Which best describes the incenter of a triangle helpppppp plzzzz

Which Best Describes The Incenter Of A Triangle Helpppppp Plzzzz

Answers

Answer 1

Answer:  A . The point where the three angle bisector intersect.

Step-by-step explanation:

The incenter of a triangle is a point constructing the origin of a circle inscribed inside it. The incenter of a triangle is created by taking the intersection of the angle bisectors of the three vertices of the triangle such that it is equidistant from all the vertices of the triangle.

Therefore, the statement which best describes the incenter of a triangle is " the point where the three angle bisector intersect"

Answer 2

Answer:

The point where the three angle bisector intersect.

Step-by-step explanation:


Related Questions

If z is a standard normal variable, find the probability.
The probability that z lies between –1.10 and –0.36

0.4951

–0.2237

0.2237

0.2239

Answers

Answer:

0.2237

Step-by-step explanation:

Use the Table of Standard Normal Probabilities for Negative z-scores.

For z= -0.36 NORMSDIST(-0.36)=0.3594 (read value from the table)

For z= -1.10  NORMSDIST(-1.10)=0.1357 (value from the table)

You know P(-1.10<z<-0.36) = 0.3594-0.1357=0.2237

The isosceles triangle has a perimeter of 7.5 m which equation can be used to find the value of x if the shortest side, y measures 2.1 m ?

Answers

Answer:

7.5 = 2x + 2.1

Step-by-step explanation:

The perimeter of a triangle is the sum of the sides.  In an isosceles triangle, two sides are the same length.  If x is the length of the two sides and y is the length of the third side, then:

P = 2x + y

Given that P = 7.5 and y = 2.1:

7.5 = 2x + 2.1

Answer: The equation that can be used to find the value of x is

2x + 2.1 = 7.5

Step-by-step explanation: An isosceles triangle is a type of triangle which has two of its sides equal to each other. It also has two it's angles (the base angles) equal to each other.

From the question, the given triangle has the shortest side, y to be 2.1 m. This means side y is shorter than the other two sides. Hence, the other two sides must be the sides that are equal to each other. These other two sides are denoted by x ( see the attachment for an illustrative diagram).

The perimeter of a triangle is the sum of all its sides. Therefore, the perimeter (P) of the given triangle is

P = x + x + y

P = 2x + y

From the question, P = 7.5 m

and y = 2.1 m

Hence,

7.5 m = 2x + 2.1 m

2x + 2.1 m = 7.5 m

This equation can be used to find the value of x. The equation can also be written as:

2x = 7.5 m - 2.1m OR

x = (7.5 m - 2.1m) / 2

The given line passes through the points (0, -3) and (2, 3).
What is the equation, in point-slope form of the line that is
parallel to the given line and passes through the point
-1, - 1)?
y+1=3(x+1)
y+1=-=(x + 1)
-
532
v+1={(x+1)
y+1 =3(x+1)
Mark this and return
Save and Exit
S

Answers

Answer:

[tex]y+1=3(x+1)[/tex]

Step-by-step explanation:

Ok so we are looking for line parallel to the line containing points (0,-3) and (2,3).

Parallel lines have the same slope.

So let's find the slope of the line containing the points (0,-3) and (2,3).

You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

However, I just like to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference. Like this:

(0 , -3)

-(2 ,  3)

-----------

-2     -6

So the slope is -6/-2 or just 3.

So the slope of the line we are looking for has slope 3 (or m=3) and your line should contain the point (-1,-1).

The point slope form of a line is:

[tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point you know on the line.

So we just plug into that equation now.  That gives us:

[tex]y-(-1)=3(x-(-1))[/tex]

Simplify a bit:

[tex]y+1=3(x+1)[/tex]

Answer:

The answer is: y+1=(3x+1)

Step-by-step explanation:

I Need Help Plz I’m Failingggg!!

Answers

Answer:

I believe it would be B

Step-by-step explanation:

take x and y values and figure it out what it is by itself

A ball is released at a height of 27 inches to roll inside a half-cylinder. It rolls
to a height of 9 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point th
high as it
had reached on the other side.
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.
How high does the ball roll on its 4th time up the cylinder's side?

