x^{2}x^{1-1}+x^{1}\times 2x^{2-1} The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ...Step 1: Enter the radical expression below for which you want to calculate the square root. The square root calculator finds the square root of the given radical expression. If a given number is a perfect square, you will get a final answer in exact form. If a given number is not a perfect square, you will get a final answer in exact form and ...By ‘ The law of exponents ‘ , a^n × a^m = a^n+m. Therefore , e^x × e^x = e^x+x = e^2x . Find out how many invertible and diagonal solutions X 2 − 2X = 0 has when X ∈ R3×3. If X is invertible, then multiplying each side of X 2−2X = 0 by the inverse of X gives us that X −2I = 0 and so X = 2I. For the case where X is diagonal, let X ...The background is Munkres's topology says: Every closed interval in $\\mathbb{R}$ is compact. and A subspace A of $\\mathbb{R}^n$ is compact if and only if it is closed and is bounded in the square (orFree Algebraic Properties Calculator - Simplify radicals, exponents, logarithms, absolute values and complex numbers step-by-stepSolve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. The fraction calculator is easy to use. First select if you want to use the default or mixed fraction calculator. Fill in two fractions and choose if you want to add, subtract, multiply or divide and click the "Calculate" button. The result is a (mixed) fraction reduced to it’s simplest form. Also a table with the result fraction converted in ...By ‘ The law of exponents ‘ , a^n × a^m = a^n+m. Therefore , e^x × e^x = e^x+x = e^2x . Find out how many invertible and diagonal solutions X 2 − 2X = 0 has when X ∈ R3×3. If X is invertible, then multiplying each side of X 2−2X = 0 by the inverse of X gives us that X −2I = 0 and so X = 2I. For the case where X is diagonal, let X ...Like, what does “multiply ‘x’ by itself -1 times” mean? The expression x n only means “multiply x by itself n times” when n is a positive integer. When the exponent is 0, a negative integer, an arbitrary rational number, an arbitrary real number, or an arbitrary complex number you need a different definition for x n to make sense ...Remember, 2x times 4x is the same thing as-- you can rearrange the order of multiplication. This is the same thing as 2 times 4, times x times x. Which is the same thing as 8 times x squared. Remember, x to the 1, times x to the 1, add the exponents. I mean, you know x times x is x squared. So this first term is going to be 8x squared.To write 1 y 1 y as a fraction with a common denominator, multiply by x x x x. 1 x ⋅ y y + 1 y ⋅ x x 1 x ⋅ y y + 1 y ⋅ x x. Write each expression with a common denominator of xy x y, by multiplying each by an appropriate factor of 1 1. Tap for more steps... y xy + x xy y x y + x x y. Combine the numerators over the common denominator. By ‘ The law of exponents ‘ , a^n × a^m = a^n+m. Therefore , e^x × e^x = e^x+x = e^2x . Find out how many invertible and diagonal solutions X 2 − 2X = 0 has when X ∈ R3×3. If X is invertible, then multiplying each side of X 2−2X = 0 by the inverse of X gives us that X −2I = 0 and so X = 2I. For the case where X is diagonal, let X ...Free Square Roots calculator - Find square roots of any number step-by-step f of x is equal to 7x minus 5. g of x is equal to x to the third power plus 4x. And then they ask us to find f times g of x So the first thing to realize is that this notation f times g of x is just referring to a function that is a product of f of x and g of x. Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem. The pH scale is logarithmic, meaning that an increase or decrease of an integer value changes the concentration by a tenfold. For example, a pH of 3 is ten times more acidic than a pH of 4. Likewise, a pH of 3 is one hundred times more acidic than a pH of 5. Similarly a pH of 11 is ten times more basic than a pH of 10.An exponent is a way to represent how many times a number, known as the base, is multiplied by itself. It is represented as a small number in the upper right hand corner of the base. For example: x² means you multiply x by itself two times, which is x × x. Likewise, 4² = 4 × 4, etc. If the exponent is 3, in the example 5³, then the result ...Like, what does “multiply ‘x’ by itself -1 times” mean? The expression x n only means “multiply x by itself n times” when n is a positive integer. When the exponent is 0, a negative integer, an arbitrary