Solve the equation tricky test 2
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The second car will catch the first car when both have traveled the same distance. Let t represent the number of hours the second car travels.Ĥ0(t + 3) = distance that first car travels Use the rate formula,, to find the answer. Therefore, the vertical asymptotes are the lines x = 3 and x = 5.Ĩ. For the given function, set up and solve an equation to determine when x2 – 8x + 15 is zero. For a rational function like the given one, the vertical asymptotes are vertical lines that occur at every x-value for which the denominator is zero. An asymptote is a line that the graph of a function approaches but never touches. Adding 36 to both sides of the original equation will complete the square: notice that x2 – 12x + 36 is indeed a perfect square trinomial because it can be factored as (x – 6)2.ħ. To calculate that constant, divide the coefficient of the x-term (which is –12) by 2 (giving –6) and square the result ( (-6)2 = 36). In the given equation, the left side only has two terms, an x2-term and an x-term a constant term needed to make the expression a perfect square trinomial. Recall that a perfect square trinomial is a trinomial that can be factored as (ax + b)2or (ax – b)2. To solve an equation by completing the square, manipulate it algebraically so that one side (in this case, the left side) is a perfect square trinomial and the other side (the right side) is a constant. For this equation, a = 5, b = 6, and c =–3.Ħ. Since the left side cannot be factored, use the quadratic formula to solve the equation, which is written in the form ax2 + bx + c = 0. To begin, rewrite the equation in the form ax2 + bx + c = 0 by subtracting 3 from both sides of the equation.
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Therefore, factor out 2x.įinally, factor the trinomial, 3×2 – 2x – 8, into two binomials.ĥ. Notice that the greatest common factor (GCF) of the coefficients is 2, and each term is divisible by x. First, factor out any common factors from each of the three terms, 6×3, -4×2, and -16x. Therefore, the solutions are x = –5 and x = 2.Ĥ. To do this, substitute them into the given equations and make sure that the result is a true statement. Consequently, the two possible solutions must be verified. Unfortunately, there is a risk of finding an incorrect solution when solving rational equations in this manner. Therefore, the possible solutions are x = –5 and x = 2. Solve it by factoring the left side and setting each factor equal to zero. First, eliminate the denominators by multiplying both sides by x(x + 4). Therefore, it will take John and Julie hours, or 1 hour 12 minutes, to mow the lawn if they work together.ģ. Substitute this value into the original rate formula and solve for t, the variable that represents time spent mowing. In other words, their total rate working together is lawns per hour. Next, if John and Julie work together, their total rate can be found by adding the individual rates together. To make the calculation easier, rewrite the formula as. Using, rate x time = amount, determine the rate at which John and Julie each mows the lawn if they work separately. Check this solution by substituting the values into the second equation and making sure the resulting equality is true.Ģ. Therefore, the solution of the given system of equations is x = 2,y = –2. To find the value of y, substitute 2 for x in the first equation. To begin, substitute the left side of the first equation, –3x+4, for y into the second equation, and then solve for x. Since the first equation already has y isolated on the left side, it will be easier to use the substitution method than the elimination method to solve the system of equations. Therefore, the solution of the system of equations will have values for each variable. Notice that the given system has two equations, and each equation has two variables, x and y. What is the domain of the function f(x) = 2x – 4?ġ. How long after the second car leaves will it take for the second car to catch the first?ĩ. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. Two cars are traveling north along a highway. Find the vertical asymptotes of the function.Ĩ.
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What should be added to both sides of the equation x2 – 12x = 5 in order to solve it by completing the square?ħ. How long will it take them to mow their lawn if they work together?Ħ. John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours.