Answers created by Binayaka C.

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• What is the slope of the tangent line of #r=theta-sin((theta)/6+(2pi)/3)# at #theta=(pi)/6#?
  
• How do you graph the parabola #y=x^2-3x# using vertex, intercepts and additional points?
  
• Triangle A has sides of lengths #18 ,3 3 #, and #21 #. Triangle B is similar to triangle A and has a side of length #14 #. What are the possible lengths of the other two sides of triangle B?
  
• How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=(x^3)-12x+2#?
  
• How can I solve this equation system? #x + 5y + 2z = 19" "3x + 2y+ z = 13" "2x - y - z = 0# How should I think about this?
  
• How do you find the asymptotes for #g(x)= (x^3 -16x )/ (4x^2 - 4x)#?
  
• How do you graph by using the zeros for #g(x)=1/10(x+1)^2(x-3)^3#?
  
• A strong man takes 2 minutes to make one cut through a log. How long will he need to cut a ten-foot log into 4 equal pieces?
  
• How do you find the intercepts, vertex and graph #f(x)=x^2-2/3x-8/9#?
  
• How do you divide # (7-i) / (3-i) # in trigonometric form?
  
• What are the coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) ?
  
• A merchant has 20 pounds of an $8 per pound tea. how many pounds of a $4 per pound tea should he add to the 8$ per pound tea to get a mixture worth $5 per pound?
  
• For what values of x is #f(x)=(2x-2)(x-3)(x+3)# concave or convex?
  
• What are the asymptote(s) and hole(s), if any, of #f(x)= (x(x-3))/(x^2-9x+3)#?
  
• At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $2.35. One day, the receipts for a total of 172 cones and sundaes were $294.20. How many cones were sold?
  
• How do you identify the conic of ##r = 3/(1 - sinx)?
  
• If P dollars is invested at r percent compounded annually, at the end of 2 yers it will grow to A = P(1+r)^2. At what interest rate will $1,000 grow to $1,210 in 2 years?
  
• For a 25 ft. ladder to reach a certain window, it must make an angle of 63 deg. with the ground. How do you find the angle that a 30 ft. ladder must make with the ground to reach the some window?
  
• What are the first and second derivatives of #f(x)=e^(2x)(lnx) #?
  
• How do you find the vertical, horizontal or slant asymptotes for #f(x)= 1/x^2#?
  
• How do you graph the parabola #y= (x+4)^2+4# using vertex, intercepts and additional points?
  
• Cups A and B are cone shaped and have heights of #27 cm# and #24 cm# and openings with radii of #7 cm# and #14 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?
  
• How do you find the domain of #f(x)=abs(x+4)#?
  
• What is the equation of the tangent line to the polar curve # f(theta)=2thetasin(theta)+thetacot^2(4theta) # at #theta = pi/3#?
  
• How do you graph #f(x) = x + (5x)/(x-1)# and identify all the asymptotes?
  
• If #A = <5 ,2 ,-5 >#, #B = <6 ,5 ,3 ># and #C=A-B#, what is the angle between A and C?
  
• How do you find the domain and range of #f(x)= ln(3x-2)#?
  
• How do you graph #y=(5x+3)/(-x+10)# using asymptotes, intercepts, end behavior?
  
• What are the important points needed to graph #y=3x^2+6x-1 #?
  
• Mr Tan bought a laptop at a discount. If he sold the laptop at its usual price, he would gain a $550 profit. If he sold it at 80% of its usual price, he would lose $350 (receive $350 less than the amount he paid). How much did Mr Tan pay for the laptop?
  
• How do you find the compositions given #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2#?
  
• What is the second derivative of #f(t) = (3e^-2t) - (5e^-t) #?
  
• How do you find the 10th partial sum of the arithmetic sequence #40, 37, 34, 31,...#?
  
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(5pi)/12 #, and the triangle's area is #24 #. What is the area of the triangle's incircle?
  
• If the cost of a telephone conversation varies directly as the length of the time of conversation, and if the cost of six minutes is $0.90, what would be the cost for a nine-minute call?
  
