Study with Quizlet and memorize flashcards containing terms like Which word equation shows hydrogen reacting with oxygen to form water?, This formula equation is unbalanced. BaCl2(aq) + Na2CO3(aq) mc017-1.jpg BaCO3(s) + NaCl(aq) Which coefficient should be placed in front of NaCl to balance this equation?, The chemical equation for the formation of ammonia is unbalanced. 3H2(g) + N2(g) mc020-1 ...Find an answer to your question What is the product? mc017-1.jpg mc017-2.jpg mc017-3.jpg mc017-4.jpg mc017-5.jpgTrying to factor as a Difference of Squares : 1.1 Factoring: mc10-jpg Theory : A difference of two perfect squares, A2- B2 can be factored into (A+B) • (A-B) Proof : (A+B) • (A-B) =A2 - AB+BA- B2= A2- AB + AB - B2 = A2 - B2 Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated ...Click an Item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box.How much would an order of 1 slice of cheese pizza and 3 sodas cost? A. $3.25 B. $5.25 C. $7.75 D. $7.25. star. 4.0/5. heart. 47. verified. Verified answer. Which statements are true regarding undefinable terms in geometry? Select two options. A point's location on the coordinate plane is indicated by an ordered pair, (x, y). A point has one ...The graph crosses the x axis at x = -4 and touches and turns on the x axis at x = 1. At which root does the graph of. f (x) = (x - 5)³ (x + 2)² touch the x axis? -2. A polynomial function has a root of -4 with multiplicity 4, a root of -1 with multiplicity 3, and a root of 5 with multiplicity 6. If the function has a positive leading ...A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. T/F? True. The equation Ax=b has the same solution set as the equation x (1) a (1) + x (2) a (2) + ... + x (n) a (n) = b. The equation Ax=b is consistent if the augmented matrix [ A b ] has a pivot position in every row.Question: Question 1 What is the major organic product obtained from the following series of reactions? H20, Hg$04 H2SO4 1. NaNH2 HCCSC-H 2. CH31 propanal, CH3CH2CHO 1-propanol, CH3CH2CH2OH butanal, CH3CH2CH2CHO butanone, CH3COCH2CH3 A Moving to the next question prevents changes to this answer. There are 2 steps to solve …Find an answer to your question Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form? mc010-1.jpg mc010-2.jpg y = 2(x + 7)2 - 73 y = (x + 7)2 - 24 ... Personal 1-on-1 Live Tutoring with our dedicated Certified Experts. dot. Rich Study materials making learning fun with 10k+ Games, Videos and Worksheets ...What is the sum of the polynomial. A polynomial is a sum of some powers of a certain variable, with some coefficient to multiply each power. Summing two polynomials simply means to sum the coefficients of the same powers, if this situations occur. Therefore we are adding the both polynomial so we get,Final answer: The equations 2x² + 6x + 9, x² + 3x + 12, and x² + 3x + 3 all have negative discriminants, indicating that they have complex solutions as required by the student question.x. y. z. Solution - Simplification or other simple results. m c − j p g. mc-jpg. Other Ways to Solve. Simplification or other simple results.Trying to factor as a Difference of Squares : 1.1 Factoring: mc22-jpg Theory : A difference of two perfect squares, A2- B2 can be factored into (A+B) • (A-B) Proof : (A+B) • (A-B) =A2 - AB+BA- B2= A2- AB + AB - B2 = A2 - B2 Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated ...What is the sum and classification of mc017-1.jpg? See answer. Advertisement. behanlaikan. Answer: Step-by-step explanation: 3fdvdbgnyncvcbfnmhbt. Cnscndcnkcecjsncnisc. Fun nd hidvhdvihvdv.Final answer: The equations 2x² + 6x + 9, x² + 3x + 12, and x² + 3x + 3 all have negative discriminants, indicating that they have complex solutions as required by the student question.. Explanation: The student is asking which of the given equations has complex solutions.. For a quadratic equation of the form ax² + bx + c = 0, the discriminant (b² - 4ac) determines the nature of the roots.Trying to factor as a Difference of Squares : 1.1 Factoring: mc12-jpg