Exercise given in textbook: A farmer has 40m of fencing with which to enclose a rectangular pen.Given that the pen is x m wide - show that it's area is (20x - x^2)m^2 and deduce that the maximum area that he can enclose (Answer given 100m^2). I have completed lots and lots of exercises involving completing the squar
Section 1.1 Exercises Pages 10-12 Problems 44, 48, 92, 98, 110 Write each interval of real numbers in interval notation and graph it. 44. The set of real numbers greater than or equal to _1 and less than 6 48. The set of real numbers less than or equal to _4 Consider the following nine integers: -4, -3, -2, -1,
#1) Find the quotient and the remainder. (x64-2x^2+3) ÷ (x+1) Here are my choices, but I can't seem to come up with any of them. A) x^3+x^2-x-1, 2 B) x^3-x^2-x=1, 2 C) x^2-3x=3, 0 D) x^2-3x+4, -1 #2) Factor and Match. I cannot come up with any answers that match. Help. z^2-12wz+13w^2 A) (
1) Simplify: (4+ √48) / 4 2) Find all real solutions: x^2= 81 3) Solve: 3√(x-2) = 4 4) Solve: 3x^2+5=11 5) Solve by factoring: x^2-4x-5=0 6)Solve: x^2= 49/36 7) Find the perfect square trinomial whose first two terms are q^2+7q. 8) solve using the quadratic formula: 2
1) Simplify. (2/a)+b / (a/b)+(3/a) 2)solve the equation. 1/(x-1) - 3/x = x/(x-1) 3) solve the equation for y. (y-3)/(x+2) = 2 4) Find the route 5 √z^20 5) Simplify: √(18/49) 6) Write the expression using expnent notation: √5z 7) Write the expression usin
1) Factor out the greatest common factor. 3x^4 - 6x^3 - 15x^2 2)Factor completely. 12p^2 + 20p 3)Factor. z^2 - 12wz + 13w^2 4) Factor completely. 12y^2 + 2y - 2 5) Factor: 64y^3 - 125z^3 6) Solve the given equation. x^2 + x - 6 = 0 7) Reduce the given expression to lowest terms.
Problem #1 Surface area of a cube. The formula A=6V^2/3 gives the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet? Problem #2 Sailboat Speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a
Problem #2: sqrt(3) / sqrt((6) - 1) + sqrt(3) / sqrt((6) - 1) Problem #3: 3 + sqrtx^2-8x) = 0 Problem #4: X^-2=4
Problem #1 sqrt(2t^5) * sqrt(10t^4) Problem #2 (3-2*sqrt7)(3+ 2*sqrt7) Problem #3 Area of a triangle. Find the exact area of a triangle with a base of sqrt(30) meters and a height of sqrt(6) meters. Note: sqrt is the square root
Please solve the 10 question and check the 5 problems that are asked. I am struggling with algebra and need all the help I can get, I'm not certain of the answers that I have so your help would be greatly appreciated.
Details: From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material.
Please see the attached file for the fully formatted problems. 1. Simplify. 2. Simplify. Write your answer with only positive exponents. A) B) C) r10 D) r2 3. A triangle has sides 2x - 5, 3x + 1, and 4x + 2. Find the polynomial that represents its perimeter. A) (2x - 5)(3x + 1)(4x + 2)
1. Solve. 3(x - 2) - 2x = x - 6 A) Identity B) 0 C) No solution D) 1 2. Find the GCF for 21, 28, and 35. 3. Find the LCM for 6, 28, and 48. 4. Solve the following system of linear inequalities by graphing. x + 2y <= 3 2x - 3y <= 6 5. Evaluate. 6. Evaluate. (15 - 5) ÷ [(12 ÷ 2 ? 2)
1. The area of a square is 82 ft2. Find the length of the side to the nearest hundredth. 2. How long must a guywire be to run from the top of a 18 ft pole to a point on the ground 12 feet away? 3. A picture is 2.5 m long by 2.0 m wide. It is held by a frame of uniform width around its outside edge. If the picture it
Prove the following problems. 1-If b>0 and a = bq + r , prove that (a , b) = (b , r). 2- Prove that (ab,c) = 1 if and only if (a,c) = 1 and (b,c)=1.
Problems #'s 12, 16, 18, 20, 26, 28, 30, 32, 46 these I need help completing Find the slope and y-intercept of the line represented by each of the following equations. 12. 2x - y = 6 Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept. 16. Slope: -2
1. Express the following product powers of t as a single power of t 2. Write without parenthesis 3. 4. Simplify without negative exponents 5. Simplify without negative exponents 6. Multiply and simplify (4z - 2u - 2)(6z - 5u + 6) 7. Write in simplest form without parentheses
I need help proving the following 3 problems : Problem 1: Prove by induction that if a prime number p divides the product a1a2....an then p must divide at least one of the factors, aj for some j=1...n Problem 2: Prove by induction that if gcd(a,b)=1 then gcd(a,b^n)=1 for any positive integer n Problem 3: Use problem 2 t
Please show work so that I can get a better understanding. Thank you. (For question 1 - find the value of y in each the formula if x = -3) 1.) y + 1 = 2(x - 5) (For question 2 - Fill the tables using the given formulas) 2.) y = 10x + 100 x y -20 -10 0 10 (For question 3 - Translate ea
What is the situation when two inequalities have no solution? What is the meaning of the VERTEX of the quadratic equation? Why does the graph of a quadratic intercept the y-axis at only ONE point?
Word Problem Diagonal Brace: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures √6m. Find the width and height. ************** Graph each parabola. y = -1/3*(x^2) + 5 ************** Find the vertex and intercept for each parabola. g(x) = x^2 +x-6 **
Solve each equation: 1) 2y^2 - 3y -6 = 0 2) (x-10)(x-2) = -20 Find all real or imaginary solutions for each equation: 1) W^2=-225 2) 3v^2+4v-1=0 3) sqrt (7x+29) = x+3 Word Problem Time to Swing. The period T (time in seconds for one complete cycle) of simple pendulum is related to the length L (in feet) o
(x+3)/ x ≤ -2
A ___ > 0 a+2
B^4 + 13 b^2 + 36=0
Y= - 1/2 x^2 + 3
How do you solve for x? (x - 10)(x - 2) = -20
Please see the attached file for the fully formatted problems. For the equation: x = e^-pt (C_1e^qt + C_2e^-qt), where C1 and C2 are arbitrary constants, if I let F = C1 + C2 and G = C1 - C2, how do I obtain: x = e^-pt[F/2 (e^qt + e^-qt) + G/2(e^qt - e^-wt)]
Please see the attached file for the fully formatted problems. The Chain Rule states how to differentiate composite functions If and be differentiable, then the derivative of the composite function is In Leibnitz notation, if and , then . For example, or The derivative of the exponential function is
Text Book: - Contemporary Abstract Algebra, Author:- Gallien In page 424 : - Theorem 25.1( Please mention each and every step). In page 424:- Theorem 25.2 (Please mention each and every step). Page 425 : - Theorem 25.3 (Please mention each and every step). Page 426 :- Corollary 1 and Corollary 2 (Please mention each