This lesson is about graphing an absolute value function when the expression inside the absolute value symbol is linear. It is linear if the variable "[latex]x[/latex]" has a power of [latex]1[/latex]. The graph of absolute value function has a shape of "V" or inverted "V". Absolute Value Function in Equation Form.In this example, we have the exact same shape as the graph of y = |x| only the "v" shape is upside down now.. Based on the examples we've seen so far, there appears to be a pattern when it comes to graphing absolute value functions.. When you have a function in the form y = |x + h| the graph will move h units to the left. When you have a function in the form y = |x - h| the graph will ...Now, let us find the absolute value of a complex number z = 6 + 8i is ${\sqrt{6^{2}+8^{2}}}$ = ${\sqrt{100}}$ = 10. In Unit Circle. Complex numbers can have an absolute value of 1. It is the same for -1, just as for the imaginary numbers i and -i. This is because all of them are one unit away from 0, either on the real number line or the ...The only way for the value of the absolute value to be 3 is for the quantity inside to be either -3 or 3. In other words, we get rid of the absolute value bars by using the formula from the notes. Show Step 2. At this point all we need to do is solve each of the linear equations we got in the previous step. Doing that gives,Recall that in its basic form f (x) = |x|, f ( x) = | x |, the absolute value function is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign.The absolute maximum and minimum value of f (x)= 3x4 −8x3 +12x2 −48x+25,x ∈ [0,3] are respectively. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:the absolute value of 4xx4 if 0 x 4 is.One way of thinking of the concept of absolute numbers is that it is the distance of that number from 0 – -4 is four away from 0, while 4 is also four away from 0. Example. What is the absolute value of the following numbers? -4, -18.2, and 17 1/3-4 – the absolute value is 4, as -4 is four numbers from 0.-18.2 – the absolute value is 18.2 ...5 people found it helpful. marimendoza3434. report flag outlined. The absolute value of 3/4 is. 3=1. 4=2. since is un even and is the distance between 0 to the number its 1. arrow right. Explore similar answers.In the Illustration titled Factoring a Degree Six Polynomial, we consider a version of the identity. (1− x)(1+ x + x2 + x3 + + xn−1) = 1− xn. This is a formal identity, so it holds true for any real value of x. One way to look at this is to multiply all the terms by (1 - x) and watch the terms fall away.So 12 worked 0 shouldn't work. Lets try 0. Zero minus 12 so it's the absolute value of 0. I wanna do this in a different color. It is the absolute value of 0 minus 12 plus 4. This should not be less than 14. This should not work. So we get the absolute value of negative 12. Plus 4 should not be less than 14. Then we should end up with a ...With the absolute value calculator, the function abs can calculate the absolute value online of a number. To calculate the absolute value of a number, just enter the number and to apply the function abs. Thus, for calculating the absolute value of the number -5, you must enter abs ( − 5 - 5) or directly -5, if the button abs already appears ...The absolute value of the sum of the abscissas of all the points on the line x + y = 4 that lie at a unit distance from the line 4 x + 3 y − 10 = 0 is_____ View Solution If the equations x 2 − 3 x + 4 = 0 and x ( b − 3 x ) + 2 x + a = 0 have a common root then the absolute value of ( a − b ) is equal toThe real way to look at absolute values is that they are a number's distance from 0 on the number line: TRY IT: Use a number line to show the answers to these. 1. of 1. What's an Absolute Value? - Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus ...Remember, the absolute value of a number is always nonnegative (positive or zero). If a number is negative, negating that number will make it positive. | − 5| = − (−5) = 5, and similarly, | − 12| = − (−12) = 12. Thus, if x < 0 (if x is negative), then |x| = −x. If x = 0, then |x| = 0.The absolute value function f ( x ) is defined by. f ( x ) = | x | = {-x, x<0 0, x=0 x, x>0. is called an absolute value function. It is also called a modulus function. We observe that the domain of the absolute function is the set R of all real numbers and the range is the set of all non-negative real numbers.Recall that in its basic form f (x) = |x|, f ( x) = | x |, the absolute value function is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign.The function returns the absolute value (modulus) of the specified numeric value. double MathAbs ( double value // numeric value ); Parameters. value [in] Numeric value. Return Value. Value of double type more than or equal to zero. Note. Instead the MathAbs() function you can use fabs (). Math Functions MathArccos . Join us — download ...Absolute Value for a number x is denoted by |x|, pronounced as “module x”. Absolute values are only numeric values and do not include the sign of the numeric value. Learn about Absolute valueS in detail, including …4·(-2) + 1 = |2·(-2) - 3| => -8 + 1 = |-4 - 3| => -7 = +7, which is a mathematical absurdity. This same process of dividing the absolute value equation or absolute value …A. Solve absolute value equations by isolating the absolute value expression and then use both positive and negative answers to solve for the variable. Your variable will most likely equal two different values. Ex. 2|x - 3| = 14. First, isolate the absolute value expression by dividing both sides by 2. |x - 3| = 7.Compare the values found for each value of in order to determine the absolute maximum and minimum over the given interval. The maximum will occur at the highest value and the minimum will occur at the lowest value. No absolute maximum. No absolute minimum. Step 4The absolute value function is commonly used to measure distances between points. Applied problems, such as ranges of possible values, can also be solved using the absolute value function. The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.If the number is not negative then the absolute value of the number is itself. Thus the absolute value of 6 is 6, the absolute value of 1/3 is 1/3 and the absolute value of 0 is 0. If the number is negative then to find the absolute value you just drop the negative sign. Thus the absolute value of -2 is 2 and the absolute value of -1/7 is 1/7 ...The standard absolute value graph y=|x| has its vertex at (0, 0). If you want to change the point to be at (3,0), that means you are making x=3. Notice, these are on opposite sides of the "=". if you need to place them on the same side of the "=", then you would have x-3=0.The absolute value of a number is its distance from zero on the number line. The symbol for absolute value is @$\begin{align*}| \ |\end{align*}@$ . Let's look at an example. @$\begin{align*}|-3|\end{align*}@$ This is read as "the absolute value of -3". To figure out the absolute value of -3, think about how far the number -3 is from zero ...Explore this ensemble of printable absolute value equations and functions worksheets to hone the skills of high school students in evaluating absolute functions with input and output table, evaluating absolute value expressions, solving absolute value equations and graphing functions. Give a head-start to your practice with the free worksheets ... The absolute value of any integer, whether positive or negative, will be the real numbers, regardless of which sign it has. It is represented by two vertical lines |a|, which is known as the modulus of a. For example: 5 is the absolute value for both 5 and -5. |-5| = +5 and |+ 5| = +5. In this article, we will learn what is the absolute value ... If the number is not negative then the absolute value of the number is itself. Thus the absolute value of 6 is 6, the absolute value of 1/3 is 1/3 and the absolute value of 0 is 0. If the number is negative then to find the absolute value you just drop the negative sign. Thus the absolute value of -2 is 2 and the absolute value of -1/7 is 1/7 ...So 12 worked 0 shouldn't work. Lets try 0. Zero minus 12 so it's the absolute value of 0. I wanna do this in a different color. It is the absolute value of 0 minus 12 plus 4. This should not be less than 14. This should not work. So we get the absolute value of negative 12. Plus 4 should not be less than 14. Then we should end up with a ...To get from −8 − 8 to the answer you really want, just take the absolute value! Thus, absolute value provides a convenient way to talk about the distance between any two real numbers: DISTANCE BETWEEN TWO REAL NUMBERS absolute value of the difference. Let x x and y y be real numbers. Then: |x−y| =the distance between x and y | x − y ...Find the Absolute Value of ... Calculator. Input any integer or decimal value into ourAbsolute Value Calculator. You can type a fraction by typing the numerator then '/' then the denominator. Examples: 3/4 (three-quarters); 2/5 (two-fifths); 4/9 (four nineths). You can type a mixed number by typing the number part, then a space then the fraction.The absolute value of -5 is 5. The distance from -5 to 0 is 5 units. The absolute value of 2 + (-7) is 5. When representing the sum on a number line, the resulting point is 5 units from zero. The absolute value of 0 is 0. (This is why we don't say that the absolute value of a number is positive. Zero is neither negative nor positive.)Jul 24, 2023 · This page titled 1.2: Solving Absolute Value Equations is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Simplify absolute value expressions using algebraic rules step-by-step. absolute-value-calculator. en. Related Symbolab blog posts. Middle School Math Solutions – …Click here to see ALL problems on absolute-value. Question 394646: Find the absolute value [11/4] Answer by edjones (8007) ( Show Source ): You can put this solution on YOUR website! 