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Answers by Steve S.

solve for x (answer)

18=4+|2x|   14 = 2|x|   7 = |x|   x = ±7

Perform the operation (answer)

Paula, did you leave out some parentheses?:   (c+8)/(c^2-5c+4) + (3c+5)/(c^2-9c+20) =   (c+8)/((c-1)(c-4)) + (3c+5)/((c-4)(c-5)) =   (c+8)(c-5)/((c-1)(c-4)(c-5)) + (3c+5)(c-1)/((c-1)(c-4)(c-5)) =   ((c+8)(c-5)...

what line passes through point (-2,3) (1,-6) ? (answer)

Let (x,y) be another point on the line.   Slope, m = (y - 3)/(x- -2) = (-6 - 3)/(1- -2) = -9/3 = -3   Multiply both sides by x+2:   y - 3 = -3(x+2) = -3x - 6   Add 3x + 3 to both sides:   3x + y = -3

what type of conic is 16x^2-9y^2-32x-54y-209=0 (answer)

16x^2 - 9y^2 - 32x - 54y - 209 = 0   16x^2 - 32x - 9y^2 - 54y - 209 = 0   16(x^2 - 2x) - 9(y^2 + 6y) - 209 = 0   16(x^2 + 2(–1)x + (–1)^2 – (–1)^2) – 9(y^2 + 2(3)y + (3)^2 – (3)^2) - 209 = 0   16((x–1)^2 – 1) – 9((y+3)^2...

volume help. show work (answer)

At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 60t +1060, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 3t^2, where t is in minutes...

help simplfy expressions (answer)

1. (√a+√b)/(√a–√b)   = (√a+√b)^2/((√a+√b)(√a–√b))   = (a + 2√(ab) + b)/(a–b) 2. Same technique as for 1. 3. 3√2 - 2√3   No simplification possible. 4. √3(√6 - 2√3)   = √3(√2 √3 - 2√3)   =...

solve for distance (answer)

√3h/2 ???   = √(3)*h/2, or √(3h)/2, or√(3h/2) ???   =====   4√x = 20   Divide both sides by 4:   √x = 5   Square both sides:   x = 25

What end of an egg is stronger the blunt or sharp (answer)

Take two eggs.   Smash the blunt end of one on the counter.   Smash the sharp end of the other on the counter.   Which is stronger?   [Now scrape up the mess, pick out the shells, and make scrambled eggs.]

simplify radicals (answer)

1. √(-25)√(-9) = (5i)(3i) = –15 2. (6i)^2 = (6i)(6i) = –36 3. 1/i = i/i^2 = –i 4. – √(3)√(-3) = – √(3) i√(3) = –3i 5. 1/(2–i) = (2+i)/((2+i)(2–i)) = (2+i)/5 = 2/5 + 1/5 i

f(x)=64x^4-192x^3+x^2-3x (answer)

f(x) = 64x^4 - 192x^3 + x^2 - 3x   f(x) = x(64x^3 - 192x^2 + x - 3)   f(x) = x( 64x^2(x - 3) + 1(x - 3) )   f(x) = x(x - 3)(64x^2 + 1)   f(x) = x(x - 3)((8x)^2 – (i^2))   f(x) = x(x - 3)(8x – i)(8x + i)

Definition of tangent (answer)

For any point on the x-y plane, (x,y) = (r cos(θ), r sin(θ)), where the Initial Ray of θ is the positive x-axis and the Terminal Ray of θ starts at the origin and goes through (x,y).   r = √(x^2+y^2) is the distance from the origin to the point.   Then:   sin(θ)...

(x^-4x+8)/(5x-3) (answer)

Please put parentheses around the exponent. Right now it looks like you have   (x^(-4) x + 8)/(5 x - 3)   = (x^(-3) + 8)/(5 x - 3)   = ((1/x)^3 + 2^3)/(5 x - 3)   =(1/x + 2)((1/x)^2 + 2/x + 4)/(5 x - 3)

Find the exact value of sin 11?/12. (answer)

Should this be sin(11 pi/12)?   11 pi/12 is in 4th quadrant where sine is negative.   sin(11 pi/6/2) = –√(( 1-cos(11 pi/6) )/2)   cos(11 pi/6) = cos(12 pi/6 - pi/6)   = cos(- pi/6) = cos(pi/6) = √(3)/2   sin(11 pi/6/2) = –√(( 1-√(3)/2...

CAN I GET HELP WITH PARENT FUNCTIONS? (answer)

Carefully graph the points and you will see they seem to lie on a straight line.   To prove it, find slopes between adjacent points in the list; if they all are the same, then it's a line.   (3,11) (-1,3): (11-3)/(3- -1)=8/4=2 (5,15): (15-3)/(5- -1)=12/6=2 (-4,-3):...

Word problem show work please (answer)

A farmer is planning to put in a garden next to his barn. He is planning to fence in the garden on three sides (the barn will make the fourth side). He has 100 feet of fencing to use. FIND AN EQUATION FOR THE AREA OF THE GARDEN. Explain/Show work. x = width of garden y = length...

Writing Hyperbolas in Standard Form? 2 Questions (answer)

1.) I am given the vertices (14,-6),(-8,-6) and the endpoints of the conjugate axis, (3,1) and (3,-13). The transverse axis is the segment connecting the vertices, so it’s horizontal and (14-(-8)) = 22 units long. The conjugate axis is vertical and (1-(-13)) = 14 units long. The...