Answers edited by Noah G

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• Question #cea51
  
• How do you simplify #(3x)/(x²-3x-18)- ( x-4)/(x-6)#?
  
• How do you evaluate #log_a x = 3/2log_a 9 + log_a 2#?
  
• The sum of half a number and its reciprocal is the same as 51 divided by the number. How do you find the number?
  
• What is the fourth term in the expansion of #(2x-y)^5#?
  
• How do you balance #P_4 + Br_2 -> PBr_3#?
  
• How do you prove #cos 2x = (1-tan^2x)/(1+tan^2x)#?
  
• What is the slope of the line passing through the following points: # (-3, -2) ; (0, -1) #?
  
• What is the equation of the line with slope # m= -2/7 # that passes through # (3/4,-1/7) #?
  
• How do you verify #sec^4x-sec^2x=tan^4x+tan^2x#?
  
• How do you factor completely #x^2 - 8x + 16#?
  
• How do you solve the following system: #-x+y=5, 6x+3y=-12#?
  
• How do you solve the inequality #(x-1)(x-4) <2(x-4)#?
  
• How do you write the equation of the parabola in vertex form given vertex (2,-1) and a point (0,3)?
  
• How do you graph using the intercepts for #4y-16=x#?
  
• How do you simplify #(a^2)/(a-3)= 9/ (a-3)#?
  
• #csc lambda = 17/8# in quadrant 2. What is #tan 2lambda#?
  
• How do you solve #sqrt( x-5) = x-7#?
  
• How do you solve #tantheta - 4 = 3tantheta + 4#?
  
• How do you write an equation of a line passing through (2,3) with x-intercept 4?
  
• What is the equation of the parabola that has a vertex at # (7, 9) # and passes through point # (3, -2) #?
  
• How do you expand #(1+x^3)^4# using Pascal’s Triangle?
  
• How do you expand #(x-3)^5# using Pascal’s Triangle?
  
• How do you solve #3/2 (x+8)=6x#?
  
• How do you find the explicit formula for the following sequence 41, 46, 51, 56, 61, . . . ?
  
• If #f(n) = 9^-n#, then what is #f(-1/4)#?
  
• How do you solve #log(x+1) - log(x-1)=1#?
  
• How do you solve #log (x+6)=1-log(x-5)#?
  
• How do you find [f o g](2) and [gof](2)] given #f(x)=2x-1#, #g(x)=-3x#?
  
• How do you solve #3x(x - 5) = 7x^2 - 16x#?
  
• The outer surfaces of a box are covered with gold foil, except the bottom. The box measure 6 in. long, 4 in. wide, and 3 in. high. How much gold foil was used?
  
• How do you solve #(8sqrt( 2x-1)) / 3 = x#?
  
• The perimeter of a rectangle is 18 feet, and the area of the rectangle is 20 square feet. What is the width?
  
• How do you evaluate #sin(-pi/6)#?
  
• How do solve the following linear system?: # -x+5y=-13 , -4x-2y=14 #?
  
• How do you find the sum of the first 30 positive multiples of 3?
  
• How do you solve the system 2x = y + 1 and 2x - y = 5?
  
• How do you find the solution to #((sin 120)(cos ((2pi)/3)) ) / tan 315#?
  
• How do solve the following linear system?: # 1/3x + 3y = 9 , 8x + 3y= -9 #?
  
• How many four–letter permutations can be formed from the letters of the word OHIO?
  
• How do you find the vertex and intercepts for #f(x)=9x^2+7x+5#?
  
• How do you factor the trinomial #x^2-11x+18#?
  
• How do you solve the equation #|x + 3| + 10 = 4 #?
  
• How do you solve #sqrt (x+9)=4#?
  
• Emma takes a job with a starting salary of $42,000. Her salary increases by 4% at the beginning of each year. What will be Emma's salary, to the nearest thousand dollars, at the beginning of year 10?
  
• How do you solve the following system?: # 2x + y = -5, 3x - 5y = 2 #
  
• How do you find the x intercept of #y = -|x+10|#?
  
• 40% of what number is 108?
  
• Find the area of the shaded region (green) knowing the side of square is #s = 25 cm#?
  
• How do you solve rational equations #(6x + 4 )/(x+4)=(2x+2)/(x-1)#?
  
• How do you solve #x^2 - 6x - 46 = -5# by completing the square?
  
• What is #7 + 9 * (3+8)#?
  
• Are adjacent angles in a parallelogram supplementary?
  
• What is the product of #(3 + sqrt5)# and #(3- sqrt5)#?
  
• The perimeter of a triangle is 18 feet. The second side is two feet longer than the first. The third side is two feet longer then the second. What are the lengths of the sides?
  
• How do you prove #cos 2x = (1-tan^2x)/(1+tan^2x)#?
  
• The area of the rectangular playground enclosure at South School is 500 square meters. The length of the playground is 5 meters longer than the width. How do you find the dimensions of the playground in meters?
  
• How do you simplify #1/sqrt7#?
  
• How do you solve #log_2 x - log_8 x = 4#?
  
• What is the equation of the parabola that has a vertex at # (-8, 5) # and passes through point # (-18,32) #?
  
• How do you simplify #( 7x^2 + 5x -7 ) + ( x^2 -3x + 5 )#?
  
• How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?
  
• How do you find the sum of the infinite geometric series 1-(1/3) + (1/9) - (1/27) + .....?
  
• Let #f(x) = 3x - 4# and #g(x) = x^2 - 2#, what is the value of #f(g(2))# and #f(g(x))#?
  
• How do you solve #|10x + 2| - 18 = -12#?
  
• One more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a pole barn. The area of the piece is #30# #ft^2#. The length is 1 less than 3 times the width. How wide should the metal piece be?
  
• What is the sum of the arithmetic sequence 3, 9, 15…, if there are 24 terms?
  
• The sum of 2 numbers is 14 and the sum of their squares is 148, how do you find the numbers?
  
• Maggie says, "The positive square root of a number is always less than the original number." Is this true?
  
• How do you simplify #sinx/(1 + sinx) - sinx/(1 -sinx)#?
  
• How do you find (f of g of h) given #f(x)=x^2+1# #g(x)=2x# and #h(x)=x-1#?
  
• How do you solve the inequality #9>= 4 - 2sqrt( 5x+7)# ?
  
• How do you express the following function, f(x) as a composition of two functions f and g given #f(x)=x^2/(x^2+4)#?
  
• A triangle has side lengths of 11 cm and 9 cm. Which could be the value of the third side, 20 cm or 15 cm?
  
• How do you solve #-4/x = 1/3x - 10 #?
  
• How do you find the inverse of #h(X)= 5 / (2x + 3)# and is it a function?
  
• How do you find the inverse of #y=-2(x+3)²+# and is it a function?
  
• How do you solve for y in #M= x(1 + y)#?
  
• Given #f(x)=1/(x-2)#, how do you find f(f^-1(x))?
  
• How do you find the inverse of #f(x)= 5x + 10#?
  
• How do you convert -30 degrees to radians?
  
• How do you solve #log_2(x-4)+log_2(x+4)=3#?
  
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