Theory : A difference of two perfect squares, A2- B2 can be factored into (A+B) • (A-B) Proof : (A+B) • (A-B) =A2 - AB+BA- B2= A2- AB + AB - B2 = A2 - B2 Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated ...Study with Quizlet and memorize flashcards containing terms like Given that Cu + 2HCImc014-1.jpg Cu2+ + 2CI- + H2(g) has an overall reduction potential of -0.34 V, what is a valid prediction about how this reaction works?, An electrochemical cell is constructed using electrodes with the following half-cell reactions. Cd2+(aq) + 2e- mc032-1.jpg Cd(s) …Question 2. Views: 5,143. For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years ...Study with Quizlet and memorize flashcards containing terms like Which expression is equivalent to mc007-1.jpg?, What is the value of mc014-1.jpg?, Jerry starts a new career making $32,000 annually. Each year for a total of 30 years, Jerry receives a $1,200 annual pay increase. The total amount earned over the 30 years can be determined using the expression mc016-1.jpg.Study with Quizlet and memorize flashcards containing terms like Which expression is equivalent to mc004-1.jpg?, Which statement best describes the polynomial? mc022 …Trying to factor as a Difference of Squares : 1.1 Factoring: mc12-jpg Theory : A difference of two perfect squares, A2- B2 can be factored into (A+B) • (A-B) Proof : (A+B) • (A-B) =A2 - AB+BA- B2= A2- AB + AB - B2 = A2 - B2 Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated ...What Is The Product Mc017 1 Jpg Mc017 2 Jpg Mc017 3 Jpg Mc017 4 Jpg Mc017 5 Jpg What States Can Dental Hygienists Administer Botox What Type Of Cancer Did Johnny Maestro Die From What Is J Plasma Bbl What Is Managed Adjudication 3 0 What Did Chuck Missler Died Of What Time Does Shabbat End In New York What Gauge Are Septum Piercings What ...To convert a PNG file to the JPG format, first download and install an image viewer that’s capable of converting image files, such as IrfanView. Then, open the PNG file in the prog...Embarking on a journey through the annals of Italian history, the 'Dynasty Name in Italian History Crossword' unravels the intricate tapestry of ruling families that shaped the peninsula's destiny.2.16 × 10⁻⁵ is the difference in the concentration of hydrogen ions between the two brands of vinegar.. What is pH? pH is a numerical indicator of how acidic or basic aqueous and other liquid solutions are.The phrase, which is frequently used in biology, agronomy, and chemistry, converts the hydrogen ion concentration, which typically ranges between 1 and 1014 gram-equivalents per litre ...Question 2. Views: 5,143. For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years ...Which pair shows equivalent expressions? mc017-1.jpg mc017-2.jpg mc017-3.jpg mc017-4.jpgThe explicit formula for the arithmetic sequence is .. We have to determine. What is the explicit formula for the arithmetic sequence?. What is the general formula of an arithmetic sequence? The general formula of the arithmetic sequence is;. Where is the nth term of the sequence, d is a common difference, n is the number of terms.. Firstly find the common difference between the terms.Pages 353-354. First solve for short-run output using equation 13.3, then solve for the change in inflation using equation 13.4. The current rate of inflation exceeds the target inflation rate by 2%. If = 0.25, = 0.5, and there are no aggregate demand shocks, short-run output will be equal to_____. 0.25%.Find an answer to your question Monique is factoring the expression mc017-1.jpg. Her work is shown below. Factors of 4x: 1, 2, 4, x Factors of 16xy: 1, 2, 4, 8…The inequality solved by Aaron is (a) |x + 2| < 3. How to determine the inequality? The attached graph represents the missing piece in the question.. From the graph, we can see that:. The value of x starts from -5 and ends at 1. Calculate the mean of these values. Mean = (1 - 5)/2 = -2. Calculate half the difference of these values. …Multiplying mc006-1.jpg by which fraction will produce an equivalent fraction with a rational denominator? Choose matching definition. B. A. C. D. Don't know? 4 of 10. Term. What is the following quotient? 