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- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(LibreTexts)/06%3A_Factoring_and_Solving_by_Factoring/6.07%3A_Applications_Involving_Quadratic_EquationsRecall that a right triangle is a triangle where one of the angles measures 90°. The side opposite of the right angle is the longest side of the triangle and is called the hypotenuse. The Pythagor...Recall that a right triangle is a triangle where one of the angles measures 90°. The side opposite of the right angle is the longest side of the triangle and is called the hypotenuse. The Pythagorean theorem gives us a relationship between the legs and hypotenuse of any right triangle, where a and b are the lengths of the legs and c is the length of the hypotenuse:
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(LibreTexts)/06%3A_Factoring_and_Solving_by_Factoring/6.01%3A_Introduction_to_FactoringStep 3: The GCF of the monomials is the product of the common variable factors and the GCF of the coefficients. The GCF of two or more monomials is the product of the GCF of the coefficients and the c...Step 3: The GCF of the monomials is the product of the common variable factors and the GCF of the coefficients. The GCF of two or more monomials is the product of the GCF of the coefficients and the common variable factors with the smallest power. The surface area of a cylinder is given by the formula SA=2πr2+2πrh, where r represents the radius of the base and h is the height of the cylinder.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(LibreTexts)/06%3A_Factoring_and_Solving_by_Factoring/6.04%3A_Factoring_Special_Binomials\(\begin{aligned} (a+b)(a^{2}-ab+b^{2})&=a^{3}-a^{2}b+ab^{2}-ab^{2}+b^{3} \\ &=a^{3}+b^{3}\quad\color{Cerulean}{\checkmark} \\ (a-b)(a^{2}+ab+b^{2})&=a^{3}+a^{2}b+ab^{2}=a^{2}b-ab^{2}-b^{3} \\ &=a^{3}...(a+b)(a2−ab+b2)=a3−a2b+ab2−ab2+b3=a3+b3✓(a−b)(a2+ab+b2)=a3+a2b+ab2=a2b−ab2−b3=a3−b3✓
- https://math.libretexts.org/Courses/Minnesota_State_Community_and_Technical_College/MATH_95%3A_Elementary_Algebra_II_(Halling)/01%3A_Solving_Linear_Systems/1.06%3A_Applications_of_Linear_SystemsThe amount of salt is obtained by multiplying the percentage times the amount, where the variables x and y represent the amounts of the solutions. The speed of the airplane is 445 miles pe...The amount of salt is obtained by multiplying the percentage times the amount, where the variables x and y represent the amounts of the solutions. The speed of the airplane is 445 miles per hour and the speed of the wind is 10 miles per hour. The average speed for the first leg of the trip was 70 miles per hour and the average speed for the second leg of the trip was 60 miles per hour.
- https://math.libretexts.org/Courses/Minnesota_State_Community_and_Technical_College/MATH_95%3A_Elementary_Algebra_II_(Halling)/01%3A_Solving_Linear_Systems/1.04%3A_Solving_Linear_Systems_by_SubstitutionWhen the value of one of the variables is determined, go back and substitute it into one of the original equations, or their equivalent equations, to determine the corresponding value of the other var...When the value of one of the variables is determined, go back and substitute it into one of the original equations, or their equivalent equations, to determine the corresponding value of the other variable. If the process of solving a system of equations leads to a true statement, then the system is dependent and there are infinitely many solutions that can be expressed using the form (x,mx+b).
- https://math.libretexts.org/Courses/Minnesota_State_Community_and_Technical_College/MATH_95%3A_Elementary_Algebra_II_(Halling)/02%3A_Polynomials_and_Their_Operations/2.06%3A_Dividing_PolynomialsCheck your division by multiplying the answer, the quotient, by the monomial in the denominator, the divisor, to see if you obtain the original numerator, the dividend. Step 1: To determine the first ...Check your division by multiplying the answer, the quotient, by the monomial in the denominator, the divisor, to see if you obtain the original numerator, the dividend. Step 1: To determine the first term of the quotient, divide the leading term of the dividend by the leading term of the divisor. Just as with real numbers, the final answer adds the fraction where the remainder is the numerator and the divisor is the denominator to the quotient.
