Let us first simplify the equation.
(1-cox5x)/(1-cos7x) .... multiply numerator and denominator by (1+cos5x)(1+cos7x)
=[(1-cos5x)(1+cos5x)(1+cos7x)]/[(1-cos7x)(1+cos7x)(1+cos5x)]......remember that (a+b)(a-b)=a2-b2
=[(1-cos25x)(1+cos7x)]/[(1-cos27x)(1+cos5x)] ...

1) use perfect square formula a2+2ab+b2=(a+b)2
16y2 + 24y + 9 = (4y)2 + 2.4y.3 + 32 = (4y+3)2
2) use difference of squares formula a2 - b2 = (a+b)(a-b)
49x2 - 100y2 = (7x)2 - (10y)2 = (7x-10y)(7x+10y)
3) use sum of cubes formula, a3 + b3 =...

a) Easiest way to solve this problem is to remember that a2 - b2 = (a+b) (a-b) and recognize the pattern from the problem
100x2-1 = (10x)2 - (1)2 = (10x+1)(10x-1)
b) If you do not remember the formula for a2 - b2, then you will need to solve the problem by using usual factoring method...

Let the moving point P be (x, y)
remember that slope m of line joining points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2)
slope of line joining point P(x, y) to A(1, 3) is (y-3)/(x-1)
slope of line joining point P(x, y) to B(3, 1) is (y-1)/(x-3)
We have been told that, slope of...

This polynomial is not prime since it has the factors.
1) Fastest and easiest way to solve this problem is to remember the formula for (a+b)2 and observe the pattern.
We know that, a2+2ab+b2 =(a+b)2
16x2 - 24xy + 9y2 = (4x)2 - 2.4x.3y + (3y)2
=(4x-3y)2
2) If...

P(x)=P=x2+14x+54
Function y=ax2+bx+c is a parabola with vertex at x= -b/2a. It opens up if a>0 and it opens down if a <0.
So function P(x)=P=x2+14x+54 is a parabola with a=1, b=14, c=54. Since a=1 >0, it opens up.
Its vertex is at
x = -b/2a = -14/2...

f(x) = - |x+2|, substitute x = -8 to get
f(-8) = - |-8 +2|
f(-8) = - |-6|, absolute value of a negative number is a positive number
f(-8) = -6

Ratio of height to new height = height:new height = 147/30.5 = 4.82
This is a ratio problem and not a proportion problem.
Ratio is the answer obtained by dividing two similar quantities (quantities with same units). We use symbol
: to specify ratio.
Equality of two ratios is...

Radical expression contains a square root (√) of some expression. It undefined when value inside radical (called discriminant) is negative.
Square root is not defined for negative values of discriminant. It is defined only for all values of discriminant that are greater than or equal to zero...

Let me restate this cryptic question.
2.4 million lb (pounds) of almonds are sold when the selling price is $5.50 per lb.
4.8 million lb (pounds) of almonds are sold when the selling price is $4.50 per lb.
What linear function expresses the amount of almonds sold as a function of the...

For converting this to a fraction, we need to combine the two terms in the equation into a single term. This is done by making denominators of both the terms same and then subtracting the numerators.
For making the denominator same, we need to find the Least Common Multiple (LCM) of...

Absolute value of x is always positive.
So |x|+6=2x-3 means
x+6=2x-3 only if x is positive or -(x)+6=2x-3
only if x is negative
x+6-x=2x-3-x ...

Let driving speed of Fritz = X miles per hour
so train speed = X+80 miles per hour
Train travels for 15 minutes = 15/60 = 1/4 hours
Distance travelled by train = speed x time = (X+80) x 1/4 = (X+80)/4 = (X/4 +20) miles
Fritz travels for 35 minutes = 35/60 = 7/12 hours
Distance...

Say A liters of 68% alcohol solution must be used.
So it will have a total alcohol contents of Ax68/100=68xA/100 liters
Therefore (460-A) liters of 22% alcohol is used with total alcohol contents of (460-A)x22/100 liters
Total alcohol contents in 460 liter of 68% alcohol solution is
68xA/100+22x(460-A)/100=(68A+22x460-22A)/100=(46A+10120)/100...