find the inverse of each given function f(x)=4x-12f^-1(x)=______x+______

15 ° C

Explanation

to convert form Farenheit to Celcius degree we need to use the formula

then

Let

F=59

now, replace and evaluate

therefore, the answer is

15 ° C

I hope this helps you

Remember the equation of a line with slope m and y-intercept b:

Which can be expressed in terms of functions by replacing y=f(x)

Any line with the same slope will be parallel to that equation.

By comparing with:

We can know that its slope is equal to -5.

Since the "parallel slope" is just the slope, then

Solution

Part d

T= -2ºC, V=15 km/hr

We can convert to F and mi/h like this:

T= 1.8*(-2)+ 32= 28.4ºF

Ms= As/0.62= 15 km/hr /0.62= 24.19 mi/hr

Replacing we have:

Solving we got:

Rounded to one decimal we got:

14.1

Part e

T= 10ºC = 1.8(10)+ 32=50ºF

Ms = 34 km/hr

Ms= As/0.62= 34 km/hr/ 0.62= 54.84 mi/hr

Replacing we got:

Rounded to the nearest tenth we got:

39,5

Althought the reported temperature is 50 ºFahrenheit, because of wind it feels like 39.5 Fahrenheit

If they are congruent, then;

3x + 5 = 2x + 10

collect like term

3x - 2x = 10 - 5

x = 5

Similarly,

y + 6 = 2y - 12

collect like term

2y - y = 6 + 12

y = 18

Given:

Two points (5, 5) and (-1, 3).

To find the midpoint and distance:

Using the midpoint formula,

Thus, the mid-point formula is (2, 4).

Using the distance formula,

Thus, the distance between the two points is,

Given:

There are 4 equation representations are given.

To find:

The nonlinear equation.

Explanation:

A)

Which is of the linear form,

B)

Which is of the linear form,

C)

Let us consider the two points.

Using the two-point formula,

Substituting the first point to verify the linear equation,

Therefore, the linear equation is satisfied for all 4 points.

Thus, options A, B, and C are linear equation.

So, the nonlinear equation must be given options D.

Final answer:

The correct option is D.

Recall that the circumference of a circle is given by the following formula:

where r is the radius of the circle.

We are given that:

therefore:

Now, the area of a circle is given by the following formula:

Therefore, the area of the hub cap is:

Answer:

Given that the radius of the circle and the circumference are proportionally related, if the circumference is smaller then the radius is smaller. The area is proportionally related to the radius squared, therefore, a smaller circumference implies a smaller radius which implies a smaller area.

1) Gathering the data

Last week

28 worked hours = $266

What is your hourly pay rate?

2) To find out that, let's set a proportion

Worked hours $

28------------------------ 266

1--------------------------- x

Let's use the fundamental property of a proportion that allows us to cross multiply the ratios of that proportion

So the hourly pay rate is approximately $11.08 per hour.

a) Option C

b) A linear model

To determine the correct plot from the options, we trace the x and y values given

Option A:

When x = 5, y = 1

when x = 6.6, y = 2

We see this is exact opposite of the values in the given table

Option B:

when x = 5, y = 5

when x = 6.6, y = 6.6

This is also different from the given values in the table

Option C:

when x = 1, y = 5

when x = 2, y = 6.6

when x = 3, y = 8.4

This is the same as the given values in the table.

Hence, the correct scatter plot is option C

We need to check if the points are linear:

A linear model fit the data

Let's define the next variables:

x: price of one senior ticket

y: the price of one child ticket

On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:

8x + 5y = 94 (eq. 1)

The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:

4x + 10y = 152 (eq. 2)

Multiplying equation 2 by 2, we get:

2(4x + 10y) = 2*152

8x + 20y = 304 (eq. 3)

Subtracting equation 1 to equation 3, we get:

8x + 20y = 304

-

8x + 5y = 94

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

15y = 210

y = 210/15

y = 14

Substituting this result into equation 1:

8x + 5(14) = 94

8x + 70 = 94

8x = 94 - 70

8x = 24

x = 24/8

x = 3

Each senior citizen ticket cost $3 and each child ticket cost $14

We solve as follows:

*First: Given one function, we corroborate and find the second one.

*We have that the first function passes by the points (0, -1) & (1, 0); we find its function:

we are given the horizontal line. To determine the equation of this line let's remember that the equation of any horizontal line is of the form:

Where "k" is the point where the line touches the y-axis, in this case, the equation of the line is:

Answer:

No solutions

Explanation:

The given system of equations is

2y = x + 9

3x - 6y = -15

To solve the system, we first need to solve the first equation for x, so

2y = x + 9

2y - 9 = x + 9 - 9

2y - 9 = x

Then, replace x = 2y - 9 on the second equation

3x - 6y = -15

3(2y - 9) - 6y = -15

3(2y) + 3(-9) - 6y = -15

6y - 27 - 6y = -15

-27 = -15

Since -27 is not equal to -15, we get that this system of equation doesn't have solutions.

We have that the general equation of the hyperbola is the following:

where 'a' and '-a' are the x-intercepts.

In this case, we have the following equation:

then, we have to divide both sides by 144 to get on the right side 1, thus, we have the following:

now, notice that we have that:

then, the x-intercepts are:

therefore, the x-intercepts are 4 and -4.

Now that we know that the intercepts are on those points, we can see that the hyperbola has the following graph:

we can see that the hyperbola is not defined between -4 and 4, therefore, the domain of the hyperbola is:

finally, to perform the symmetry test, we have to check first both axis simmetries by changing x to -x and y to -y:

since the hyperbola got symmetry about the x-axis and the y-axis, we have that the hyperbola got symmetry about the origin

Given data:

The given graph is shown.

a)

The initial height of the ball is 3 units.

b)

The maximum height of the ball is approx 12.5 units.

c)

The time taken by the ball to reach maximum height is 1.5 units.

d)

The time ball was in air is 3 units.

e)

The point (3,0) denoted the coordinate of time is 3 when height is zero.

