Algebra question and answers for December 18, 2023
- Q Find the solution set of the equation.log(5+x) -log(x - 3) = log 5a) b) {5}c) {-5}d) { 1/12 }
- Q Solve the equation. Approximate the solution(s) to the nearest hundredth.ex-ex- 12 = 0
- Q Apply the change of base formula to rewrite log 4 (x - 3) in terms of natural logarithms.
- Q Write the equation of the line with slope 1/9 and y-intercept 2.
- Q Find r for the infinite geometric sequence. Determine whether the sum will converge.1, 6, 36, 216, ...
- Q Rewrite sec40 in terms of the appropriate cofunction.
- Q Find the sum of the first 8 terms for the following arithmetic sequence.a4 = 12, a6 = 18
- Q Find the arc-length of a circle with the given radius r and central angle ?. Give the answer in the given unit of measure.r = 52 cm; ?= 12 rad
- Q Determine the amplitude, period, and phase shift of the following trigonometric equation.3y = 1/2 sin (?x/4+ 2/3)
- Q Find the coefficient a of the term in the expansion of the binomial.Binomial Terms(x-6y)10 ax8ya. 1,619b. 1,623c. 1,620d. 1,621e. 1,618
- Q Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 2?). Round your answer to four decimal places, if...
- Q Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood-chipped path running through their yard. What...
- Q Consider the following parametric equations:X = ?t-1 and y = t - 4 Determine the domain and range of the equation obtained by eliminating the parameter. Please write your answer...
- Q If a and n are integers, n > 0, then there exist integers q and r such that a = qn+r, where |r|<n/2.
- Q A Freshman is planning for a trip to Europe when she graduates in 4 years. She estimates she will need $2000 to pay for the trip. If she has a...
- Q The weights for 10 adults are 72, 78, 76, 86, 77, 77, 80, 77, 82, 80 kilograms.Determine the standard deviation.A. 4.28B. 3.88C. 3.78D. 3.96
- Q T-Mobile Park is home to the Seattle Mariners baseball team.For each game, the amount of money the team brings in as revenue is a function of the number of people...
- Q Which of the following are true about a one-to-one function? Select all that apply.Its graph will pass both the vertical line test and the horizontal line testIt will always have...
- Q If f (a) = b, then which of these points is on the graph of f(x)?(a, b)(a, f(b))(b, a)(f (a), f(b))
- Q Suppose the function f(t) = 55000e0.061t gives the number of subscribers to a particular YouTube channel t years since 2015.Which of the following is true?The number of subscribers decreases as...
- Q Solve for the remaining angles and side of the triangle described below. Round to the nearest thousandth:B = 70, c = 6, a = 3
- Q Which of the following situations would be best modeled by an exponential function? Select ALL that apply.The future value of an investment earning a constant interest rate.The decay of a...
- Q Providence Park is home to the Portland Timbers soccer team. or each game, the amount of money the team brings in as revenue is a function of the number of...
- Q If caffeine leaves the body at a continuous rate of about 16% per hour. How much caffeine is left in the body 8 hours after drinking a cup of coffee...
- Q Use the sum-to-product identities to rewrite the following expression as a product.cos (45) - cos (70)Answer 4 Pointscos (45) - cos (70) =
- Q Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x
- Q Given a circle of radius 12 in., find the length of the arc subtended by a central angle of 270. Round decimals to the nearest hundredth.
- Q Rewrite the following polar equation in rectangular form.r = -9sin0
- Q Let g(x) = 7(x + 2)(x - 3)(x + 1). Which of the following has the same end behavior as g(x)?f(x) = -5(2-1) (+5)f(x)=3(x - 3)(x+3)f(x) =f(x)=1f(x) = 2x(x -...
- Q What is the average rate of change of f(x) = 2x 3x + 7 from x = 0 to x = 4?-
- Q The following is the graph y = f(x). Graph the transformation image of the graphthat is represented by the equation y + 2 = -2f(2(x + 3)). State the domainand...
- Q Given f(x) = e which of the following is the equation of the graph of f shifted left 3 and then reflectedvertically?g(x) = 3e-2g(x) = e* - 3g(x) = -...
- Q Simplify the following, using only positive exponents. Do not evaluate.
- Q Use the formula for S? to find the sum of the first five terms of the geometric sequence15, -5, 5/3, -5/9, ...
- Q Show that if f is a bounded function on [a, b] then for any two measurable partitions of [a, b] we have U(P?,f) ? L(P?, f) and Lof(x) dxzLf(x)dx [7]
- Q Points A and B are separated by a lake. To find the distance between them, a surveyor locates apoint Con land such than ZCAB 43.3". Find the distance across the...
- Q The length of a parking lot is 5 yards more than the width. If the area of the parking lot is 50 square yards, find the dimensions of the parking...
