The graph shows the distance a car traveled, y, in x hours: What is the rise-over-run value for the relationship represented in the graph?

Answer:

[tex]\large \text{$f^{-1}(x) = 3x -6$}[/tex]

Graphs attached

Step-by-step explanation:

Your inverse function is correct.  So not sure what additional information you need

I am not familiar with the graphing tool you have been provided with. My graph is attached. I used a free online graphing tool

Given:

There are two equation given in the question.

Required:

We have to find the lowest common denominator of both equation.

Explanation:

are given equations

first of all we need to factorization both denominator

so here (p+2) is common in both so take (p+2) for one time only

so now the lowest common denominator is

Final answer:

The lowest common denominator for given two equations is

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

Therefore, a hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

To learn more about hyperbola refer to:

brainly.com/question/26250569

#SPJ1

Since J is the midpoint of the CT segment, then:

Now, you can solve the equation for x:

Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:

Finally, you have

Therefore, the measure of the segment CT is 74.

Given the equation system:

The first step is to replace the first equation in the second equation

With this, we have a one unknown equation. Now we can calculate the value of x:

Now that we know the value of x, we can determine the value of y, by replacing x=5 in the first equation

This system has only one solution and that is (5,20)

we know that

the circumference of a circle is giving by

we have

C=30pi

substitute

Find the area of the circle

substitute the value of r

Given:

The function is,

Explanation:

Determine the function for f(x + h).

Determine the value of expression.

So exprression after simplification is,

-2h - 4x - 1

Given:

length of the piece of string = 3/4 inches

length of the piece that we need = 1/8 inches

The number of smaller piece that we can get from the original piece of string can be calculated using the formula:

Applying this formula:

If the number of pieces is represented as n:

Answer:

Answer: a is 51

Step-by-step explanation:

Hope this help.

Answer:

a==51

Step-by-step explanation:

15=a/3-2

a/3-2+2=15+2

a/3=17

a=17*3

a=51

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The original number is 13.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x = 4 is an equation.

We have,

Let the number be K.

K thinks of a number, then doubles the number, and then multiplies the result by 3.

This can be written as:

(2 x k) = 2k ____(1)

3 x (2k) = 6k ____(2)

If her final number is 65 more than her original number can be written as:

6k = 65 + k _____(3)

From (3) we get,

6k = 65 + k

Subtract k on both sides.

6k - k = 65 + k - k

5k = 65

Divide both sides by 5.

5k / 5 = 65 / 5

k = 13

Thus,

The original number is 13.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

Step-by-step explanation:

A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.

So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.

An equation of line with a slope of 1/3 and containing the point (-4,7) is

y = 1/3 x + 25/7

In this question, we have been given

slope (m) = 1/3

and a point (-4, 7)

We need to find an equation of a line with a slope of 1/3 and containing the point (-4,7)

Using the formula for the slope-point form of equation of line,

y - y1 = m(x - x1)

y - 7 = 1/3(x + 4)

y - 7 = (1/3)x + 4/3

y = (1/3)x + 4/3 + 7

y = 1/3 x + 25/7

Therefore, an equation of line with a slope of 1/3 and containing the point (-4,7) is y = 1/3 x + 25/7

Learn more about the equation of line here:

https://brainly.com/question/24524587

#SPJ1

What we have is a fractional division, this is following expression

For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator

In conclusion after splitting and simplifying this, the answer is 9/5

The volume of the cylinder is

The diameter of the cylinder is 25 feet, then

The radius of it = 1/2 x diameter

Since the height is 4.5 ft

Substitute them in the rule above

Now we will change the cubic feet to gallons

Then multiply the volume by 7.48 to find the number of gallons

Now let us divide the number of gallons by 3000 to find how many gallons of liquid chlorin he needs to buy

Then he has to buy 6 full gallons

We are given two similar triangles which are;

Note that the sides are not equal, but similar in the sense that the ratio of two sides in one triangle is equal to that of the two corresponding sides in the other triangle.

To calculate the length of side BC, we can use any of the following ratios (proportions);

Using the first ratio as stated above, we shall have;

Next we cross multiply and we have;

ANSWER:

We have the following:

Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.

On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.

Therefore the correct answer is Martin's graph.

Answer:

Step-by-step explanation:

SOLUTION:

Step 1:

In this question, we are given the following:

Solve the system of equations y = 5x + 1 and -2x + 3y =-10 ?

What is the solution?

Step 2:

The solution to the systems of equations:

check:

Given y = -4 , x = -1

Let us put the values into the equation:

y = 5x + 1 and -2x + 3y = -10

CONCLUSION:

The solution to the system of equations are:

We have:

x = total pens

n = number of black pens

so:

and for black pen:

answer: 2 black pens

The average velocities of the stone are: i) 12.96 m / s, ii) 13.20 m / s, iii) 13.20 m / s, iv) 13 m / s. The instantaneous velocity is approximately equal to 13 meters per second.

The average velocity (u), in meters per second, is the change in the height (h), in meters, divided by the change in time (t), in seconds. And the instantaneous velocity (v), in meters per second, is equal to the average velocity when the change in time tends to zero.

a) Then, the average velocities are determined below:

Case i)

u = [f(1.05) - f(1)] / (1.05 - 1)

u = (18.748 - 18.1) / 0.05

u = 12.96 m / s

Case ii)

u = [f(1.01) - f(1)] / (1.01 - 1)

u = (18.232 - 18.1) / 0.01

u = 13.20 m / s

Case iii)

u = [f(1.005) - f(1)] / (1.005 - 1)

u = (18.166 - 18.1) / 0.005

u = 13.20 m / s

Case iv)

u = [f(1.001) - f(1)] / (1.001 - 1)

u = (18.113 - 18.1) / 0.001

u = 13 m / s

The fourth option offers the best estimation for the instantaneous velocity at t = 1 s. Then, the instantaneous velocity is approximately equal to 13 meters per second.

To learn more on average velocities and instantaneous velocities: https://brainly.com/question/13372043

#SPJ1

Step by step explanation:

sum of co-exterior angle is 180°

(10x-48)+(6x)=180°

4x-48=180°

4x=180-48

4x=132

x=132/4

x=33

To solve the exercise, it is easier to make a drawing, like this

So, you have

Now solving

Therefore, the length of the longest piece is 60ft.

The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.

A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).

During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.

Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.

Read more on colonists here: https://brainly.com/question/18306385

#SPJ1

Complete Question:

Which statement best completes the diagram?

A. British leaders limit the ability of colonists to expand westward.

B. British merchants refuse to buy raw materials from the colonies.

C. British military forces are ordered to leave North America.

D. British leaders end policies that strictly controlled the colonies.

First, calculate the slope (m) of both lines.

Line 1:

Point 1 = (x1,y1) = (1,4)

Point 2 = (x2,y2) = (-2,5)

Replacing:

Line 2:

Point 1 = (x1,y1) = (1,0)

Point 2 = (x2,y2) = (0,3)

Lines to be parallel must have the same slope, and to be perpendicular, they must have negative reciprocal slope.

None of the slopes are equal or negative reciprocal. SO, A and B are false-

Now, for the increase/ decrease

We can see that both lines have a negative slope, so they both decrease.

Correct option: C

The solution for the given inequality is x >7.

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a number and a graph solution for the given inequality.

The given inequality is [tex]1-\frac{6}{7}x < -5[/tex] . Then,

          [tex]-\frac{6}{7}x < -5 -1\\ \\ -\frac{6}{7}x < -6[/tex]

          [tex]-\frac{6}{7}x < -6 *(-1)\\ \\ \frac{6}{7}x > 6[/tex]

         [tex]\frac{6}{7}x > 6\\ \\ 6x > 42\\ \\ x > \frac{42}{6} \\ \\ x > 7[/tex]

You should also show the results t > 7 in a number line. Thus, plot the number line. See the attached image.

Read more about inequalities here.

brainly.com/question/25275758

#SPJ1

The figure for the height of flagpole, wire and ground is,

Determine height of the pole by using the pythagoras theorem in triangle.

Thus, height of the flagpole is 32.08 feet.

c) Set x to be the number we need to find; therefore, the inequality to be solved is

Therefore, any number greater than 1/2 (greater, not equal to) satisfies the inequality; particularly 1/1=1>1/2. Thus, 1/1 is a possible answer

Notice that in the statement of the exercise are the values of a, b and c. Then, to evaluate the given expression, we replace the given values of a, b, and c. So, we have:

Therefore, the result of evaluating the given expression when a = 9, b = 3, and c = 7.4 is 1.4.

Solution

the measure of each angle will be 2340/n then if n=15 the measure of each one of the angles will be 2340/15=156 degrees

IN order to find the area of the shaded region, proceed as follow:

calculate the area of the right triangle:

A = b·h/2

A = (21 yd)(34 yd)/2 = 357 yd²

next, calculate the area of the circle:

A' = π r²

A' = (3.1415)(7 yd)² = 153.93 yd²

next, subtract the area of the circle to the area of the rectangle:

AT = A - A' = 357 yd² - 153.93 yd²

AT = 203.07 yd²

Hence, the area of the shaded region is 203.07 yd²