• How do you solve #y^3-2y^2-9y+18>=0# using a sign chart?
  
• James and billy have ages that are two consecutive odd integers whose products is 399. Use a quadratic equation to find out the age of each boy if james is the younger of the two boys?
  
• How do you find the five remaining trigonometric function satisfying #costheta=-2/5#, #sintheta>0#?
  
• How do you graph the function, label the vertex, axis of symmetry, and x-intercepts. #y=x^2-2x+1#?
  
• How do you find the vertex, focus and directrix of #x+y^2=0#?
  
• What is the slope, y-intercept and equation for the line that passes through these points: (-1, -8), (-6, -33), (-10, -53) and (-13, -68)?
  
• How do you solve #(x-2)(x+10) = 13#?
  
• A sporting goods store sells 90 jackets for $200 dollars each. Each $10 decrease in price would result in 5 more jackets sold. How do you find the number of jackets sold and the selling price to give revenues of $17600 from jacket sales?
  
• How do you find the area of a triangle bounded by the y axis, the line f(x) = 7 - 4/5 x, and the line perpendicular to f(x) that passes through the origin?
  
• What is the range of the function #f(x) = |x - 2|#?
  
• The weight of a nickel is 80%of the weight of a quarter. If a nickel weighs 5 grams , how much does the quarter weigh? Thanks
  
• A steel ball was dropped from a height of 81 and rebounded , on each bounce,Two thirds of he distance from which it fell.How far it travel before coming to rest.?
  
• How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=x^2-4#?
  
• You are given two sides of a triangle, a = 4.5 and b = 6, the angle between them is 35 degrees, how do you find the third side and the area of the triangle.?
  
• The perimeter of a square is 4 times as great as the length of any of its sides. Is the perimeter of a square proportional to its side length?
  
• You have a container whose box whose volume is 216 cubic centimeters. If your container is a cube, what is the length of each of its dimensions?
  
• Miguel is making a stained glass window. He cuts a 12 cm square along the diagonal to create two right triangles. What is the perimeter of each triangle to the nearest tenth of a centimeter?
  
• What are the points of inflection, if any, of #f(x)= x^5 -2 x^3 - x^2-2 #?
  
• What is the equation of the tangent line of #f(x)=(x-2)(x-2)(lnx-x)# at #x=3#?
  
• Raul works 2 h daily after school, Monday through Friday. On Saturdays he works 8 h at $2 more per hour than on weekdays. If he makes $142 per week, how much does he make per hour on weekdays?
  
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/6 #, and the triangle's area is #18 #. What is the area of the triangle's incircle?
  
• 1)The nth term of a progression is 6(#-4/3##)^2#. Prove that the progression is a geometric progression(G.P.).Obtain the first term and common ratio. (one more question, pls see below). ?
  
• A circle has a center that falls on the line #y = 12/7x +8 # and passes through # ( 9 ,1 )# and #(8 ,7 )#. What is the equation of the circle?
  
• How do you find the inverse of #f(x) = x^3 + 5# and is it a function?
  
• How do you find the standard form of the equation of the ellipse given the properties foci #(0,+-5)#, vertices #(0, +-8)#?
  
• In triangle ABC, how do you solve the right triangle given Side AB=17 Side BC=22?
  
• The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116. The bigger and smaller number is what?
  
• What is the slope of the tangent line of #x/y^3-xy= C #, where C is an arbitrary constant, at #(1,2)#?
  
• A triangle has corners A, B, and C located at #(5 ,5 )#, #(3 ,9 )#, and #(4 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
  
• Given #f(x) = 4x + 5# and #h(x) = sqrt(5x - 4)# how do you find (hf)(4)?
  
• What is the slope of the tangent line of #r=theta-sin((theta)/3-(2pi)/3)# at #theta=(pi)/4#?
  
• A group of people bought movie tickets at the AMC Century City. They bought a total of 7 tickets, some adult and some kid tickets. They spent a total of $72. If adult tickets cost $12 and kid tickets cost $9, how much of each were purchased?
  
• How to do you graph #y = 2x^2 + x - 3# by plotting points?
  
