Answers edited by Shwetank Mauria

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• How do you rationalize the denominator and simplify #3/(6-sqrt5)#?
  
• Alyssa and Benny were able to dig a garden in 2 hours together. It takes Benny 5 hours to finish this job alone. Without help, how long would it take Alyssa to finish this job?
  
• How do you write the equation in point slope form given (–2, 15), (9, –18)?
  
• How do you express the Cartesian coordinates (0, - 3) as polar coordinates?
  
• If #vec A + vec B= vec C#, what is the magnitude of #vecC#, if #vecA# and #vecB# are unit vectors at right angle to each other?
  
• If #sinx=4/5# what is the value of #cosx#?
  
• What does it mean when something is 4 or 5 light years away from us?
  
• How do you factor #64x^3+8=0#?
  
• Simplify #-(x^2-6x+5)/(x^2-10x+25)#?
  
• How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?
  
• How do you solve #7^x = 30#?
  
• How do you factor the trinomial #3x^2-15x+16#?
  
• How do you simplify #6lne#?
  
• How do you graph #x^2+y^2+2x+2y=23#?
  
• What is the the vertex of #y=4x^2 + 9x + 15#?
  
• A person uses 870 kcal on a long walk. What is the energy used for the walk in joules?
  
• What is the angle between #<-3,2,0> # and #< 5,0,2 >#?
  
• How do you express #cos( (5 pi)/6 ) * cos (( 11 pi) /6 ) # without using products of trigonometric functions?
  
• How do you find the vertical, horizontal or slant asymptotes for #(x^2 + 3) / (x^2 - 4)#?
  
• How do you find the intercepts and graph the equation by plotting points y= -2?
  
• What is 3/4 as a decimal?
  
• What is the divisibility rule for 11, 12, and 13?
  
• What is #-.75 * 5.5#?
  
• How do you rationalize the denominator and simplify #6/(sqrt4+sqrt5)#?
  
• How do you subtract and simplify #2##11/12# #- 3/16#?
  
• How do you solve #cos2x = sinx + cosx# on the interval [0,2pi]?
  
• How do you solve #4x^2 - x = 0# by completing the square?
  
• If #a#, #b#, #c# are in A.P.; #ap#, #bq#, #cr# are in G.P and #p#, #q#, #r# are in H.P., then prove that #(p/r)+(r/p)=(a/c)+(c/a)#?
  
• Prove that #tanx/(1+secx)+(1+secx)/tanx=2secx#?
  
• What are the components of the vector between the origin and the polar coordinate #(9, (-11pi)/6)#?
  
• What is the z-score of X, if n = 72, #mu= 137#, SD =25, and X =13?
  
• How do you find the zeros, real and imaginary, of #y=- x^2-22x+6 # using the quadratic formula?
  
• Can every quadratic equation be solved by factorization or by splitting the middle term? When does one use quadratic formula?
  
• How do you use the rational roots theorem to find all possible zeros of #f(x)=3x^5-2x^4-15x^3+10x^2+12x-8 #?
  
• How do you find all values of x in the interval [0, 2pi] in the equation #2 + cos2x = 3cosx#?
  
• When both the current and voltage in a circuit are doubled, what happens to resistance and power?
  
• What is #(5b-(-6))^2# when #b=0#?
  
• How can a number line help you measure objects?
  
• How do you divide #{(17mn^3)/(m^2+2m-35)}/{(34m^8n^4)/(m^2+7m)}#?
  
• How do you factor #y=x^3-4x^2-17x+60# ?
  
• How do you simplify #(5+ sqrt 5)/(8- sqrt 5)#?
  
• How do you find the asymptotes for #(x^3 + 1) / (x^2 - 2x + 2)#?
  
• The base of a triangular pyramid is a triangle with corners at #(2 ,2 )#, #(3 ,1 )#, and #(7 ,5 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?
  
• How do you plot rational numbers on a number line?
  