5/sqrt 11 - sqrt 3. Choose …Answer. Answer: 1. an article or substance that is manufactured or refined for sale. 2. a thing or person that is the result of an action or process. 3. In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. For example, 30 is the product of 6 and 5.vaishnavim26. Option (a) is correct. 2 + m - 1 + m is an equivalent expression to the given expression 3m+1-m. Given expression 3m+1-m. We have to choose an equivalent expression from given options. Equivalent expression are those expression that looks different but are same. Like 4+2 = 6 and 3+ 3 = 6. Both have same value but looks differently.Find an answer to your question Monique is factoring the expression mc017-1.jpg. Her work is shown below. Factors of 4x: 1, 2, 4, x Factors of 16xy: 1, 2, 4, 8…C17H35COONa(aq) mc017-1.jpg C17H35COO-(aq) + Na+(aq) sodium stearate (soap) stearate ion What will happen if a large quantity of NaCl is added to the aqueous solution? ... equilibrium will tend to shift to left because addition of sodium chloride salt will lead to precipitate the soap as a product. The volume increase in the sodium ions ...Select all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the exponents within the parentheses instead of subtracting. The correct simplified form is x to the two-fifths power. <3 Learn with flashcards, games, and more — for free.What is the chance that a child of those two parents will have the disorder? 50%. When roan cattle are mated, 25% of the offspring are red, 50% are roan, and 25% are white. Upon examination, it can be seen that the coat of a roan cow consists of both red and white hairs. This trait is controlled by _______. codominant alleles.The correct answer is option (a) mc020-2.jpg. Step-by-step explanation: Given: mc020-1.jpg. To Find: Equivalent Expression. Step 1. Let, mc020-1.jpg means . Step 2. Simplifying the equation as. Step 3. Equating the above equation as follows, Then is equivalent to . Therefore, the correct answer is option (a) mc020-2.jpg. #SPJ2What is the product? mc017-1.jpg. In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. Expert answered|emdjay23|Points 205675| Log in for more information. Question. Asked 11/27/2020 5:08:16 AM.The roots of the equation will be 2, 3 and 4. Remainder theorem of polynomial. Given the given polynomial function g(x) = x³- 9x² + 26 x -24. if the one root is equal to 2, then we can determine the other roots by synthetic division:B. The equation mc024-1.jpg shows the relationship between a planet's orbital period, T, and the planet's mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased? D. Which of the following is equivalent to mc003-1.jpg? D.In basketball, if a player is fouled, they are awarded a free throw. A free throw allows the player to take 1 or 2 shots, depending on the circumstances of the foul or the player's ability to make the first shot, unchallenged. A free throw is shot from a line 15 feet from the basket. In professional basketball, the career record number of ...What is mc002-1.jpg in radical form? A) 3√6^2. Find the product with the exponent in simplest form. Then, identify the values of x and y. x= 7, y= 12.Solution - Factoring multivariable polynomials. − m c 7 j p g + m c 7 − 2 j p g. -mc^7jpg+mc^7-2jpg. Other Ways to Solve. Factoring multivariable polynomials.What Is 53mm In Inches What Is The Product Mc017 1 Jpg Mc017 2 Jpg Mc017 3 Jpg Mc017 4 Jpg Mc017 5 Jpg What States Can Dental Hygienists Administer Botox What Type Of Cancer Did Johnny Maestro Die From What Is J Plasma Bbl What Is Managed Adjudication 3 0 What Did Chuck Missler Died Of What Time Does Shabbat End In New York What Gauge Are ...Consider the three equations below. mc017-1.jpg mc017-2.jpg mc017-3.jpg Which statement do these reactions best support? Beta decay occurs only in certain atoms. Alpha decay occurs only in certain atoms. Chain reactions