• The angle of depression from top of a building 200 meters tall to a point on the ground is 75 degrees how far is the point on the ground from the base of the building? Round your answer to the nearest tenth of a meter.
  
• The cost of a first-class postage stamp in 1962 was 4. In 1999 it is 33. The cost was (and is) growing exponentially. What was the growth rate?
  
• You invest an initial $1,000 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you have in the account after 5 years? Round your answer to the nearest whole number and include units.
  
• How do you graph and identify the vertex and axis of symmetry for #y=-3/5(x-4)^2+6#?
  
• What is the vertex form of the equation of the parabola with a focus at (29,37) and a directrix of #y=34 #?
  
• A triangle has two corners with angles of # pi / 4 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #15 #, what is the largest possible area of the triangle?
  
• How do I draw the right triangle ABC whose sides have the following values given below, and then find the six trigonometric functions of each triangle’s angle A? a = 2, b= #sqrt5# , c = 3
  
• What is the most precise term for quadrilateral ABCD with vertices A(4,4), B(5,8), C(8,8), and D(8,5)? square rhombus kite parallelogram
  
• How do you use the important points to sketch the graph of #y = 6x^2 + 7x - 20#?
  
• How do you find the eccentricity, directrix, focus and classify the conic section #r=8/(4-1.6sintheta)#?
  
• How do you graph the parabola #x^2 + 10x +8y +17 = 0# using vertex, intercepts and additional points?
  
• If $20,000 is invested and compounded continuously for four years, at what rate would you need to compound to guarantee a final value of $100,000?
  
• What is the equation of the tangent line to the polar curve # f(theta)= 5thetasin(3theta)+2cot(11theta) # at #theta = pi/12#?
  
• How do you determine whether the situation is an example of an inverse or direct variation: the drama club can afford to purchase 10 wigs at $2 each or 5 wigs at $4 each?
  
• Find the amount of fencing needed to enclose the triangular piece of land? <A = 48 degrees <B = 56 degrees Side b(opposite of angle B) = 300 meters
  
• How do you know if #x^2+2y^2+2x-12y+11=0# is a hyperbola, parabola, circle or ellipse?
  
• A chemist wants to mix a 65% alcohol solution with 10 liters of a 45% alcohol solution to produce a solution that is 55% alcohol. How many liters of the 65% alcohol solution should be used?
  
• How do you evaluate the function with the given values of x: h(x)=4x^-2 x=2, x=3?
  
• How do you graph the parabola #y= x^2-4x+4# using vertex, intercepts and additional points?
  
• What is the gradient of the tangent to the curve y = 4x^3-5x^2+x-7 at the point (2,7)?
  
• How do you graph #y=(x^2+4x)/(2x-1)# using asymptotes, intercepts, end behavior?
  
• A triangle ABC, right angled at B, is inscribed with a circle having 4cm diameter. The side BC is 5cm. What is the perimeter of the triangle?
  
• How do you find the domain and range of #sqrt{1 - x}#?
  
• A jar of mixed nuts has 45% peanuts, 30% almonds, and 25% cashews by weight. if the jar contains 12 ounces of almonds how many ounces of cashews does it contain?
  
• How do you write an equation of an ellipse in standard form given Foci (0,3),(0,-3) Passing through points (-1,2√2)?
  
• Which is the domain and range of #f(x) = -3sqrt (x+2) - 6#?
  
• How do you find the vertex and axis of symmetry, and then graph the parabola given by: #y=x^2 +2x -5#?
  
• What is the vertex form of #y=13x^2 + 14x + 24#?
  
• How do you write a standard form equation for the hyperbola with #y^2 - 4y - 4x^2 + 8x = 4#?
  
• How many ounces of pure water would have to be added to 30 ounces of 30% solution of alcohol to reduce the original solution to 25%?
  
• A copy machine accepts nickels, dimes, and quarters. After 1 hour, there are 30 coins total, and their value is $5.10. How many nickels, quarters, and dimes are in the machine? (Hint: There are exactly five different solutions.)
  
• What is the end behavior of #f(x) = x^3 + 4x#?
  
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