rational number, an arbitrary real number, or an arbitrary complex number you need a different definition for x n to make sense ...The three integrals from 1 to 2, from 2 to 4, and from 4 to 8 are all equal. Each region is the previous region halved vertically and doubled horizontally. Extending this, the integral from 1 to 2 k is k times the integral from 1 to 2, just as ln 2 k = k ln 2. Calculus. In real calculus, the derivative of 1/x = x −1 is given by the power rule ... In order to show that T is a function, you need to prove that for each pair of subsets A and B of X there is one and only one subset U of X\times X such that T(A,B)=U, that is, ((A,B),U) \in T ...Step 1: Enter the radical expression below for which you want to calculate the square root. The square root calculator finds the square root of the given radical expression. If a given number is a perfect square, you will get a final answer in exact form. If a given number is not a perfect square, you will get a final answer in exact form and ... To write 1 y 1 y as a fraction with a common denominator, multiply by x x x x. 1 x ⋅ y y + 1 y ⋅ x x 1 x ⋅ y y + 1 y ⋅ x x. Write each expression with a common denominator of xy x y, by multiplying each by an appropriate factor of 1 1. Tap for more steps... y xy + x xy y x y + x x y. Combine the numerators over the common denominator. Here's the rule: When you multiply two terms with the same base, the exponents add. So: x*x 1/2 = x 1+1/2 = x3/2. Upvote • 0 Downvote.x^{5}\times 3x^{3-1}+x^{3}\times 5x^{5-1} The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The ...Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app. X-Times is a technology company that creates high-end digital chip design solutions. The company is focusing on independent research and development of the digital implementation EDA platform in accordance with the 3S concept (Smart, Speedy, Simple), including a new generation of layout and wiring technology while providing high-end digital chipFor Question 1, observe that Z = (B×X)∩V. (Just notice that x ∈ V b means (b,x)∈ V .) Question 2: consider the map f:(B×C)×Pn → (B ×Pn)×(C ×Pn), (b,c,x) ↦((b,x),(c,x)). ... The problem is that in order to remedy the problems and paradoxes of naive set theory, the mathematicians around the turn of the century realised that you ... First we prove an intermediate result. Subtract 0 × 0 0 × 0 from each side to get 0 = 0 × 0 0 = 0 × 0. Now we are ready for the final kill. = 1 × 1 + 1 × (−1) + (−1) × 1 + (−1) × (−1) = 1 × 1 + 1 × ( − 1) + ( − 1) × 1 + ( − 1) × ( − 1) Add 1 1 to each side to get 1 = (−1) × (−1) 1 = ( − 1) × ( − 1). 25.6k 4 ... Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. In order to show that T is a function, you need to prove that for each pair of subsets A and B of X there is one and only one subset U of X\times X such that T(A,B)=U, that is, ((A,B),U) \in T ... What is the ''right" norm for the Banach space tensor product in this situation?While "10% more" means 1.1x the original, making "300% more" logically mean 4x the original, this doesn't happen with "X times more." You would never say "a tenth times more" or "half times more" or even "one time (s) more." And "one and a half times more" should be 1.5x the original. On the other hand, "three times as many more" would indeed ...X-Times is a technology company that creates high-end digital chip design solutions. The company is focusing on independent research and development of the digital implementation EDA platform in accordance with the 3S concept (Smart, Speedy, Simple), including a new generation of layout and wiring technology while providing high-end digital chipTo write 1 y 1 y as a fraction with a common denominator, multiply by x x x x. 1 x ⋅ y y + 1 y ⋅ x x 1 x ⋅ y y + 1 y ⋅ x x. Write each expression with a common denominator of xy x y, by multiplying each by an appropriate factor of 1 1. Tap for more steps... y xy + x xy y x y + x x y. Combine the numerators over the common denominator.In school you were taught that 1/x+y is not the same as 1/x + 1/y, but for which x and y is it actually true? Watch this video and find out!Subscribe to my c...May 25, 2020 · Which expression is equivalent to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction? 