Answers created by Binayaka C.

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What is the slope of the tangent line of $r = θ - sin (\frac{θ}{6} + \frac{2 π}{3})$ $r=theta-sin((theta)/6+(2pi)/3)$ at $θ = \frac{π}{6}$ $theta=(pi)/6$ ?
How do you graph the parabola $y = x^{2} - 3 x$ $y=x^2-3x$ using vertex, intercepts and additional points?
Triangle A has sides of lengths $18, 33$ $18 ,3 3$ , and $21$ $21$ . Triangle B is similar to triangle A and has a side of length $14$ $14$ . 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 $f (x) = (x^{3}) - 12 x + 2$ $f(x)=(x^3)-12x+2$ ?
How can I solve this equation system? $x + 5 y + 2 z = 193 x + 2 y + z = 132 x - y - z = 0$ $x + 5y + 2z = 19" "3x + 2y+ z = 13" "2x - y - z = 0$ How should I think about this?
How do you find the asymptotes for $g (x) = \frac{x^{3} - 16 x}{4 x^{2} - 4 x}$ $g(x)= (x^3 -16x )/ (4x^2 - 4x)$ ?
How do you graph by using the zeros for $g (x) = \frac{1}{10} {(x + 1)}^{2} {(x - 3)}^{3}$ $g(x)=1/10(x+1)^2(x-3)^3$ ?
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 $f (x) = x^{2} - \frac{2}{3} x - \frac{8}{9}$ $f(x)=x^2-2/3x-8/9$ ?
How do you divide $\frac{7 - i}{3 - i}$ $(7-i) / (3-i)$ 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 $f (x) = (2 x - 2) (x - 3) (x + 3)$ $f(x)=(2x-2)(x-3)(x+3)$ concave or convex?
What are the asymptote(s) and hole(s), if any, of $f (x) = \frac{x (x - 3)}{x^{2} - 9 x + 3}$ $f(x)= (x(x-3))/(x^2-9x+3)$ ?
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 $f (x) = e^{2 x} (ln x)$ $f(x)=e^(2x)(lnx)$ ?
How do you find the vertical, horizontal or slant asymptotes for $f (x) = \frac{1}{x^{2}}$ $f(x)= 1/x^2$ ?
How do you graph the parabola $y = {(x + 4)}^{2} + 4$ $y= (x+4)^2+4$ using vertex, intercepts and additional points?
Cups A and B are cone shaped and have heights of $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $7 c m$ $7 cm$ and $14 c m$ $14 cm$ , 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 $f (x) = | x + 4 |$ $f(x)=abs(x+4)$ ?
What is the equation of the tangent line to the polar curve $f (θ) = 2 θ sin (θ) + θ {cot}^{2} (4 θ)$ $f(theta)=2thetasin(theta)+thetacot^2(4theta)$ at $θ = \frac{π}{3}$ $theta = pi/3$ ?
How do you graph $f (x) = x + \frac{5 x}{x - 1}$ $f(x) = x + (5x)/(x-1)$ and identify all the asymptotes?
If $A = < 5, 2, - 5 >$ $A = <5 ,2 ,-5 >$ , $B = < 6, 5, 3 >$ $B = <6 ,5 ,3 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?
How do you find the domain and range of $f (x) = ln (3 x - 2)$ $f(x)= ln(3x-2)$ ?
How do you graph $y = \frac{5 x + 3}{- x + 10}$ $y=(5x+3)/(-x+10)$ using asymptotes, intercepts, end behavior?
What are the important points needed to graph $y = 3 x^{2} + 6 x - 1$ $y=3x^2+6x-1$ ?
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 $f (x) = x - 7$ $f(x)=x-7$ , $g (x) = x^{2}$ $g(x)=x^2$ and $h (x) = {(x - 7)}^{2}$ $h(x)=(x-7)^2$ ?
What is the second derivative of $f (t) = (3 e^{- 2} t) - (5 e^{- t})$ $f(t) = (3e^-2t) - (5e^-t)$ ?
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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