Answers

Answer:

[tex]\frac{1}{3}\ in[/tex]

Step-by-step explanation:

we have

[tex]a(n)=9(\frac{1}{3})^{n-1}[/tex]

For n=4

substitute

[tex]a(4)=9(\frac{1}{3})^{4-1}[/tex]

[tex]a(4)=9(\frac{1}{3})^{3}[/tex]

[tex]a(4)=9(\frac{1}{27})[/tex]

[tex]a(4)=\frac{1}{3}\ in[/tex]

Answer:

1/3

Step-by-step explanation:

Jimmy spent $121.60 on shirts. Tee shirts cost $9.10 and long sleeve shirts cost $14.20. If he bought a total of 10, how many of each kind did he buy? Please answer

Answers

The answer my friend is 6 long shirts and 4 teeny shirts

Do you guys know the answer for 3 and 4

Answers

Answer:

Problem 3: H. 350 = r * 5

Problem 4: rate of speed = 70 miles per hour

Step-by-step explanation:

Problem 3:

speed = distance/time

Multiply both sides by time.

speed * time = distance/time * time

speed * time = distance

distance = speed * time

distance = 350

speed = r

times = 5

350 = r * 5

Answer: H. 350 = r * 5

Problem 4:

350 = r * 5

Divide both sides by 5.

350/5 = r * 5/5

70 = r

r = 7

rate of speed = 70 miles per hour

Answer:

H. 350 = r*5

Her average rate: 70 miles

Step-by-step explanation:

When finding average rate, you are always either multiplying or dividing so all the choices except for H, won't work.

Also, r represents the rate so its how many miles per hour. So you would multiply the miles per hour by the amount of hours you have.

So r*5.

To find her average you would solve for r in the equation.

So r*5 = 350

You would divide 5 by itself and then by 350, because whatever you do to one side of the equation, you do to the other.

So 5/5 = 1 or just r

350/5 = 70

r = 70


Which factor do 9x2 – 12x + 4 and 9x^2 – 4 have in common?

Answers

Answer:

3x-2

Step-by-step explanation:

[tex]9x^{2} -12x+4[/tex] can be factored using the perfect square rule into [tex](3x-2)^{2}[/tex]

and

[tex]9x^{2}-4[/tex] can be factored by using the difference of squares formula into [tex](3x+2)(3x-2)[/tex]

Both can be factored by (3x-2) so it is a common factor.

Hence, there are no common factors between the two equations.

What is a factor?

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

How to solve?

given equation is [tex]9x^2-4[/tex]

solving for x,

                     [tex]9x^2=4\\x^2=\frac{9}{4} \\x=\frac{3}{2}, -\frac{3}{2}[/tex]

putting values of x in equation 1,

x = [tex]\frac{3}{2}[/tex],

      [tex]\frac{81}{4}-12.\frac{3}{2}+4\\ \frac{25}{4}[/tex]Therefore, 3/2 is not a common factor

x=[tex]-\frac{3}{2}[/tex],

      [tex]\frac{81}{4}+12.\frac{3}{2}+4\\ \frac{169}{4}[/tex]Therefore, -3/2 is not a common factor

Hence, there are no common factors between the two equations.

To learn more about factors: https://brainly.com/question/1892656

#SPJ2

Mixed 3 liters 20% solutions with 2 liters 70% solution. What’s the final concentration,

Answers

Answer:

(3×20%+2×70%)/3+2=40%

Step-by-step explanation:

Assuming the potions are the same type or do mix then probably the concentration of the potion depends on the type of reaction they have to each other.

Yet we can average the percentage of the active ingredient by the principle mentioned above

Answer:

The final concentration is 40%.

Step-by-step explanation:

Let x the concentration of final solution.

3 liters of solution (1) with 20% concentration is mixed with 2 liters of 70% solution producing (3 + 2) = 5 liters of x% mixture.

Now 3 × (20%) + 2 × (70% = 5 (x%)

3 × 0.2 + 2 × 0.7 = 5 (0.1x)

0.6 + 1.4 = 0.05x

2 = 0.5x

x = 2/0.05

= 40%

The final concentration is 40%.