11/4.Alternatively, NumPy's np.abs() can convert list elements to their absolute values.. NumPy: Convert array elements to absolute values (np.abs, np.fabs) Difference between math.fabs() and abs(). math.fabs() also returns the absolute value but always as a floating point number (float), unlike abs().Even for integers (int), math.fabs() returns a floating point number (float). Correct answer: f (x) = x 4 + (1 – x) 2. Explanation: When we take the absolute value of a function, any negative values get changed into positive values. Essentially, | f ( x )| will take all of the negative values of f ( x) and reflect them across the x -axis. However, any values of f ( x) that are positive or equal to zero will not be ... For example, $ 2$ and $ -2$ are opposites. Remember that numbers with a larger absolute value can actually be smaller when the numbers are negative - for example, $ -6<-5$, and, in the case of fractions, $ \displaystyle -\frac {3} {4}<-\frac {1} {2}$. So if we're comparing negative numbers, it's actually backwards compared to what we're ...Assuming "absolute value" is a math function | Use as. referring to a mathematical definition.How to simplify absolute value with negatives. The opposite of absolute values of real numbers. Be careful with the order of operations when simplifying expr...Compare |-4| and |-4|. Solution : Step 1 : The absolute value of a number is the number’s distance from 0 on a number line. To understand this, let us mark -4 and 4 on a number line. Step 2 : On the above number line, -4 is 4 units from 0 to the left. Since -4 is 4 units from 0, we say that the absolute value of -4 is 7.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Solution. Here's the ideal situation to apply our new concept of distance. Instead of saying "the absolute value of x minus 3 is 8," we pronounce the equation |x − 3| = 8 as "the distance between x and 3 is 8.". Draw a number line and locate the number 3 on the line. Recall that the "distance between x and 3 is 8.".Absolute value is like a clock it has only positive numbers. Absolute value is talking about distance, distance is always measured by positive numbers. 6. Multiple Choice. Edit. 1 minute. 1 pt. Evaluate the expression. |-5| + 8. 3. 13-13-3. 7. Multiple Choice. Edit. 1 minute. 1 pt. Which is the greatest integer?-33-31-28-17. 8. Multiple Choice.The absolute value of A minus B is the distance between A and B and that's what this green distance is as well. So, this is going to be equivalent to the absolute value of A minus B. And if you wanna really verify it, you could try it with some numbers. I mean what they tell us about A and B is that both of them are going to be negative.The absolute value function f ( x ) is defined by. f ( x ) = | x | = {-x, x<0 0, x=0 x, x>0. is called an absolute value function. It is also called a modulus function. We observe that the domain of the absolute function is the set R of all real numbers and the range is the set of all non-negative real numbers.1. report flag outlined. Answer: 4/25 is the absolute value of -4/25. Step-by-step explanation: The absolute value of a number is the distance a number is from 0. For example 3 would be the same distance from 0 as -3. Hope this helped you understand more about absolute value! Thank you so much that is exactly what I needed. report flag outlined. So the absolute value of negative 1 is 1. And the absolute value of 1 is also 1 away from 0. It's also equal to 1. So on some level, absolute value is the distance from 0. But another, I guess simpler way to think of it, it always results in the positive version of the number. The absolute value of negative 7,346 is equal to 7,346. absolute value, Measure of the magnitude of a real number, complex number, or vector. Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnegative. If a real number a is positive or zero, its absolute value is itself. The absolute value of − a is a.The absolute value of a number is the number without its sign. Syntax. ABS(number) The ABS function syntax has the following arguments: Number Required. The real number of which you want the absolute value. Example. Copy the table below, and paste into cell A1 in Excel. You may need to select any cells that contain formulas and press F2 and ...2) The absolute values (besides being the distance from zero) act as grouping symbols. Once you get to the point that you can actually drop the absolute values, if there is a number in front, that number must be distributed. Example: 14 |x+7| = 2 becomes 14 (x+7) = 2 and 14 (x+7) = -2.Compare the f (x) f ( x) values found for each value of x x in order to determine the absolute maximum and minimum over the given interval. The maximum will occur at the highest f (x) f ( x) value and the minimum will occur at the lowest f (x) f ( x) value. Absolute Maximum: (4,15) ( 4, 15)Absolute Value means ..... how far a number is from zero: "6" is 6 away from zero, and "−6" is also 6 away from zero. So the absolute value of 6 is 6, and the absolute value …In this example, we have the exact same shape as the graph of y = |x| only the "v" shape is upside down now.. Based on the examples we've seen so far, there appears to be a pattern when it comes to graphing absolute value functions.. When you have a function in the form y = |x + h| the graph will move h units to the left. When you have a function in the form y = |x - h| the graph will ...After determining that the absolute value is equal to 4 at x = 1 x = 1 and x = 9, x = 9, we know the graph can change only from being less than 4 to greater than 4 at these values. This divides the number line up into three intervals: x < 1, 1 < x < 9, and x > 9. x < 1, 1 < x < 9, and x > 9.It include all complex numbers of absolute value 1, so it has the equation | z | = 1. A complex number z = x + yi will lie on the unit circle when x2 + y2 = 1. Some examples, besides 1, -1, i, and - 1 are ±√2/2 ± i √2/2, where the pluses and minuses can be taken in any order. They are the four points at the intersections of the ...3. I would guess it is your first option. A usual terminology in calculus is about absolute and relative (or local) maxima and minima. The absolute maximum would be then max{f(x): x ∈ [−2, 4]} max { f ( x): x ∈ [ − 2, 4] }. The phrase "absolute maximum value " probably has to do with the fact that when looking at extrema of functions ...The absolute value is a special case of parentheses. We do the work inside the parentheses 1st. The absolute value gets applied to the result, not the parts. Consider this numeric example: |3 (5)-9|. 1) Using PEMDAS: Mulitply, substract, then do absolute value once there is one number. |3 (5)-9| = |15 -9| = |6| = 6.So 12 worked 0 shouldn't work. Lets try 0. Zero minus 12 so it's the absolute value of 0. I wanna do this in a different color. It is the absolute value of 0 minus 12 plus 4. This should not be less than 14. This should not work. So we get the absolute value of negative 12. Plus 4 should not be less than 14. Then we should end up with a ...Example 4: Solve the absolute value equation [latex]\left| { - 2x + 7} \right| = 25[/latex] . You may think that this problem is complex because of the [latex]-2[/latex] next to the variable [latex]x[/latex]. However, that shouldn't intimidate you because the key idea remains the same. We have the absolute value symbol isolated on one ... The absolute value of complex number is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex number's absolute value is measured on the complex number plane. Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are. Questions.A complex number is any number of the form x + yi where x,y are real numbers and i is the imaginary number √ (-1). (All real and imaginary numbers are also complex numbers.) Let N be the complex number x + yi. The complex conjugate of N is equal to x - yi. The modulus of N is √ (x^2 + y^2). The modulus N and its conjugate are equal.Find step-by-step Algebra 2 solutions and your answer to the following textbook question: Find the absolute value of 4 - 3i..Welcome to the Two Numbers Absolute Value Calculator. This calculator calculates the two numbers that have the absolute value of any number. Please enter your number below to find the two numbers that have it as their absolute value. Here are some examples of what our calculator can explain and answer. What two numbers have an absolute value of 6?Abstract. 