You can put this solution on YOUR website!
xw - yz

You can put this solution on YOUR website!
<==> <==> <==> (2 cosx + 1)(cosx - 1) = 0 ==> cosx = -1/2 or cos x = 1.
From cosx = -1/2, x = ,.
From cos x = 1, x = 0.
The solutions are then 0,,.

You can put this solution on YOUR website!
0.60p = p - 32
==> -0.40p = -32
==> p = -32/-0.40 = $80, the original price of the desk.

You can put this solution on YOUR website!
= q cos A - p sin A
= p cos A - q sin A
after using Cramer's rule to solve for x and y.
Then

=
=
=.

You can put this solution on YOUR website!
, and . They are inverses, because
, and
.

You can put this solution on YOUR website!
No, not inverse functions, because fog = -4x, and not equal to x. Similarly gof = -4x, and not equal to x.

You can put this solution on YOUR website!
The values between 32 and 40 inches are within 2 standard deviations from the mean 36, and so covers around 95.4% of the distribution. The values between 34 and 38 inches are within 1 standard deviation from the mean 36, and so covers around 68.2% of the distribution.

You can put this solution on YOUR website!
35t + 40t = 50 ==> 75t = 50 ==> t = 2/3 hr, or 40 minutes. You and Mr. Jones will meet at 5:40.

You can put this solution on YOUR website!
original area =
new area =
==> percentage increase is %.
You stated: "When we divide a whole number by a FRACTION [caps mine], our answer is larger than we started with. Explain why."
In fact, this is true only if the dividing FRACTION is between 0 and 1 exclusive, and the number we're dividing is positive.
Let a, b be positive integers, and let a > b, so that b/a < 1.
Then by a multiplicative property of inequality.

You can put this solution on YOUR website!
==>

You can put this solution on YOUR website!
hours longer.

You can put this solution on YOUR website!
a) The tangent lines are horizontal at the points (0,4) and (0,-4).
b) The tangent lines have slope 1 at the intersection points of the circle with the line y = -x. Solving:
==> , or
, .
Then the points are (,) and (,).

You can put this solution on YOUR website!
(1/3)*(1/3) = 1/9

You can put this solution on YOUR website!
I will assume that YOU invested $1500 AT THE BEGINNING of the month of March, and that at the END of December, YOUR stock portfolio has worth $5200. So that's after 10 months. YOUR portfolio's monthly rate of change r is then computed as follows:

==> , to 4 decimal places.
That is 13.24% per month.

You can put this solution on YOUR website!
g(3) = 4*3 - 9 = 12 - 9 = 3,
g(5) = 4*5 - 9 = 20 - 9 = 11.

You can put this solution on YOUR website!
sec x = 1 ==> cos x = 1. The only x-value satisfying the last equation in [0,] is x = 0.

You can put this solution on YOUR website!
g(x) could be 0.05x, while f(x) could be .

You can put this solution on YOUR website!
I will assume that the least number you're asking for is a positive number.
Then we have to find the smallest positive integer n that satisfies the simultaneous system of congruences
n = 4 mod 7,
n = 5 mod 8,
n = 6 mod 9.
We use the Chinese Remainder Theorem using the extended Euclidean algorithm. (For the statement of the theorem and symbolism go to http://en.wikipedia.org/wiki/Chinese_remainder_theorem).
(31)(7) + (-3)(8*9) = 31*7 + -3*72 = 1 ==> e1 = -216 (=-3*72)
8*8 + -1*(7*9) = 8*8 + -1*63 = 1 ==>e2 = -63 (=-1*63), and
25*9 + -4*(7*8) = 25*9 + -4*56 = 1 ==> e3 = -224. ( = -4*56)
Then the solution n is the linear combination n = 4*e1 + 5*e2 + 6*e3 = 4*-216 +5*-63 +6*-224 = -2523 mod 504, where 504 = 7*8*9.
The least positive integer satisfying n = -2523 mod 504 is 501.
Therefore the final answer is 501.

You can put this solution on YOUR website!
The circumscribing circle must have center (-4, -2), which is actually the midpoint of the segment AC.

You can put this solution on YOUR website!
tan A = -1/2 ==> ==> ==> .
tan B = -2/3 ==> ==> ==> .
Now

You can put this solution on YOUR website!
,
==> ,
==> ,after squaring both sides.
==> , or x(x - 5) = 0.
==> x = 0 or x = 5. The 1st x-value will not satisfy the original equation, and the 2nd x-value does. Therefore final answer is x = 5.

You can put this solution on YOUR website!
log(2x+7) base 4 = log(81) base 3
<==> log(2x+7) base 4 = 4
<==>
==> 2x + 7 = 256,
x = 249/2.

You can put this solution on YOUR website!
(gof)(x) = g(f(x)) = g() = 2 + 5.
The domain of gof is [0, ).

You can put this solution on YOUR website!
The range of tan(2x) is still (, ). What changes is its period. From a period of (from tanx), the period becomes .

You can put this solution on YOUR website!
3x+y = 60
2x+ 40 = 60
2y = 60, because equilateral <==> equiangular.
Then y = 30 degrees, and x = 10 degrees.

You can put this solution on YOUR website!
and , thus log7 2401 - log3 243 = 4 - 5 = -1.

You can put this solution on YOUR website!
<==> , so x = 1 foot.

You can put this solution on YOUR website!
5x+3x>-8
==>8x > -8
==>x > -1 after division by 8, a positive number.
In interval notation , (-1, ).

You can put this solution on YOUR website!
I will assume that your function is .
To find the range solve for x in terms of y and then state conditions on y that may arise.

<==>
<==>
==> , using the quadratic formula.
Since the values of x must be real, the conditions we should impose on y are
and y is not equal to -1.
The solution set to this inequality is the union of intervals (, -1)U[3/4, ). This is the RANGE of the function.

You can put this solution on YOUR website!
y/t miles per hour average speed

You can put this solution on YOUR website!
years, or 910 years.