Convert 93 pints to quart

Answers

Answer:

Step-by-step explanation:

There are 2 pints in one quart.

93 pints = 93/2 = 46 quarts and 1 pint left over.

Answer:

46.5 quarts

Step-by-step explanation:

There are 2 pints in 1 quart.

Hence,

93 pints     1 quart

------------ * ------------- = 46.5 quarts

      1           2 pints

Solve the inequality. 1/3+x+2/9>5/6

Answers

Answer:

5⁄18 < x

Step-by-step explanation:

Start by adding like-terms [⅓ and 2⁄9] with 9 being the Least Common Denominator [LCD]. Since 2⁄9 already has a 9 in the denominator, it does not get touched, so in order to make ⅓ a denominator of 9, we simply multiply both terms by 3, to get 3⁄9. So, adding that to 2⁄9 gives you 5⁄9, also giving you 5⁄9 + x > ⅚. Now, we have to find the LCD again because we have two unlike fractions. Now, our Least Common Denominator is 18, so multiply both terms in ⅚ by 3 [15⁄18] and multiply both terms in 5⁄9 by 2 [10⁄18]. Now you have two like fractions to work with, and you can clearly see that your answer is x > 5⁄18. Although the answer is written in reverse, it is still the same concept.

I am joyous to assist you anytime.

What is most likely the correlation coefficient for the set of data shown

Answers

Answer:

0.19

Step-by-step explanation:

A correlation coefficient is a measure of how well the line of best fit fits the data.  The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.

We can see that this line of best fit is increasing, so our correlation coefficient will be positive.

However we can also see that the points are fairly scattered; this means this is not a very good fit.  This means that 0.19 is the better fit.

If x= yand y = Z, which statement must be true?

Answers

Answer:

The answer is

B. x =>z

They all equal the same.

Given that the first term and the common difference of an arithmetic progression are 6 and 3 respectively. Calculate the sum of all terms from 4th term to the 14th term.​

Answers

Answer:

330

Step-by-step explanation:

Evaluate the sum of 14 terms and subtract the sum of the first 3 terms

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], so

[tex]S_{14}[/tex] = 7 [ (2 × 6) + (13 × 3)]

                         = 7(12 + 39) = 7 × 51 = 357

[tex]S_{3}[/tex] = 6 + 9 + 12 = 27

Sum of terms from 4 th to 14 th = 357 - 27 = 330

A parallelogram has vertices at (-5, -1), (-2, -1), (-3, -4), and (-6, -4). What is the approximate perimeter of the parallelogram? Round your answers to the nearest hundredth.

a. 9.16

b. 12 units

c. 12.32 units

d. 14

e. 14.32

I NEED THE ANSWER ASAP!!

Answers

Answer:

option C

Step-by-step explanation:

We will call :

A=(-5, -1)    B=(-2, -1)   C=(-3, -4)   D= (-3, -4)

Perimeter= 2*AB+2BC

Where AB= [tex]\sqrt{(-5+2)^{2} +(-1+1)^{2} } = \sqrt{9} =3\\[/tex]

BC =[tex]\sqrt{(-2+3)^{2} +(-1+4)^{2} } = \sqrt{10} =3.16\\[/tex]

So We have:

Perimeter=2*3+2*3.16= 12.32  

Answer:

C.

Step-by-step explanation:

Determine the theoretical probability of rolling a number larger than two and a standard 66 sided cube

Answers

Answer:

Required probability = 2/3

Step-by-step explanation:

When rolling a 6 sided die, the out comes are

1, 2, 3, 4, 5 and 6

Total number of outcomes = 6

To find the probability

The required outcome is a number greater than 2, therefore possible outcomes are,

3, 4, 5, and 6

Number of possible outcomes = 4

Required probability = 4/6 = 2/3

Answer:

Determine the theoretical probability of rolling a number larger than 2 on a standard 6-sided cube.

