Use point-slope form, y + 6 = (-1/4)(x + 1) -------- Attn: You don't need to change it to slope-intercept form.

Find an equation? (answer)

Use point-slope form, y + 6 = (-1/4)(x + 1) -------- Attn: You don't need to change it to slope-intercept form.

can you help me with a word problem (answer)

Let x be the amount contributed by her parents. Using proportion, x/203 = 3/7 Solving for x, x = $87

Factoring an expression (answer)

-216x^3+1 = 1 - (6x)^3 = (1-6x)(1+6x+36x^2) = (-6x+1)(1+6x+36x^2) So, the answer is A.

Find an antiderivative? (answer)

Use mental substitution, ∫e^(x+e^x)dx = ∫e^x * e^(e^x) dx = ∫e^(e^x) de^x = e^(e^x) <==Answer

Find the rate of the jet (answer)

Let v = the rate of the holicopter. So 4v = the rate of the jet. Balance by the total time, 1080/(4v) + 180/v = 5 Multiply both sides by 4v, 1080+720 = 20v v = 90 mph 4v = 360 mph Answer: The rate of the jet is 360 mph.

there are 12 questions,you only have to answer 10. How many different combinations are there? (answer)

To answer 10 out 12 questions, you can take 2 away out of 12. So the number of ways is 12C2 = 12*11/2 = 66 ways. If you have to answer 1-3, then you need to take 2 away out the remaining 9 questions. So the number of ways is 9C2 = 9*8/2 = 36 ways

Take away the 40 butterflies collected by the teacher, and divide the result by 12. That's the answer. (100-40)/12 = 5 butterflies collected by each child.

y = ax2+bx+c Plug in (0, 8), 8 = c Plug in (2, 20), (-2,-4), 20 = 4a+2b+c ......(1) -4 = 4a-2b+c ......(2) (1)-(2): 24 = 4b b = 6 From (2), a = (1/4)(2b-c-4) = (1/4)(2*6-8-4) = 0 Answer: y = 6x+8 (This is a straight line.)

amount originated (answer)

Let x be the original amount. Balance by spending, x - (4/5)^2 x = 72, focusing on the remaining part each time. Solve for x, x = $200 Answer: The original amount was $200. ------- Hi Murtaza; You are correct. I misread the problem. This problem can be done as above...

sin(sin^-1x-cos^-1x) = sin(sin^-1x)cos(cos^-1x) - cos(sin^-1x)sin(cos^-1x) = x^2 - (1-x^2) = 2x^2 - 1 ------ Attn: cos(sin^-1x) = sqrt(1-x^2), since the domain of sin^-1x is in the first and fourth quadrants, where cos x is positive. sin(cos^-1x) = sqrt(1-x^2),...

Let x = fada (tanx + cotx)/(secx cscx) = tanx/(secx cscx) + cotx/(secx cscx) = sin^2x + cos^2x, since tanx/(secx cscx) = sin^2x, cotx/(secx cscx) = cos^2x = 1

csc [cos^-1(-square root of 3 divided by 2)] = csc(5pi/6) = 1/sin(5pi/6) = 2

Verify tan^4x+2tan^2x+1=sec^4x (answer)

tan^4x+2tan^2x+1 = (tan^2x+1)^2 = sec^4x, since tan^2x+1 = sec^2x

By completing the square, (tanx+3)^2 = 5 tanx = -3+/-sqrt(5) Can you get x now?

(sin9x+sin5x)/(cos9x-cos5x) = (sin(7x+2x) + sin(7x-2x))/(cos(7x+2x)-cos(7x-2x)) = 2sin7x cos2x / (2sin7x sin 2x) = cot2x

sin x = 4/5 cos x = -3/5, by 3-4-5 Pythagorean triple and Q. II cos x/2 = sqrt[(1/2)(1+cos x)] = sqrt[(1/2)(1-3/5)] = sqrt(5)/5

Completing the square, (tanx-3)^2 = 9-4 = 5 tan x = 3+sqrt(5), x = 1.38 rad, 4.52 rad or tan x = 3-sqrt(5), x = .65 rad, 3.79 rad. Answer: x = .65 rad, 1.38 rad, 3.79 rad, 4.52 rad.

Method 1. sin(x+pi)+sin(x-pi) = 2sin x cos pi, after expanding and collecting like terms = -2sin x Method 2. sin(x+pi)+sin(x-pi) = -sin x - sin x, using reference angle = -2sin x

Factor, (tan x + sqrt3)(tan x - 1) = 0 tan x = -sqrt3, => x = 2pi/3, 5pi/3 or tan x = 1, => x = pi/4, 5pi/4 Answer: x = pi/4, 2pi/3, 5pi/4, 5pi/3

sin^2x = 1/4 sin x = 1/2, x = pi/6, 5pi/6 or sin x = -1/2, x = 7pi/6, 11pi/6 Answer: x = pi/6, 5pi, 7pi.6, 11pi/6.

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