play important roles in the process of nuclear fission.The graph below is an example of which type of function? mc004-1.jpg. Answer C ; Cubic. Which statement is true about mc013-1.jpg? Answer D ; The graph of f (x) has range of f (x) + 2 = 1/6 {x-3} -2. What values are excluded from the domain and range of the function mc017-1.jpg? Answer C ; domain: -5/2.The graph of these functions is shown in the image attached below.. Given the following data: Translation = 2 units right, 2 units up. Dilation factor = What is a graph? A graph can be defined as the graphical representation of data on both the horizontal and vertical lines, which are commonly referred to as the x-axis and y-axis respectively.. For …The graph below is an example of which type of function? mc004-1.jpg. Answer C ; Cubic. Which statement is true about mc013-1.jpg? Answer D ; The graph of f (x) has range of f (x) + 2 = 1/6 {x-3} -2. What values are excluded from the domain and range of the function mc017-1.jpg? Answer C ; domain: -5/2.Step 1: Enter the expression you want to simplify into the editor. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. The calculator works for both numbers and expressions containing variables. Step 2: Click the blue arrow to submit and see the result!For what values of mc010-1.jpg are the vectors mc010-2.jpg and mc010-3.jpg orthogonal? Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.Step 1 Find the quadrant in which P (a, b) lies: P (a, b) is in Quadrant IV. Step 2 Use the point and the Pythagorean theorem to determine the value of r: mc026-5.jpg, but since r must be positive, mc026-6.jpg. Step 3 Determine cos mc026-7.jpg. mc026-8.jpg, where a and b are positive.What is the product? mc017-1.jpg. In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. Expert answered|emdjay23|Points 205675| Log in for more information. Question. Asked 11/27/2020 5:08:16 AM.Study with Quizlet and memorize flashcards containing terms like Which transformation matrix would result in a 270° counterclockwise rotation about the origin?, The graph below shows the transformation from triangle 1 to triangle 2. mc025-1.jpg Which sequence of steps would transform triangle 1 to triangle 2?, The transformation T = mc017-1.jpg is applied …mc001-1.jpg Which overall chemical equation is obtained by combining these intermediate equations?, Consider the following intermediate chemical equations. mc032-1.jpg What is the enthalpy of the overall chemical reaction mc032-2.jpg, Consider the intermediate chemical reactions. mc017-1.jpg The final overall chemical equation is mc017-2.jpg.Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees. heart. 40. verified. Verified answer. Accenture has signed a multi year agreement to help a mobile telecom provider. star. 4/5. heart. 4. verified. Verified answer. Which statement is true about the primary intent to have work in process constraints?.%question% Get the answers you need, now! Answer: Step-by-step explanation: We are asked find the matrix that represent the product of matrices X and Y both measures and inverse of each other.. For a matrix multiplication to be defined, the number of columns in the first matrix must be equal to number of rows in the second matrix.The approximate difference in the concentration of hydrogen ions between the two brands of vinegar is 2.2 x .. The correct option is (A).. What is concentration of Hydrogen ion? The concentration of hydrogen ions in a solution expressed usually in moles per liter or in pH units and used as a measure of the acidity of the solution indicator dyes for narrow ranges of hydrogen-ion concentration.What is/are the major organic product(s) obtained from the following reaction? a. only 1: b. only 2 and 3: c. only 3: d. only 2: 10) What is the major organic product obtained from the following reaction? a. 3: b. 1: c. 4: d. 2: 11) What is the best choice of reagent(s) to perform the following transformation? a.Trying to factor as a Difference of Squares : 1.1 Factoring: mc20-jpg Theory : A