2/3

Step-by-step explanation:

A set of equations is given below: equation C:y=5x+10 equation D:y=5x+2 which of the following best describes the solution to the given set of equations? One solution no solution two solutions infinitely many solutions

Answers

Answer:

The system has no solution

Step-by-step explanation:

we have

y=5x+10 -----> equation C

The slope of the equation C is m=5 and the y-intercept is b=10

y=5x+2 -----> equation D

The slope of the equation C is m=5 and the y-intercept is b=2

Remember that

If two lines are parallel, then their slopes are the same

Equation C and equation D are parallel lines with different y-intercept

therefore

The system has no solution (the lines do not intersect)

Ben has 9 pizza’s with 8 slices each. 59 were eaten. How many slices are left?

Answers

Answer:

13 slices.

Step-by-step explanation:

To find your total amount of slices at the start, multiply your pizzas by your slices.

[tex]9*8=72[/tex]

Next, find the difference between your total amount of slices and the amount of slices which have been eaten.

[tex]72-59=13[/tex]

13 slices are left.

13 because 9 pizzas with 8 slices each would mean you multiply to find the total number of slices (8x9=72) and if you eat 59 of those 72 you are left with 13

What is solution to equation X-5/7=-3/7

Answers

x = 2/7
steps:
add 5/7 to both sides
The answer to the equation is x=2/7
This is because the equation requires you to add 5/7 to -3/7 which results in x equaling 2/7.
(Hope you have a nice day. Could you give me brainliest so I can level up? I only need one more)

Three times a number increases by 4 is the same as four
times that number decreased by 11. Find the number.​

Answers

Answer:

15 is your answer.

Step-by-step explanation:

Let "a number" = x

"Three times a number increase(d) by 4" = 3x + 4

"...is the same as" = "="

"four times that number decreased by 11" = 4x - 11

Set the equation:

3x + 4 = 4x - 11

Isolate the variable, x. Subtract 4x and 4 from both sides:

3x (-4x) + 4 (-4) = 4x (-4x) - 11 (-4)

3x - 4x = -11 - 4

Simplify. Combine like terms:

-x = -15

Isolate the variable, x. Divide -1 from both sides:

(-x)/-1 = (-15)/-1

x = (-15)/(-1)

x = 15

15 is your answer.

~


Please Help.
Tracey built a small boat and recorded the distance it traveled. The table below shows the distance traveled (f) during the first 4 seconds after starting (p).



Elapsed Time

(seconds) Distance Traveled

(feet)

1 4.2

2 8.4

3 12.6

4 16.8




Which of the following equations represents the relationship between the distance traveled and the elapsed time?

p = 4.2f

f = 4.2p

p = 4.2 + f

f = 4.2 + p

Answers

Answer:

Expressing the distance from the shore by the time needed to reach that distance at an invariable speed of 4.2f/s then f=4.2 p

Answer:

f=4.2p

Step-by-step explanation:

18-r=12
[tex]18 - r = 12[/tex]

Answers

Answer:

r = 6

Step-by-step explanation:

18 - r = 12         subtract 18 from both sides

18 - 18 - r = 12 - 18

-r = -6            change the signs

r = 6

Check

18 - 6 = 12         CORRECT

A cube has side length 0.7 metres.

Work out the total surface area of the cube.
Give your answer in square centimetres

Answers

6*0.7*0.7=2.94
6 sides; area of 1 side = length*width. Length = width = 0.7

Answer:

2.94cm^2

Step-by-step explanation:

If you're referring to the mathswatch question, this gets you 2/3 :)

Find the value of x in the picture please

Answers

Answer:

Option D 74°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

The arcs that the outer angle encompasses are

254° and (360-254)=106°

therefore

∠x=(1/2)[254°-106°]

∠x=(1/2)[148°]

∠x=74°

Use the distributive property to evaluate 4(2x-1) when x=6 .

Answers

Answer:

44

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

4(2x - 1) = (4)(2x) + (4)(-1) = 8x - 4

Put x = 6 to the expression:

8(6) - 4 = 48 - 4 = 44

The solution to the given expression is 44.

What is the distribution property of multiplication?