4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1) That you could view as x to the negative 1. You have a first power here. 1 minus 2 is negative 1. So this right here is equal to x to the negative 1 power. Or it could also be equal to 1 over x. These are equivalent. So let's say that this is equal into 1 over x, just like that. And it would be. x over x times x.Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x+1 is \left(x-1\right)\left(x+1\right).x^{5}\times 3x^{3-1}+x^{3}\times 5x^{5-1} The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The ...Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.An exponent is the number of times to multiply a number by itself. Write an exponent as a raised number. In the number 2 4 (2 to the exponent 4, or 2 to the power of 4), the ‘4’ is the exponent. The ‘2’ is the number to multiply by itself 4 times over. In this case 2 x 2 x 2 x 2 = 16.Simplify x^ (1/2)*x^ (1/2) x1 2 ⋅ x1 2 x 1 2 ⋅ x 1 2. Multiply x1 2 x 1 2 by x1 2 x 1 2 by adding the exponents. Tap for more steps... x1 x 1. Simplify x1 x 1.You want to have your decimal q such that q \times (1.15 \times x ) = 1.15 \times x - x = 0.15 \times x so q \times 1.15 \times x = 0.15 \times x for all x Finally, you have q = \frac{0.15}{1.15} \simeq 0.1304347826 ...18 seconds. =. 55 seconds. Subtract minutes. 9 minutes is less than 56 minutes so borrow 1 from hours. There are 0 hours so borrow 1 from days. 1 day = 24 hours and 1 hour = 60 minutes, so add 24 to hours, then borrow 1 from hours to leave 23. Add 60 minutes to 9 to get 69. 69 minutes - 56 minutes = 13 minutes.Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.View solution steps Evaluate x Graph Quiz Polynomial x×1 Similar Problems from Web Search What does X × {0} and Y × {1} mean in this proof? https://math.stackexchange.com/q/2332997 A×B = {(a,b):a ∈ A,b ∈ B}. This is called the Cartesian product. For example {a,b,c}×{0,1} ={(a,0),(b,0),(c,0),(a,1),(b,1),(c,1)} In the context of the proof, ...Simplify 1/ ( square root of x) 1 √x 1 x. Multiply 1 √x 1 x by √x √x x x. 1 √x ⋅ √x √x 1 x ⋅ x x. Combine and simplify the denominator.Simplify ( square root of x-1)( square root of x+1) Step 1. Expand using the FOIL Method. Tap for more steps... Step 1.1. Apply the distributive property. Step 1.2.Simplify x^ (1/2)*x^ (1/2) x1 2 ⋅ x1 2 x 1 2 ⋅ x 1 2. Multiply x1 2 x 1 2 by x1 2 x 1 2 by adding the exponents. Tap for more steps... x1 x 1. Simplify x1 x 1. The numpy.repeat has been mentioned, and that's clearly the equivalent to what you want. But for completenes' sake, there's also repeat from the itertools standard library. . However, this is intended for iterables in general, so it doesn't allow repetions by index (because iterables in general do not have an index definIdentify H (A) and H (B) with H (pt). Then f ∗ = (g∗,−g∗), so kerf ∗ = kerg∗. Proof that Sorgenfrey plane is not normal using points x × (-x) They mean all x,−x +ϵ such that x ∈ (a,b) and 0 < ϵ < 1/n; that includes both rational and irrational x. You have a particular n and a non-empty open interval (a,b) ...Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.See the entire simplification process below: Explanation: The rules for order of operation say to execute the multiplication in this problem first: 2x−9×x+8 →2x−9x+8 ... Equivalent metrics gives the same topology, so we can show that the metrics are equivalent, I'll replace d(x1,y1)= x and d(x2,y2) = y and show that they are equivalent. Like, what does “multiply ‘x’ by itself -1 times” mean? The expression x n only means “multiply x by itself n times” when n is a positive integer. When the exponent is 0, a negative integer, an arbitrary rational number, an arbitrary real number, or an arbitrary complex number you need a different definition for x n to make sense ... Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.Simplify x^ (1/2)*x^ (1/2) x1 2 ⋅ x1 2 x 1 2 ⋅ x 1 2. Multiply x1 2 x 1 2 by x1 2 x 1 2 by adding the exponents. Tap for more steps... x1 x 1. Simplify x1 x 1. You enter the first fraction, you enter the second fraction, click "Calculate" and hey presto, you get the answer. You can also click the little icon after the calculator to find out more information about the process of subtracting one fraction from another. (Note: you need to have performed a calculation first or the link won't work!) The pH scale is logarithmic, meaning that an increase or decrease of an integer value changes the concentration by a tenfold. For example, a pH of 3 is ten times more acidic than a pH of 4. Likewise, a pH of 3 is one hundred times more acidic than a pH of 5. Similarly a pH of 11 is ten times more basic than a pH of 10.Multiply the inside terms: 1 ⋅ x = x. Multiply the last term: 1 ⋅ − 1 = − 1. This is equal to. x2 +x −x −1. The middle terms cancel, and we're left with. x2 −1. Remember, FOIL will work every time, but if we see a product of binomials of the form (a + b)(a −b), we can immediately recognize that it fits the difference of squares ...x^{5}\times 3x^{3-1}+x^{3}\times 5x^{5-1} The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The ..., the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore beAlgebra. Divide 1/ (1/x) 1 1 x 1 1 x. Multiply the numerator by the reciprocal of the denominator. 