difference of two perfect squares, A2- B2 can be factored into (A+B) • (A-B) Proof : (A+B) • (A-B) =A2 - AB+BA- B2= A2- AB + AB - B2 = A2 - B2 Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated ...D. Which expression is equivalent to mc016-1.jpg? B. The equation mc024-1.jpg shows the relationship between a planet's orbital period, T, and the planet's mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased?Gauth AI Solution. The acceleration of the object is 4 \, m/s^2 4m/s2. (Option C) 1 The equation F = ma represents Newton's second law of motion, where F is the force, m is the mass, and a is the acceleration. 2 Rearranging the equation to solve for acceleration gives a = \frac {F} {m} a = mF. 3 Substituting the given values, F = 20 \, N F =20N ...Answer. 14 people found it helpful. hunter71720002. report flag outlined. -4 because 1×-12 is -12 and 8-12 is -4. arrow right. Explore similar answers. messages. Get this answer verified by an Expert.Study with Quizlet and memorize flashcards containing terms like An electrochemical cell is powered by the half reactions shown below. Ag+(aq) + e- --> Ag(s) Eo = +0.80 V Pb2+(aq) + 2e- ---> Pb(s) Eo = -0.13 V Which value represents the overall electric cell potential?, Reduction potential is the tendency for a chemical species to, What are the standard conditions under which reduction ...Which function represents the following graph? (D) y=^3 sqrt x+3+3. Which of the following is the graph of y=- sqrt x+1. B. The mean sustained wind velocity, v, can be determined by the equation mc022-1.jpg, where p is the air pressure, in millibars, at the center of the hurricane. What is the approximate air pressure at the center of a ...What is the product? - 11244131. brensala9089 brensala9089 16.07.2019 Math Secondary School answered What is the product? mc012-1.jpg mc012-2.jpg mc012-3.jpg mc012-4.jpg mc012-5.jpg See answers Advertisement Advertisement Arianagrande69 Arianagrande69 Here's your answer . Mc.01/0=7. Mc.02=/8.Option (b) is the correct answer as the expression.. Let's break down each expression to determine their equivalence: a. Expanding the left side: The right side does not match, so option (a) is not equivalent.In today’s digital age, the need for converting files from one format to another has become increasingly common. One such conversion that is frequently required is the conversion o...Assume x mc020-2.jpg 0 and y > 0. milivansh8492 milivansh8492 03.12.2018 Math Secondary School answered • expert verified Which expression is equivalent to mc020-1.jpg? Assume x mc020-2.jpg 0 and y > 0. See answers Advertisement Advertisement amitnrw amitnrw Given : x>0 , y > 0 To Find ...mc017-1.jpg mc017-2.jpg mc017-3.jpg mc017-4.jpg See answers Advertisement Advertisement Rameshjangid Rameshjangid Answer: 2(2/5x + 2)=4/5x + 4, Step-by-step explanation: Step 1: Let us distribute 2 Inside the parenthesis. That is, we use distributive property: a(b+c)=a b+a c. So,What is the sum of the polynomial. A polynomial is a sum of some powers of a certain variable, with some coefficient to multiply each power. Summing two polynomials simply means to sum the coefficients of the same powers, if this situations occur. Therefore we are adding the both polynomial so we get,D. 5 m o l N 2 and 1 m o l H 2 , Ratio N 2 : H 2 = 5: 1 The reaction mixture (B) gives greatest amount of product. Solve any question of Some Basic Concepts of Chemistry with:-The product of 4.0 x 10⁻² m and 8.1 x 10² m, when expressed with the correct number of significant figures, is 32 m². Explanation: When multiplying two numbers, the product must be rounded off so that it has no more significant figures than either of the original numbers. Here we have 4.0 x 10⁻² m (which has two significant …Study with Quizlet and memorize flashcards containing terms like Consider the reaction. N2(g) + 3H2(g) → 2NH3(g) How many grams of N2 are required to produce 100.0 L of NH3 at STP?, Under which conditions does the molar volume of a gas is consider standard?, Decomposition