The Solution:

Given:

We are required to use the Quadratic Formula to solve the equation above.

The Quadratic Formula is:

In this case:

Substitute:

Therefore, the correct answer is [option A]

The question gives the function h(x) as

To find the value that will make the function 12, we equate the function to 12, such that

Solving to get x, we have

Therefore, h(x) = 12 when x = 4.

Answer:

$312 will be paid for the addditional tile

Explanation:

Given that the property owner paid $960 for tiles to cover a 800 sq. ft yard

Since he decided to tile an additional 260 sq. ft, to know how much will be paid for the additional tiles, we need to know how much he paid for each of the last set of tiles.

The amount is

960/800 = 1.2

He paid $1.2 per tile.

For 260 sq. ft, he will pay:

$1.2 * 260

= $312

Given the initial expression

Then,

Therefore,

And sqrt(x)>=0 for any real number.

Therefore, there is no real solution to the equation.

Let's solve the equation:

3/x = 8/7

8x = 3 * 7 Cross product

8x = 21 Rewrite 3 * 7 as 21

Dividing both sides by 8:

8x/8 = 21/8

x = 2.625

As you can see, we do not follow step 3. Divide both sides of the equation by 3.

The Euler circuit for the graph using Fleury's algorithm is attached below.

The following steps are to be used to form the circuit.

Of the three edges coming from vertex "2" should I choose? We avoid choosing the edge "2-3" because it is a bridge and we cannot return to "3".

Any of the two remaining edges is ours to choose. Let's say we choose "2-0." By eliminating this edge, we can travel to vertex "0."

We pick the one edge from vertex "0" that is present, remove it, and then move to vertex "1." The Euler tour changes to "2-0 0-1."

We take the lone edge from vertex "1," delete it, and then move to vertex "2." The Euler tour is now "2-0 0-1 1-2."

Once more, vertex 2 has just one edge, so we pick it, remove it, and continue on to vertex 3.

Hence we get the required circuit.

The term "Eulerian graph" has two different meanings in graph theory. One interpretation applies to a graph with an Eulerian circuit, whereas the other applies to a graph where each vertex has an even degree. These definitions apply to linked graphs.

To learn more about Euler circuit visit:

https://brainly.com/question/22089241

#SPJ9

Assuming the bar of gold has a rectangular form, its volume would be the product between all three dimensions.

Therefore, the volume is 350 cubic centimeters.

The remaining credit after 71 minutes is $21.48

To solve this, we can calculate the equation of the linear function that represents the remaining credit

x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation

34 min and $25.92 => (34,25.92)

53 min and 23.64 => (53,23.64)

the formula to calculate the slope of a line is

now we know the slope, we can get the line euqation

Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.

for x=71 min:

theremaining credit is $21.48.

Let:

y = kx

Where:

k = constant proportionality of the table

If x = 30, y = 10:

10 = k30

Solving for k:

k = 10/30 = 1/3

Verify the answer:

If x = 24, y = 8:

y = kx = 1/3*24 =24/3 = 8

Therefore, the constant proportionality of the table is 1/3

Set

a) The Z-score formula is

Therefore, in our case, if x=2000

Using a Z-score table,

A value of 2000 hrs is 14 standard deviations away from the mean. The probability is practically zero.

b) Similarly, set x=5000; then,

Thus, using a z-score table

The probability is 0.0004=0.04%. It is quite improbable but not an impossible event.

c) According to the empirical rule 99.8% of the data lies within 3 standard deviations; thus,

The lifespan of 99% of all incandescent bulbs is between 635 and 1115 hrs, whereas that of all CFL bulbs is between 5500 and 14500 hrs.

d) If we randomly select a CFL, the most probably lifespan is the mean of the distribution, in other words, 10000 hrs.

The probability of an incandescent bulb lasting 10000 hrs is

The event is practically impossible.

we have that

2 cups in a pint

2 pints in a quart

4 quarts in a gallon

so

4 cups in 2 pints

4 cups in a quart

16 cups in 4 quarts

16 cups in a gallon

and

we have

3 parts red and 5 parts yellow

3 parts +5 parts=8 parts

8 parts=1 gallon

red paint fraction is 3/8 gallon

yellow paint fraction is 5/8 gallon

Remember that

I need 16 cups for a gallon

Apply proportion

16/1=x/(3/8)

x=(3/8)16

We have the following expression:

First, let's solve the operation inside the parenthesis.

Second, we add and subtract accordingly.

Third, we apply the absolute value property.

In conclusion, the values is 7

Let's first try to rewrite the expression to see if we can write it in a fomr more familiar:

This is the same equation, but now we recognize a quadratic expression equal to 0. We can use the quadratic formula to find the solutions of this equation:

And solve:

Thus, the solution set of the equation is x = -5, x = 2

As per given by the question,

There are given that a triangle XYZ, and the hypotenuse of the triangle is 14 in., and one leg is 10 in.

Now,

First draw the triangle XYZ.

Now,

From the triangle XYZ, XZ is hypotenuse of the triangle, XY is the first leg of the triangle, and YZ is second leg of the triangle.

So,

First leg z is 10, then find the value of second leg x.

Then,

To find the value of second leg, here use pythagoras theorem.

So,

From the pythagoras theorem;

Now,

Then,

Hence, the length of the other leg is 9.79.