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

By applying the distributive property of multiplication to the given expression, we have:

4(2x - 1) = 4(2x) - 4(1)

4(2x - 1) = 8x - 4

when x = 6, we have;

8x - 4

8(6) - 4

48 - 4 = 44.

Read more on expression here: brainly.com/question/16729936

#SPJ6

help pleaseeeee solve 3-x/2=>12

Answers

Answer:

x ≤-18

Step-by-step explanation:

3-x/2≥12

Subtract 3 from each side

3-3-x/2≥12-3

-x/2≥9

Multiply each side by -2 to clear the fraction.  Remember to flip the inequality since we are multiplying by a negative

-3 * -x/2 ≤ -2 *9

x ≤-18

Answer:

x ≤ - 18

Step-by-step explanation:

Given

3 - [tex]\frac{x}{2}[/tex] ≥ 12

Multiply all terms by 2

6 - x ≥ 24 ( subtract 6 from both sides )

- x ≥ 18

Multiply both sides by - 1, remembering to reverse the sign as a consequence of multiply by a negative quantity.

x ≤ - 18

If a graph of y=-4x +2 were changed to a graph of y=-4x+5, how would the y- intercept change?

Answers

Answer:

So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.

The y-intercept was (0,2) then it becomes (0,5) in the new line.

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and the y-intercept is b.

Both of these equations given are in this form.

y=-4x+2 when compared to y=mx+b you see that m=-4 and b=2.

Since b=2 then the y-intercept is 2.

y=-4x+5 when compared to y=mx+b you see that m=-4 and b=5.

Since b=5 then the y-intercept is 5.

So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.

What is the solution set of { x I x < -5} n { x I x> 5

Answers

For this case we have to:

[tex]x <-5:[/tex] Represents the solution of all strict minor numbers to -5.

[tex]x> 5:[/tex] Represents the solution of all strict major numbers to 5.

The global solution is given by the intersection of both sets. The symbol of intersection is denoted as: ∩

If we represent the solution in a numerical line, it gives us empty. do not intersect.

Answeer:

Empty set

What is the slope of a line that includes the points (-5, 1) and (-2, 3).
Select one:A.2/3 b.-2/7 c.-2/3 d.3/2

Answers

Answer:

A

Step-by-step explanation:

Work with the two points

Formula

m = (y2 - y1)/(x2 - x1)

Givens

y2 = 3

y1 = 1

x2 = - 2

x1 = - 5

Solution

m = (3 - 1) / (-2 - - 5)

m = 2 / (-2 + 5)

m = 2 / 3

Answer: A

Answer:

[tex]\large\boxed{\text{A.}\,2/3}[/tex]

Step-by-step explanation:

In this question ,we're trying to find the slope with the given points.

We would use the slope-formula to find the slope.

Slope-formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

We would plug in the numbers to their right spots in the formula. The second y-coordinate going to y2, the second x coordinate going to x2, and etc.

Your equation should look like this:

[tex]m=\frac{3-1}{-2-(-5)}[/tex]

Now we solve:

[tex]m=\frac{3-1}{-2-(-5)} \\\\m=\frac{2}{-2-(-5)}\\\\\text{Carry the negative over to the 5, turning it to a positive 5}\\\\m=\frac{2}{-2+5}\\\\\text{Add the denominators}\\\\m=\frac{2}{3}[/tex]

When you're done solving, you should get 2/3

This means that the slope is 2/3

I hope this helped you out.Good luck on your academics.Have a fantastic day!

The data shown on the scatter plot below demonstrates the relationship between the time of day and the total number
of calories that a teenager consumes throughout the day.
That as time ___________,
the total number of calories that a teenager consumes throughout the day
___________.

Blank A options:
Stays the same
Increases
Decreases

Blank B options:
Stays the same
Decreases
Increases

Answers

Answer:

Good question! The correct answer is a) increases and b) increases.

While the pair of answers a) decreases and b) decreases or the pair a) stays the same and b) stays the same would be technically correct answers, this is the best way of describing the trend of the scatter plot; typically, trends are described by how the dependent or y-variable responds to the independent or x-variable increasing.

Answer:

a) increases and b) increases.