- https://math.libretexts.org/Courses/Minnesota_State_Community_and_Technical_College/MATH_95%3A_Elementary_Algebra_II_(Halling)/01%3A_Solving_Linear_Systems/1.01%3A_Review-__Solving_Linear_Equations/1.1.03%3A_Solving_Linear_Equations-_Part_IILinear equations typically are not given in standard form, so solving them requires additional steps. These additional steps include simplifying expressions on each side of the equal sign using the or...Linear equations typically are not given in standard form, so solving them requires additional steps. These additional steps include simplifying expressions on each side of the equal sign using the order of operations.
- https://math.libretexts.org/Courses/Minnesota_State_Community_and_Technical_College/MATH_95%3A_Elementary_Algebra_II_(Halling)/03%3A_Factoring_and_Solving_by_Factoring/3.02%3A_Factoring_Trinomials_of_the_Form_xbxcThe middle term of the trinomial, 7x, is the sum of the products of the outer and inner terms of the binomials: In short, if the leading coefficient of a factorable trinomial is one, then the fact...The middle term of the trinomial, 7x, is the sum of the products of the outer and inner terms of the binomials: In short, if the leading coefficient of a factorable trinomial is one, then the factors of the last term must add up to the coefficient of the middle term. If a trinomial of the form x2+bx+c factors into the product of two binomials, then the coefficient of the middle term is the sum of factors of the last term.
- https://math.libretexts.org/Courses/Minnesota_State_Community_and_Technical_College/MATH_95%3A_Elementary_Algebra_II_(Halling)/03%3A_Factoring_and_Solving_by_Factoring/3.E%3A_Review_Exercises_and_Sample_ExamA 20-foot ladder leaning against a wall reaches a height that is 4 feet more than the distance from the wall to the base of the ladder. The height of an object dropped from the top of a \(196\...A 20-foot ladder leaning against a wall reaches a height that is 4 feet more than the distance from the wall to the base of the ladder. The height of an object dropped from the top of a 196-foot building is given by h(t)=−16t2+196, where t represents the number of seconds after the object has been released. If the area of the triangle is 80 square centimeters, then find the measure of the base.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(LibreTexts)/zz%3A_Back_Matter/20%3A_GlossaryGiven any real numbers a, b, and c, a ( b + c ) = a b + a c or ( b + c ) a = b a + c a . The trinomials obtained by squaring the binomials ( a + b ) 2 = a 2 + 2 a b + b 2 and ( a − b ) 2 = a 2 − 2 a b...Given any real numbers a, b, and c, a ( b + c ) = a b + a c or ( b + c ) a = b a + c a . The trinomials obtained by squaring the binomials ( a + b ) 2 = a 2 + 2 a b + b 2 and ( a − b ) 2 = a 2 − 2 a b + b 2 . The formula x = − b ± b 2 − 4 a c 2 a , which gives the solutions to any quadratic equation in the form a x 2 + b x + c = 0 , where a, b, and c are real numbers and a ≠ 0 .
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(LibreTexts)/06%3A_Factoring_and_Solving_by_Factoring/6.0E%3A_6.E%3A_Review_Exercises_and_Sample_ExamA 20-foot ladder leaning against a wall reaches a height that is 4 feet more than the distance from the wall to the base of the ladder. The height of an object dropped from the top of a \(196\...A 20-foot ladder leaning against a wall reaches a height that is 4 feet more than the distance from the wall to the base of the ladder. The height of an object dropped from the top of a 196-foot building is given by h(t)=−16t2+196, where t represents the number of seconds after the object has been released. If the area of the triangle is 80 square centimeters, then find the measure of the base.