- Q Write the following expression as a single trigonometric ratio: sin4x/cos2x
- Q Using L'Hospital's rule evaluate:(a) lim2-1sin(?z)In z(b) limZ-00e1/2 - 11/z
- Q 12. If cos(?)+sin(?)=(1+?3)/2 and cos(?)-sin(?)=(1-?3)/2 find the value of sin(2?).
- Q A professor gives two types of quizzes: objective and recall. He plans to give at least 18 quizzes this quarter.The student preparation time for an objective quiz is 12 minutes...
- Q Determine the sum of the geometric series 15-45+ 135 - 405 +... - 32 805
- Q The ramp of a moving truck touches the ground 17 feet away from the end of the truck. If the ramp makes an angle of 14 relative to the ground,...
- Q According to the Rule of 72, how long would it take to double an $11,000 investment at a 1.5% compound interest rate? A. 11 years B. 18 years C. 27.3...
- Q Determine in which of the four quadrants angle ? is located givencos(?)>0 and cot(?) < 0
- Q Given the graph of f(x) =3x+8/6x-5 shown here, determine the values of x that solve 3x+8/6x-5?0
- Q Find the 15th term of an arithmetic sequence if the first term is 27 and the common difference is. Round your answer to 2 decimal places as needed.
- Q Suppose Roberto, Travis and Deandre go to a donut shop.Roberto buys 6 amaretto pumpkin, 6 black forest and 8 cotton candy donuts and ends up spending$48.70.Travis gets 5 of the...
- Q A vine maple grows fast when it is planted under the cover of cedar trees. One month after it is planted it hasgrown 9.67 inches, and after seven weeks it...
- Q Graph the function using the slope and intercept.f(x) = 1/3 x + 2The slope isThe y-intercept is
- Q Solve the system. Give your answer as (x, y, z)6c+y+4z = -552x+6y + 6z = - 546c 5y + 2z = -29(x, y, z) =
- Q Is (2, 4) a solution of the inequality y < - 2x + 4Yes, (2, -4) is a solution to y < - 2x +4No, (2, -4) is NOT a...
- Q Given f(x) = |-4 -3x|, find the following:f(-1) =f(-8)=f(- 6) =f(15) =
- Q Find the domain and range of the relation: {(-5,5), (5, 4), (-5,3), (-5, 2)}. Then determinewhether the relation is a function.Domain = {Range = {} Separate your answers by commas.}...
- Q Find the intercepts of -3x + 4y = - 12.x-intercept =y-intercept =Using the intercepts from above draw the graph of -3x + 4y = - 12
- Q Solve the inequality: -17? x + 29Enter your answer as an interval, such as [a, ?).
- Q Write the following in interval notation: x ? 20 and x ? 11If no solutions exists enter No solutions.Use reduce fraction in your answer - no decimals!
- Q Solve. Write your answer in interval notation.2x+2 12 or 3x +3> 54If no solutions exists enter No solutions.Use reduce fraction in your answer no decimals!
- Q Solve the inequality: 12 ? x + 7Enter your answer as an interval, such as [a, co).
- Q Solve for x: -2 ?-5x + 15 < 8Write your answer in interval notation:
- Q Write and inequality describing all the real numbers on the number line that are greater than or equal to 4.Inequality:Now draw the corresponding graph.
- Q Use interval notation to indicate all the real numbers on the number line that are less than -27.
- Q Which property is does 2(6 + 3) = 12 + 6 represent?commutativeassociativedistributiveidentityinverse
- Q Regular octagon ABCDEFGH is inscribed in a circle with radius r 7?/2 cm.Find the area (in square centimeters) of the circle. (Note: For the circle, use A-ar with =-3)x cm?Find...
- Q Solve.3x + 3y + z = 5x-3y + 2z=18x-2y+3z=4The solution set is {}(Type an ordered triple.)
- Q Write the equation of the line with slope m = 7 and passing through the point (1,5). Write the finalequation in slope-intercept form..
- Q Find dy/da in terms of t ifx = tet,y = 4t + 4et
- Q Use the slope-intercept form of a line (y = mx + b) to graph the equation y = -3x/4 - 1The slope isThe y-intercept is
- Q Values of c will the function y=x^2+6x+c havetwo x interceptsone x interceptno x intercept
- Q Use the wrapping function to evaluate sins and coss for the real number s.S= -17x/3Use the wrapping function to find the terminal point W(s) = (x,y) of the string of...
- Q Find the domain of the function f(x) = x + 17In interval form, the domain of f is
- Q A force of 3 pounds acts in the direction of 53 to the horizontal. The force moves an object along a straight line from the point (1,7) to the point...
- Q Would the graph for f(x) = - 9x + x + 5 open up or down, and why?, find g().Down, because a (the coefficient of 2) is negative.Up, because b...
- Q Suppose you want to have $300,000 for retirement in 25 years. Your account earns 10% interest. Round your answers to the nearest cent. a) How much would you need to...
- Q Given a right triangle with one angle measuring 0-40 and the hypotenuse of length 14, find the length x of the side opposite the angle. Round your answer to the...
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