = -8.

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The fish tank has a capacity of 64 gallons, and Emily has already filled 13 gallons of salt water. So, the amount of space left for water is:

64 - 13 = 51 gallons

To fill the fish tank to 7/8 of its capacity, Emily needs to add:

(7/8) x 64 = 56 gallons

Since she has already added 13 gallons of salt water, Emily needs to add:

56 - 13 = 43 gallons

Therefore, Emily needs to add 43 gallons of water to fill the fish tank to 7/8 of its capacity.

Answer:

a. f(x) = 5x + 12

Step-by-step explanation:

a. f(3) = 5(3) + 12 = 15 + 12 = 27

If you replace 3 into x of the other equations, the result will not be 27

Answer:

a. f(x) = 5x + 12

Step-by-step explanation:

a. f(3) = 5(3) + 12 = 15 + 12 = 27

If you replace 3 into x of the other equations, the result will not be 27

Answer:

To find f(50), we need to substitute 50 for m in the function f(m) = (3/5)m + 5:

f(50) = (3/5)(50) + 5

f(50) = 30 + 5

f(50) = 35

Therefore, f(50) is equal to 35.

The value of f for m equals 50 will be 35.

This is a basic arithmetic problem where we just need to put the values given in the question and solve using the PEMDAS rule

given, m = 50

problem, f(m) = 3/5 m + 5

putting the value of m in the problem we get

f(50) = 3/5 (50) + 5

so multiplying 3 (the numerator) by 50, we get:

f(50) = 150/5 + 5

then we divide 150 by 5 and we get:

f(50) = 30 + 5

then by adding 30 and 5 we get the answer:

f(50) = 35

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Answer:

  41.59 square meters

Step-by-step explanation:

You want the surface area of a rectangular prism with dimensions ...

You are given the formula ...

 SA = 2LW +2WH +2LH

You find the area by replacing the variables in the formula with the given values, then doing the arithmetic.

We find there is less typing involved and fewer calculator operations if we rearrange the formula first. We can factor some terms, so we have ...

  SA = 2(LW +WH +LH) . . . . factor out 2

  SA = 2(LW +H(L +W)) . . . . . factor H from the last two terms

The attached calculator screen shows the use of this formula with the given numbers.

  SA = 2(2.1·1.45 +5(2.1 +1.45)) = 41.59 . . . . square meters

The surface area is 41.59 m².

Answer:

41.59

Step-by-step explanation:

The equation given is SA= 2(lw)+2(wh)+2(lh)

What you should do in this case is input all the values first. So you should have:

SA= 2(2.1*1.45)+ 2(1.45*5)+ 2(2.1*5)

SA=6.09+14.5+21

SA= 41.59

The area of the shape with the given features is 34.625 square cm

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

Composite figures

The area of the shape is the sum of the areas of individual shapes

So, we have

Area = triangle + quarter circle

This gives

Area = 1/2 * 6 * 5 + 1/4 * 3.14 * 5^2

Evaluate

Area = 34.625

Hence, the area is 34.625 square cm

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The elements of the set after listing is:

(i) A = {1, 3, 5, 7, 9, ...}

(ii) B = {x: -8 < x < 2/9}

(iii) C = {0, 1, 2}

(iv) D = {L, O, Y, A}

(v) E = {April, June, September, November}

(vi) F = {b, c, d, f, g, h, j}

An integer is a whole number, meaning it does not have any fractional or decimal parts. It can be positive, negative, or zero. Examples of integers are -3, 0, 2, and 7. Integers are a subset of the real numbers and are often denoted by the symbol ℤ (which comes from the German word "Zahlen" meaning "numbers"). Integers have a number of important properties, such as closure under addition and multiplication, and they play a central role in many areas of mathematics and computer science.

(i) A={x:x is an odd natural number}={1,3,5,7,9.....}

(ii) B={x:x is an integer,−1/2 <x< 9/2}

Since, −1/2 = -0.5 and 9/2 = 4.5

∴B = {0,1,2,3,4}

(iii) C={x:x is an integer; x² ≤ 4}

It can be seen that

(−1)² = 1 ≤ 4

;(−2)² = 4 ≤ 4

;(−3)² = 9>4

0² = 0≤4

1² = 1≤4

2² = 4≤4

3² = 9>4

∴C = {−2,−1,0,1,2}

(iv) D={x:x is a letter in the word LOYAL}={L,O,Y,A}

(v) E={x:x is a month of a year not having 31 days}

={February, April, June, September, November}

(vi) F={x:x is a consonant in the English alphabet which precedes k}={b,c,d,f,g,h,j}

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In the permutation ,  the number of different ways, theyall sit together in a row of 6 empty Seats is 720.

What is permutation?

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Here total number of people a = 6

Total number of empty seats n= 6

Now using permutation formula then,

=> P = [tex]\frac{n!}{(n-a)!}[/tex]

=> P = [tex]\frac{6!}{(6-6)!}[/tex]

=> P = [tex]\frac{6!}{0!}=6![/tex]

=> P = 6.5.4.3.2.1=720

Hence the number of different ways, theyall sit together in a row of 6 empty Seats is 720.

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Answer: $75.00 (rounded to the nearest dollar)

Answer:

C

Step-by-step explanation:

y <= 2x - 2

the delimiter line is therefore

y = 2x - 2

that is true for all 4 answer options.

but the y-values must be smaller than the values in the line. so, the area right-down from the line is correct.

that leaves us with B and C.

dotted line or solid line - the difference is if the line values are included in the solution or excluded.

if the line is dotted, then the line is not included.

if the line is solid, then the line is included.

because the inequality uses "<=", the line is included.

so, the answer with the solid line is correct : C.

Answer: The height of the pyramid is approximately 87.58 units.

Step-by-step explanation:

The correct answer to the above question is option (a) The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.

Symmetry refers to a property of an object or a function that remains unchanged when transformed by a specific operation.

For example, a geometric shape is symmetric if it can be divided into parts that are mirror images of each other.

The answer to the above question is The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.

This is because the heights at 0.5 seconds and 2 seconds are equidistant from the line x=1.5 seconds, and they have the same magnitude but opposite signs. Therefore, the graph of the height of the cannonball over time is symmetric with respect to the vertical line x=1.5 seconds.

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Answer:

  0.3865 hours, or 23 minutes 11 seconds

Step-by-step explanation:

You want the time it takes for separation distance to be 63 km if one car is headed east at 76 km/h, and one is headed west at 87 km/h.

The speed at which the cars are separating is the sum of their speeds in opposite directions:

  76 km/h + 87 km/h = 163 km/h

The relation between time, speed, and distance is ...

  time = distance/speed

The time it takes for the separation distance to be 63 km is that distance divided by the separation speed:

  time = (63 km)/(163 km/h) ≈ 0.3865 h

In minutes and seconds, this is about 23 minutes 11 seconds.

It will be about 0.3865 hours until they are 63 km apart, or 23 minutes 11 seconds.

__

Additional comment

Numbers expressed as hours : minutes : seconds are effectively a base-60 notation. Similarly, degrees : minutes : seconds are also a base-60 notation system. The attached calculator shows the use of a →DMS function to convert hours to hours : minutes : seconds. This saves the effort of repeated division by 60 and keeping the remainder.

Answer:

A would be correct

Step-by-step explanation:

the answer is A.

The fraction of an hour does it take  Queisha to answer each question is 1/27 hour.

What is fraction?

Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

Here the time taking to complete 9 home work =  1/3 hour.

Then time taking for completing 1 home work = x.

Then,

=>  9 = 1/3

      1 = x

=> x = [tex]\frac{\frac{1}{3}}{9}[/tex]

=> x = 1/27

Hence  fraction of an hour does it take  Queisha to answer each question is 1/27 hour.

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Using the central angle theorem, the measure of angle BCD in the circle given is: b. 108°.

The central angle theorem of a circle states that the measure of a central angle of a circle is equal to the measure of the arc that it cuts off.

In other words, if you know the measure of an arc in a circle, you can find the measure of the central angle that intercepts that arc, and vice versa.

m(BD) = 180 - m(AB)

Substitute:

m(BD) = 180 - 72

m(BD) = 108°

m<BCD = m(BD) [based on the central angle theorem]

Substitute:

m<BCD = 108°

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For function [tex]f(x) = \left \{ {\frac{x+1}{x^{2} -1} ,\ {x\neq 1} \atop {1,\ x=1}} \right.[/tex] given in the problem, the limit [tex]\lim_{x \to 1} f(x)[/tex] doesn't exists.

A relation between a set of inputs and a set of allowable outputs is called a function, and it has the characteristic that every input is associated to precisely one output. When every element in set A has one end and only one image in set B, then the mapping from set A to set B is a function. Let A & B be any two non-empty sets.

Now for given function,

Limit exists, if LHL=RHL=f(a)

I.  [tex]f(x) = \frac{1-x^{2} }{x-1}=\frac{(1-x)(1+x)}{x-1} = \frac{-(x-1)(x+1)}{(x-1)} = -(x+1)[/tex]

applying limit,

[tex]\lim_{x \to 1} f(x)= -2[/tex], LHL= RHL= f(1) = -2. Hence, limit exists

II. [tex]f(x) = \frac{x^{2} -x^{3} }{x^{2} -1}=\frac{-x^{2} (x -1)}{(x-1)(x+1)} = \frac{-(x^{2} )}{(x+1)}[/tex]

applying limit,

[tex]\lim_{x \to 1} f(x)= \frac{-1}{2}[/tex] , also LHL= RHL= f(1) = -1/2. Hence, limit exists

III. [tex]f(x) = \left \{ {\frac{x+1}{x^{2} -1} ,\ {x\neq 1} \atop {1,\ x=1}} \right.[/tex]

[tex]for x\neq 1,\\f(x)=\frac{(x+1)}{x^{2} -1} = \frac{x+1}{(x-1)(x+1)} = \frac{1}{x-1}[/tex]

RHL= [tex]\lim_{x \to 1+h} f(x) = \lim_{h \to 0} f(1+h) =\lim_{h \to 0} \frac{1}{1+h-1}[/tex]

[tex]\lim_{h \to 0} \frac{1}{h} =[/tex] Undefined.

LHL = [tex]\lim_{x \to 1-h} f(x) = \lim_{h \to 0} f(1-h) =\lim_{h \to 0} \frac{1}{1-h-1}[/tex]

[tex]\lim_{h \to 0} \frac{1}{h} =[/tex] Undefined

and [tex]f(1)=1[/tex]

Hence,[tex]\lim_{x \to 1} f(x)[/tex] doesn't exists

IV. [tex]f(x) = \left \{ {\frac{x^{2} -3x+2}{x -1} ,\ {x\neq 1} \atop {-1,\ x=1}} \right.[/tex]

[tex]for x\neq 1,\\f(x)=\frac{(x^{2} -3x+2)}{x -1} = \frac{(x-1)(x-2)}{(x-1)} = {x-2}[/tex]

RHL= [tex]\lim_{x \to 1+h} f(x) = \lim_{h \to 0} f(1+h) =\lim_{h \to 0} (1+h-2)= -1[/tex]

LHL= [tex]\lim_{x \to 1-h} f(x) = \lim_{h \to 0} f(1-h) =\lim_{h \to 0} (1-h-2)= -1[/tex]

and f(1) = -1

Hence,[tex]\lim_{x \to 1} f(x)[/tex]  exists

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