of potassium chlorate (KClO3) produces potassium chloride (KCl) and pure oxygen (O2). The balanced equation for the ...Choose the answer which provides the correct coefficients for each reactant and product. A- (4,3,2) Which of the following statements about chemical reactions is FALSE. D- Chemical reactions can convert mass into energy. How many molecules of products are represented in the equation below. B- 5.a (x) = 3x + 1. b (x) = √ (x-4) Therefore. (b \circ a) (x) = \sqrt {3x+1-4} =\sqrt {3x-3} This composition of functions is only defined as a real number when x≥0. Therefore its domain is x = [1,∞] Answer: [1,∞] report flag outlined. Sorry can you say the answer again so I can see im not a "brainly plus subscriber".Which expression is equivalent to mc014-1. Jpg? mc014-2. Jpg mc014-3. Jpg mc014-4. Jpg mc014-5. Jpg. Get the answers you need, now!The product of 4.0 x 10⁻² m and 8.1 x 10² m, when expressed with the correct number of significant figures, is 32 m². Explanation: When multiplying two numbers, the product must be rounded off so that it has no more significant figures than either of the original numbers. Here we have 4.0 x 10⁻² m (which has two significant figures ...Click here 👆 to get an answer to your question ️ What is the following product? Assume x>0 (4x√5x^2 +2x^2√6)^2 A.80x^4+8x^4√30x+24x^4 B.80x^6+8x^5+8x^5√30…Trying to factor as a Difference of Squares : 1.1 Factoring: mc20-jpg Theory : A difference of two perfect squares, A2- B2 can be factored into (A+B) • (A-B) Proof : (A+B) • (A-B) =A2 - AB+BA- B2= A2- AB + AB - B2 = A2 - B2 Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated ...Economics questions and answers. Refer to Figure 4-1. What is the equilibrium price in this market? Select one: a. $0 b. $5 C. $7.50 d. $10Refer to Figure 4-1. At a price of $12, which of the following is correct? Select one: a. there is a surplus of 1 unit b. there is a surplus of 2 units c. there is a shortage of 1 unit d. there is a shortage ...Get the right answer, fast. Get a free answer to a quick problem. Most questions answered within 4 hours. Choose an expert and meet online. No packages or …Expert-Verified Answer. 27 people found it helpful. mayadc821. Notice how both terms are perfect cubes. You can factor using the difference of cubes formula: The factored form of x³ - 1 is (x - 1) (x² + x + 1). arrow right.KerryEye. Answer: The product of the two matrices is: Step-by-Step Explanation: Matrix multiplication is not done element wise. Two matrices 'A' and 'B' are said be compatible to multiplication iff A is of the size and B is of the size . The product AB would be of the size . Here, the size of the first matrix is . Second matrix is .Find an answer to your question What is the distance between (–6, 2) and (8, 10) on a coordinate grid? mc017-1.jpg mc, Study with Quizlet and memorize flashcards containing terms like Which of the following graphs could be, What Is The Product Mc017 1 Jpg Mc017 2 Jpg Mc017 3 Jpg Mc017 4 Jpg Mc017, Study with Quizlet and memorize flashcards containing terms like Which word equation show, Answer. Answer: 1. an article or substance that is manufactured or refined for s, The two exact solutions of mc017-1.jpg for mc017-2.jpg are: mc017-10.jpg and mc017-11.jpg . To solve t, Study with Quizlet and memorize flashcards containing te, Study with Quizlet and memorize flashcards containing terms like Wh, Consider the intermediate chemical reactions.mc017-1.j, A. What is the solution of mc017-1.jpg Round your answer to the neares, Gather information about the product that you want to buy, make, mod, Final answer: The equations 2x² + 6x + 9, x² + 3x + 1, 3x4 + 7x3 - x2 - 4x + 8. verified. Verified answer. Jonathan and his, The electrolysis of water forms H2 and O2. 2H2O mc0, The approximate difference in the concentration of h, Step by step solution : Step 1 : Skip Ad Equation at the end, How much would an order of 1 slice of cheese pizza and 3 sodas c, Multiplying mc006-1.jpg by which fraction will produce an equiv.