• How do you find the determinant of #((1, 7, -4, -5), (1, 5, 7, -4), (3, 21, -12, -15), (5, 25, -8, 0))#?
  
• How do you multiply # (9-i)(7-3i) # in trigonometric form?
  
• How do you express .13 as a percentage?
  
• How do you simplify #(16a^4)^(3/2)#?
  
• How much work does it take to raise a #33 kg # weight #6 m #?
  
• How do you find the derivative of #F(x) = 1/(x-5)#?
  
• An object with a mass of #2 kg# is revolving around a point at a distance of #7 m#. If the object is making revolutions at a frequency of #12 Hz#, what is the centripetal force acting on the object?
  
• Cups A and B are cone shaped and have heights of #32 cm# and #12 cm# and openings with radii of #5 cm# and #8 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
  
• Simplify the following?
  
• How do you use the rational roots theorem to find all possible zeros of #f(x) = x^4 -24x^2- 25#?
  
• How do you convert # (-6,-3)# into polar coordinates?
  
• How do you solve #2x^2+3x-3=0# using the quadratic formula?
  
• How do you find the derivative of #g(x) = sqrt(x^2-1)#?
  
• How do you solve #2x - 5y = 12# and #x - 3y = -3# using matrices?
  
• What is #938.5-:0.35#?
  
• Two rhombuses have sides with lengths of #16 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?
  
• What are the extrema of # f(x)=(x^2 -9)^3 +10# on the interval [-1,3]?
  
• How do you factor the expression #x^2-4x-12#?
  
• How do you write the answer to #13/3 + 17/5# as a mixed number?
  
• How much power is required to lift an object of weight #595# newtons by #3.15# meters in #15.2# seconds?
  
• How do you find the explicit formula for the following sequence 1, 1/2, 1/4, 1/8,...?
  
• A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #12 # and the height of the cylinder is #28 #. If the volume of the solid is #72 pi#, what is the area of the base of the cylinder?
  
• How do you express #x+22 div x^2+2x-8# in partial fractions?
  
• How can GCF help when simplifying a fraction?
  
• What is the equation of the parabola with a focus at (1,3) and a directrix of y= 2?
  
• What is the distance between #(1,3,-6)# and #(-5,1,6)#?
  
• How do you find the derivative of #-2x(x^2+3)^-2#?
  
• How do you find all the real and complex roots of #12x²+8x-15=0#?
  
• How do you solve and graph #6[5y-(3y-1)]≥4(3y-7)#?
  
• How do you convert 1000 mg to ml?
  
• How do you solve #cos(theta)= -0.6# over the interval 0 to 2pi?
  
• If #cot x=(2n^2+2mn)/(m^2+2mn)# then find #cscx#?
  
• How do you rationalize the denominator and simplify #sqrt36/sqrt8#?
  
• How do you evaluate #Sin((5pi)/12) cos(pi/4) - cos((5pi)/12) sin(pi/4)#?
  
• How do you solve #22 -5(6v-1) = -63#?
  
• It takes 42 cherries to make an cherry pie. If a chef bought 444 cherries, the last pie would need how many more cherries?
  
• What is #4 1/8 - 1 1/2#?
  
• What is the GCF of 36 and 60?
  
• Brent divided #3 1/5# by a number and got #4 1/2#. What number did he divide by?
  
• A parallelogram has sides with lengths of #18 # and #4 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?
  
• How do you find the midpoint of (2,2) and (5,6)?
  
• What are the extrema of #f(x)=4x^2-24x+1#?
  
• How do you differentiate #(2^x)x^2#?
  
• How do you find the polar coordinate of (-1,1)?
  
• A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #pi/3 #, what is the area of the parallelogram?
  
• How do you find the derivative of #f(x)=(2x+6)/(3x^2+9)#?
  
• How do you solve #2cos^2x+sinx+1=0# over the interval 0 to 2pi?
  
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