4-bits Absolute Value Detector circuit is a very commonly used circuit design. As to simplify the internal circuit design to make the total number of stage lesser which provides a less ...This rule is used for solving most absolute value questions. Absolute value equations Absolute value equations are equations in which the variable is within an absolute value operator. For example: | x-4 | = 10 Because the value of x-4 can be 10 or -10, both of which have an absolute value of 10, we need to consider both cases: x-4 = 10 and x-4 ...The absolute value of − 4 is also 4 : A number line from negative 5 to 5 with evenly spaced tick marks in increments of 1. Above the number line is a bracket labeled 4 that starts at negative 4 and ends at 0.Solve absolute value inequalities. A compound inequality includes two inequalities in one statement. A statement such as 4 < x≤ 6 4 < x ≤ 6 means 4 < x 4 < x and x ≤6 x ≤ 6. There are two ways to solve compound inequalities: separating them into two separate inequalities or leaving the compound inequality intact and performing ...The absolute value of a number is the magnitude of that number regardless of the sign before it. For example, the absolute value of both -4 and 4 is 4. Let's look at the left side of the equation, -abs(-4).The magnitude of this value. typealias Magnitude. A type that can represent the absolute value of any possible value of this type. func signum() -> Int. Returns -1 if this value is negative and 1 if it's positive; otherwise, 0. Apple. Developer. Documentation. Returns the absolute value of the given number.With the absolute value calculator, the function abs can calculate the absolute value online of a number. To calculate the absolute value of a number, just enter the number and to apply the function abs. Thus, for calculating the absolute value of the number -5, you must enter abs ( − 5 - 5) or directly -5, if the button abs already appears ...The absolute value of a number is simply the distance that number lies away from 0 on the number line. Absolute value eliminates the "direction" traveled to get there. It's like saying that you walked 3 meters frontward versus 3 meters backward. You walked 3 meters in different directions from where you started! With a number line in front of ...The absolute value of a number is its distance from zero on the number line. The symbol for absolute value is @$\begin{align*}| \ |\end{align*}@$ . Let's look at an example. @$\begin{align*}|-3|\end{align*}@$ This is read as "the absolute value of -3". To figure out the absolute value of -3, think about how far the number -3 is from zero ...\[\therefore \]The absolute value of \[4 + 3i\] is 5. Note: Many students make the mistake of writing both the values i.e. \[ + 5\] and \[ - 5\] in the final answer which is wrong as the absolute value or modulus is always positive as it denotes the distance between the complex number and the origin.Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result! The solve for x calculator allows you to enter your problem and solve the equation to see the result. For example, the absolute value of 4 is 4 : − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 4. This seems kind of obvious. Of course the distance from 0 to 4 is 4 . Where absolute value gets interesting is with negative numbers. For example, the absolute value of − 4 is also 4 : − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 4. A coordinate plane. The x- and y-axes both scale by one. The graph of f is V-shaped with a minimum at zero, zero. On the left side of the minimum is a ray with a slope of negative one, and on the right side is a ray with a slope of one.
Calculating the derivative of absolute value is challenging at first, but once you learn the formula, you can easily find the right values and functions in any problem. You will need to use many terms when working with derivatives, including continuity, discontinuity, piecewise, limits, and differential. Quick Navigation.. Persian translate
its distance from zero on the number line. * For the notation, we use two big vertical lines. Check it out: Find the absolute value of 4: Find the absolute value of -5: continue. 1. of 2. This prealgebra lesson defines and explains how to find the absolute value of a number. Simplify the expression. three tenths squared minus 17 plus the quantity negative 7 divided by the absolute value of 4.3 minus 7.8 end quantity times 2.67 This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.1. Apr 19, 2009. #1. This is one of the questions on my homework assignment. I need to find the absolute value of a 4-bit binary number. I know that I don't need to do anything to the first 8 positive numbers to find the absolute value, but my problem is with the last 8 negative numbers. I know that I need to use two's complement to invert the ...An ndarray containing the absolute value of each element in x. For complex input, a + ib , the absolute value is \(\sqrt{ a^2 + b^2 }\) . This is a scalar if x is a scalar.1. Apr 19, 2009. #1. This is one of the questions on my homework assignment. I need to find the absolute value of a 4-bit binary number. I know that I don't need to do anything to the first 8 positive numbers to find the absolute value, but my problem is with the last 8 negative numbers. I know that I need to use two's complement to invert the ...What is Absolute Difference? Absolute difference is the size of the difference between any two numbers. You can think of this as the distance between the two numbers on a number line. Whether the numbers are positive or negative, absolute difference tells you the value of this distance. Examples of Absolute Difference Formula Calculations: 1.Absolute Value. The absolute value (or modulus) of a real number is the corresponding nonnegative value that disregards the sign. For a real value, a, the absolute value is: a, if a is greater than or equal to zero. -a, if a is less than zero. abs(-0) returns 0.This math video tutorial explains how to solve absolute value equations with variables on both sides. It contains plenty of examples and practice problems.S...By taking the absolute value of the terms of a series where not all terms are positive, we are often able to apply an appropriate test and determine absolute convergence. This, in turn, determines that the series we are given also converges. The second statement relates to rearrangements of series. When dealing with a finite set of numbers, the ...Absolute Value Worksheet FREE. Part 1: Find the absolute values. Part 2: Compare numbers with absolute values. Part 3: Find two values for each variable. 6th Grade. View PDF. Compare and Order Numbers With Absolute Values. On this printable, students will compare pairs of numbers using <, >, and =. Then they will order sets of four numbers from ...The absolute value of a number is the magnitude of that number regardless of the sign before it. For example, the absolute value of both -4 and 4 is 4. Let's look at the left side of the equation, -abs(-4).The absolute value of -4 is 4, because it is four units to the right of zero on the number line. Learn how to simplify, compare and use absolute values with examples and exercises.The absolute value of the complex number -4- sqrt 2i is sqrt 18. Explanation: The absolute value of a complex number is the distance between the number and the origin on the complex plane. To find the absolute value of the complex number -4- sqrt 2i, we need to find the magnitude of the number.the absolute value is never negative; the absolute value of 0 is 0 because the distance between a number and itself is zero. The absolute value of a number a is written as ∣ a ∣ . For example, the absolute value of – 7 is written as | – 7|. Example 1: Find the absolute value of 2. Solution: Graph 2 on a number line. Answer: ∣ 2 ∣ ...In this case, a = 4 and b = -3, so: |4 - 3i| = √ ( (4)^2 + (-3)^2) = √ (16 + 9) = √25 = 5. So, the absolute value of 4 - 3i is 5. The absolute value of the complex number 4 - 3i, represented as |4-3i|, is equal to 5. This conclusion is reached by applying the formula for absolute value. Option D is answer. Learn more about complex number ...For example, the numbers 2 and -2 have a distance of 2 from 0, so their absolute value is the same, even though their sign is not: |2| = 2. |-2| = 2. The absolute value of 0 is 0. The absolute value function, f (x) = |x|, can be described as a piecewise function: f (x) =. -x, x < 0.The correct option is B 4. The absolute value of a number is the value that shows how far the number is from zero. Here, the given number is -4 and -4 is 4 units away from 0. Therefore, the absolute value of -4 is 4. Suggest Corrections.What is Absolute Difference? Absolute difference is the size of the difference between any two numbers. You can think of this as the distance between the two numbers on a number line. Whether the numbers are positive or negative, absolute difference tells you the value of this distance. Examples of Absolute Difference Formula Calculations: 1.The absolute value of 4-7i to the square root of. verified. Verified answer. Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is Jennifer. star.To use the absolute value calculator, enter the number you'd like to find the absolute value for in the Input box. Then, click the Compute Absolute Value button. We'll return the number's absolute value in the Absolute Value box. Next, try our other calculators and tools. PK started DQYDJ in 2009 to research and discuss finance and investing ....