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Climate Change During the past 50 years, the average rate of change in temperature in Antarctica ha…
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For the following exercises, determine whether the relation represents y as a function of x. x^2+…
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Write each trinomial in descending powers of one variable and factor. See Example 8 . 10 y+9+y^2
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A bag contains one tile for each letter of the word PANDA. If you selected a permutation of these l…
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Automobile trade-in value If a certain make of automobile is purchased for C dollars, its trade-in …
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The following data represent nonstop flight time (in minutes) and one-way ticket price (in dollars)…
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In Exercises 53-64, simplify each expression. Assume that each variable expression is defined for a…
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When x^2-x-8 is divided by a polynomial, the quotient is x+3 and the remainder is 4. Find the pol…
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Determine the domain and the range of each function.
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Find a quadratic model for each function. f(-4)=11, f(-5)=5, f(-6)=3
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Add the polynomials and simplify. (See Examples 1-2 . ) (3 x^4-x^3-x^2)+(3 x^…
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Find the derivative of y with respect to the given independent variable. y=log_3((…
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Finding an Indefinite Integral In Exercises 1-20 , find the indefinite integral. ∫1/4+(x…
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Solve each system of equations by using elimination. 1.25 x-y=-7 4 y=5 x+28
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Make up an arithmetic sequence. Give it to a friend and ask for its 20 th term.
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In Exercises 15-48, solve the system of linear equations and check any solution algebraically. …
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Let f(x)=2 x-3 and g(x)=-x+3 . Find each function value. (f ∘g)(4)
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A professor adds Na_2 SO_4 to water to facilitate its electrolysis in a lectu…
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Graph each exponential function. See Examples 1 through 3 . y=(1/2)^x-2
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A function value Show that the function F(x)=(x-a)^2 . (x-b)^2+x takes on the value (a+b) / 2 f…
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Determine graphically the solution set for each system of inequalities and indicate whether the sol…
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In Exercises 1–4, write the polynomial in standard form, and identify the zeros of the function and…
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Simplify each radical. See Example 6. All variables represent positive real numbers. √(%s/%s…)
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Solve using the Quadratic Formula. x^2+10 x+11=0
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(a) state the domain of the function, (b) identify all intercepts, (c) find any vertical and horizo…
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Graph equation by hand. 4 x=3 y
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Think About It In Exercises 69-78 , restrict the domain of the function f so that the function is o…
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Find the following matrices [ a. A+B b. A-B ] c,-4 A …
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Geometry The length of the base of a triangle is three times the height. The area of the triangle i…
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Solve Problems exactly. x^logx=100 x
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Find all the zeros, real and nonreal, of the polynomial. Then express p(x) as a product of linear f…
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Solve equation, and check your solution. -5/6 t=-15
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In Exercises 65–68, the graph with the given equation is shown in a[0,2 π, π/2…
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Express the polynomial f(x) in the form a_n x^n+a_n-1 x^n-1+⋯+a_1 x+a_0. Find a fo…
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A car is being driven at a rate of 40 mph when the brakes are applied. The car decelerates…
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In Exercises 67 - 84, condense the expression to the logarithm of a single quantity lnx - [
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how many different 7 digit sequences can be formed using the digits 0,1,...9 if repetition of digit…
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Whales and Pressure at Sea Depth. Whales can withstand extreme changes in atmospheric pressure beca…
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Solve each equation. Identify any extraneous roots. 6/n+3+20/n^2+n-6=5/n-2
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Solve each quadratic equation by completing the square. x^2/3+x/9-1/6=0
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Without graphing, determine whether each system has one solution, no solution, or an infinite numbe…
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Equation has a solution rin the interval indicated. Use the method of Example IO to approximate thi…
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Complete the statement with always, sometimes, or never. If k is greater than 0 and x is greater th…
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Verify each identity. (x-tanx)^2=1-sinx/1+sinx
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Expanding an Expression In Exercises 19-40, use the Binomial Theorem to expand and simplify the exp…
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Fill in the blanks. In a 30^∘-60^∘-90^∘ triangle, the shorter leg is opposite the…
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Write the radical expression in simplest form. √(21/35)
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In the following exercises, divide. 8 ÷2 2/3
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Area Find the area between the graph of y=sinx and the line segment joining the points (0,0) and …
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Explain why (a+b)^2 ≠a^2+b^2.
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Let f(x)=x^3+2 x+1, and assume that f^-1 exists and has domain (-∞, ∞). Simplify each…
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Solve the inequalities.Suggestion: A calculator may be useful for approximating key numbers. %s/%s…
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Solve each equation. √(4 x)-x+3=0
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Find the sums. ∑_k=1^7(-1)^k
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In Exercises 17-32, add or subtract as indicated. Write the result in the form a+b i (10+7 i)-(5+4 …
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Solve and check each equation. 7/4 r=42
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In Exercises 67-78, factor completely. 2 y^2-40 y+200
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Four cards are drawn from a standard deck of cards. Each card is replaced before the next one is dr…
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In Exercises 19-22 , find the determinant of the matrix by the method of expansion by cofactors. Ex…
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A driver's age has something to do with his or her chance of getting into a fatal car crash. The ba…
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