Step-by-step explanation:

Other Questions
Consider the three points graphed. What is the value of y in the fourth point that will complete the quadrilateral as a rhombus? A triangular field has sides 218.5 and 213.3 and the angle between them measures 58.96. Find the area of the field. The line of action of the force \vec{F}=5\vec{i}-10\vec{j} F =5 i 10 j N passes through the point with coordinates (in meters) (2, 2). What is the moment of this force about the coordinate origin? __is a technique similar to using a stencil Read the excerpt from part two of Trifles.MRS. HALE. It's a log cabin pattern. Pretty, isn't it? I wonder if she was goin' to quilt or just knot it? (Footsteps havebeen heard coming down the stairs. The Sheriff enters, followed by Hale and the County Attorney.)SHERIFF. They wonder if she was going to quilt or just knot it. (The men laugh, the women look abashed.)Which theme is best reinforced by the excerpt? Aluminum reacts with sulfur to form aluminum sulfide according to the following reaction:2 Al (s) + 3 S (s) Al2S3 (s)How many moles of sulfur will be need to produce 6 moles of aluminum sulfide? a.2 mol S b.3 mol S c.12 mol S d.15 mol S e.18 mol S Aluminum reacts with sulfur to form aluminum sulfide according to the following reaction:2 Al (s) + 3 S (s) Al2S3 (s)How many moles of sulfur will be need to produce 6 moles of aluminum sulfide? a.2 mol S b.3 mol S c.12 mol S d.15 mol S e.18 mol S How can the PCR process help in maintaining the identity of the killer A series circuit consists of a 0.55-H inductor with internal resistance of 8.0 connected in series with a 4.0- resistor, an open switch, and an ideal 12-V battery. (a) When the switch is closed, what is the initial current through the 4.0- resistor? (b) What is the current through the 4.0- resistor a very long time after the switch is closed? A 76-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 840 N. What is the acceleration of the elevator? 1.25 Correct: Your answer is correct. m/s2 upward What are the coordinates of the vertices of the image ofrectangle WXYZ after the transformation Ro 90(x, y)?W'(-4,-1)X'Y'Z'(-4, 2) What property do the following elements have in common?Li, C, and F Write a for loop to print all elements in courseGrades, following each element with a space (including the last). Print forwards, then backwards. End each loop with a newline. Ex: If courseGrades = {7, 9, 11, 10}, print: 7 9 11 10 10 11 9 7 Read this passage:"Elenita," my mother began as she cleared the table, "didyou forget about the fiesta tonight?""No, Mara Elena, I did not forget about the fiesta tonight."(I had also decided to call my mother by her first name asan experiment in "evolving' our roles.)Which word best describes the narrator's tone in the passage? In The Odyssey - Teiresias, when Teiresias describes the conflicts that Odysseus will face, how do these conflicts relate tothe story's theme?OOOThe conflicts describe the theme.The conflicts contrast with the theme.The conflicts reveal the theme.The conflicts hide the theme. music band came to town. The amphitheater filled all 50,000 seats at two-level pricing. Level 1 tickets are $150 each, and level 2 tickets are $250 each. The amphitheater made $125,000 in ticket sales. The system of equations that models this scenario is: x + y = 50,000 150x + 250y = 125,000 What do the x and y represent in the system? What type of force are you exerting when you stomp your foot on the ground Suppose that the functions g and h are defined for all real numbers x as follows.g(x) = 4x 4h(x) = x-5Write the expressions for (g+h)(x) and (g-h)(x) and evaluate (g.h)(1). For 20 Points.============= Pat, a world famous musician and composer, agrees to give ten piano lessons to Quinn in exchange for $1,000. Pat's attempt to delegate his contract to Ruth, an inexperienced pianist, will probably be: Houston Pumps recently reported $220,000 of sales, $140,500 of operating costs other than depreciation, and $9,250 of depreciation. The company had $35,250 of outstanding bonds that carry a 6.75% interest rate, and its federal-plus-state income tax rate was 35%. In order to sustain its operations and thus generate future sales and cash flows, the firm was required to spend $15,250 to buy new fixed assets and to invest $6,850 in net operating working capital. What was the firm's free cash flow?