1x 1 x. Multiply x x by 1 1.Identify H (A) and H (B) with H (pt). Then f ∗ = (g∗,−g∗), so kerf ∗ = kerg∗. Proof that Sorgenfrey plane is not normal using points x × (-x) They mean all x,−x +ϵ such that x ∈ (a,b) and 0 < ϵ < 1/n; that includes both rational and irrational x. You have a particular n and a non-empty open interval (a,b) ...For Question 1, observe that Z = (B×X)∩V. (Just notice that x ∈ V b means (b,x)∈ V .) Question 2: consider the map f:(B×C)×Pn → (B ×Pn)×(C ×Pn), (b,c,x) ↦((b,x),(c,x)). ... The problem is that in order to remedy the problems and paradoxes of naive set theory, the mathematicians around the turn of the century realised that you ... First we prove an intermediate result. Subtract 0 × 0 0 × 0 from each side to get 0 = 0 × 0 0 = 0 × 0. Now we are ready for the final kill. = 1 × 1 + 1 × (−1) + (−1) × 1 + (−1) × (−1) = 1 × 1 + 1 × ( − 1) + ( − 1) × 1 + ( − 1) × ( − 1) Add 1 1 to each side to get 1 = (−1) × (−1) 1 = ( − 1) × ( − 1). 25.6k 4 ...1. negative of (4 squared) is -4² = -(4)² = -(4 × 4) = -16. 2. (negative 4) squared is (-4)² = (-4 × -4) = 16. Use parentheses to clearly indicate which calculation you really want to happen. Squared. A number n squared is written as n² and n² = n × n. If n is an integer then n² is a perfect square.What is x times 1? Updated: 4/28/2022 Wiki User ∙ 11y ago Study now See answers (13) Best Answer Copy x times 1 is x. Anything times 1 is still that same anything. Wiki User ∙ 11y ago...Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepSimplify 1/ ( square root of x) 1 √x 1 x. Multiply 1 √x 1 x by √x √x x x. 1 √x ⋅ √x √x 1 x ⋅ x x. Combine and simplify the denominator.For X\times [0,M]: \times is the Cartesian product and [0,M] is the interval \{x:0 \le x \le M\}. So, X \times [0,M] = \{(x,r):x \in X \land 0 \le r \le M\} For Y ...In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.Defintion of proper homotopy https://math.stackexchange.com/questions/2532344/defintion-of-proper-homotopy Let X =R. The homotopy will be from the identity map to itself, so H (0,x)= H (1,x)= x for all x. For each integer n ≥ 1, during the time period [1/(n+1),1/n], the point n∈ X is ...Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. The three integrals from 1 to 2, from 2 to 4, and from 4 to 8 are all equal. Each region is the previous region halved vertically and doubled horizontally. Extending this, the integral from 1 to 2 k is k times the integral from 1 to 2, just as ln 2 k = k ln 2. Calculus. In real calculus, the derivative of 1/x = x −1 is given by the power rule ... Step-by-Step Examples Algebra Solve for x Calculator 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!Dec 18, 2022 · (x) x 1 =x. Why is a number to the first power equal the same number? The following is not a proof or a reason, but it's a demonstrationthat might be intuitively satisfying:'X' mentioned 4 times: X times X times X times X = X to the fourth power'X' mentioned 3 times: X times X times X = X to the third power'X' mentioned 2 times: X times X = X to the second power'X' mentioned 1 time: X = X to ... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Which expression is equivalent to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction? 4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. Algebra. Multiply (x-5) (x-1) (x − 5) (x − 1) ( x - 5) ( x - 1) Expand (x−5)(x− 1) ( x - 5) ( x - 1) using the FOIL Method. Tap for more steps... x⋅x+x⋅ −1−5x−5⋅−1 x ⋅ x + x ⋅ - 1 - 5 x - 5 ⋅ - 1. Simplify and combine like terms. Tap for more steps... x2 − 6x+5 x 2 - 6 x + 5.Associative property of multiplication: Changing the grouping of factors does not change the product. For example, (2 \times 3) \times 4 = 2 \times (3 \times 4) (2×3)×4 = 2×(3×4). Identity property of multiplication: The product of 1 1 and any number is that number. For example, 7 \times 1 = 7 7 ×1 = 7.Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Apr 28, 2022 · What is x times 1? Updated: 4/28/2022 Wiki User ∙ 11y ago Study now See answers (13) Best Answer Copy x times 1 is x. Anything times 1 is still that same anything. Wiki User ∙ 11y ago... May 25, 2020 · Which expression is equivalent to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction? 4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1) Free Square Roots calculator - Find square roots of any number step-by-stepCalculus. Solve for x 1/x=0. 1 x = 0 1 x = 0. Set the numerator equal to zero. 1 = 0 1 = 0. Since 1 ≠ 0 1 ≠ 0, there are no solutions. In order to show that T is a function, you need to prove that for each pair of subsets A and B of X there is one and only one subset U of X\times X such that T(A,B)=U, that is, ((A,B),U) \in T ... An exponent is a way to represent how many times a number, known as the base, is multiplied by itself. It is represented as a small number in the upper right hand corner of the base. For example: x² means you multiply x by itself two times, which is x × x. Likewise, 4² = 4 × 4, etc. If the exponent is 3, in the example 5³, then the result ...View solution steps Evaluate x Graph Quiz Polynomial x×1 Similar Problems from Web Search What does X × {0} and Y × {1} mean in this proof? https://math.stackexchange.com/q/2332997 A×B = {(a,b):a ∈ A,b ∈ B}. This is called the Cartesian product. For example {a,b,c}×{0,1} ={(a,0),(b,0),(c,0),(a,1),(b,1),(c,1)} In the context of the proof, ...
First we prove an intermediate result. Subtract 0 × 0 0 × 0 from each side to get 0 = 0 × 0 0 = 0 × 0. Now we are ready for the final kill. = 1 × 1 + 1 × (−1) + (−1) × 1 + (−1) × (−1) = 1 × 1 + 1 × ( − 1) + ( − 1) × 1 + ( − 1) × ( − 1) Add 1 1 to each side to get 1 = (−1) × (−1) 1 = ( − 1) × ( − 1). 25.6k 4 ... . Nprice
, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore beAlgebra. Simplify 1/2x^ (-1/2) 1 2 x−1 2 1 2 x - 1 2. Rewrite the expression using the negative exponent rule b−n = 1 bn b - n = 1 b n. 1 2 ⋅ 1 x1 2 1 2 ⋅ 1 x 1 2. Combine. 1⋅1 2x1 2 1 ⋅ 1 2 x 1 2. Multiply 1 1 by 1 1. 1 2x1 2 1 2 x 1 2.x^{5}\times 3x^{3-1}+x^{3}\times 5x^{5-1} The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The ...In order to show that T is a function, you need to prove that for each pair of subsets A and B of X there is one and only one subset U of X\times X such that T(A,B)=U, that is, ((A,B),U) \in T ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...The fraction calculator is easy to use. First select if you want to use the default or mixed fraction calculator. Fill in two fractions and choose if you want to add, subtract, multiply or divide and click the "Calculate" button. The result is a (mixed) fraction reduced to it’s simplest form. Also a table with the result fraction converted in ... Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Multiply the inside terms: 1 ⋅ x = x. Multiply the last term: 1 ⋅ − 1 = − 1. This is equal to. x2 +x −x −1. The middle terms cancel, and we're left with. x2 −1. Remember, FOIL will work every time, but if we see a product of binomials of the form (a + b)(a −b), we can immediately recognize that it fits the difference of squares ...For Question 1, observe that Z = (B×X)∩V. (Just notice that x ∈ V b means (b,x)∈ V .) Question 2: consider the map f:(B×C)×Pn → (B ×Pn)×(C ×Pn), (b,c,x) ↦((b,x),(c,x)). ... The problem is that in order to remedy the problems and paradoxes of naive set theory, the mathematicians around the turn of the century realised that you ... , the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be In order to show that T is a function, you need to prove that for each pair of subsets A and B of X there is one and only one subset U of X\times X such that T(A,B)=U, that is, ((A,B),U) \in T ...Which expression is equivalent to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction? 4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)Dec 18, 2022 · (x) x 1 =x. Why is a number to the first power equal the same number? The following is not a proof or a reason, but it's a demonstrationthat might be intuitively satisfying:'X' mentioned 4 times: X times X times X times X = X to the fourth power'X' mentioned 3 times: X times X times X = X to the third power'X' mentioned 2 times: X times X = X to the second power'X' mentioned 1 time: X = X to ... .