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Use sin(2x)=sin(6x-4x) and sin(10x)=sin(6x+4x) and simplify to arrive at the expression on the left.  Very simple.

# Are there any quadratic equations that cannot be solved by factoring? Why or why not? (answer)

If the discriminant in the quadratic formula is a perfect square, then the quadratic expression can be factored.     When we talk about factoring, the criteria we are talking about is to find four INTEGERS a, b, c and d such that the given quadratic expression can be obtained by...

# how can i see that a quadratic equation does not have factors evn before solving it (answer)

Let's consider the general second degree (quadratic) equation ax2 + bx + c = 0   If a quadratic expression on the left is to have factors, those factors will be of the form    (qx + p) and (sx + r) where p, q, r and s are all real numbers.  So...

# word problem trying to set up a formula to find the answer (answer)

Let's say there are r rabbits and b birds   Since there are 170 heads and each bird and rabbit has one head, we can write the following first equation   r + b = 170  ----------------let's call this equation 1   Also, each rabbit...

# Quarter 1 POW #5 (answer)

This is an interesting problem, just needs a little imagination to solve it.  The basic logic is this: Whey they are going in opposite directions, they meet again when they both TOGETHER cover the whole lap.  When they are going in the same direction they meet the second time (and every...

# how to solve this (answer)

Adding to Andre's answer:   The polynomial x2 -5x +15 is a quadratic and represents a parabola that opens upward and vertex at (2.5, 8.75).  This parabola does cross the x axis, so at no point is y < 0

Problems such as this (factoring quadratic expressions) can be easily solved by a technique called grouping.  First factor out any common constant factors out.  In the given problem there are no common constant factors, so we proceed to next step.     The coefficient...

# Can someone show me how to determine which of the following is a factor of th e polynomial x^-x-20? (answer)

Sandra, Your question appears to have incomplete information.  Please copy the question completely.  I am assuming the question is multiple choice but the multiple choices are missing in your question.  Also x^ should have some number (or an expression) following the ^.  Please...

The general linear equation is of the form y = mx + b We are required to form a linear equation for the elevation of the elevator from the ground in terms of time.  If we call y as the height and x as the time, then applying the general linear model y = mx + b, the question reduces...

# find the inverse equation (answer)

The best way to find inverse of an equation is by interchanging the independent variable (which in this case is t) and y.     The given function is y=√(3t)+2   The inverse function can be obtained by interchanging (switching) t and y   t=√(3y)+2   subtract...

# Express “ln va “ as a product (answer)

Logarithm of a number raised to a power can be expressed as the power * logarithm of the number   Expressed Algebraically, log(xa) = a * log(x)   ln is natural logarithm which is a logarithm to base e (natural number)   The given expression ln(√a) can...

# how do I graph a solution set of the linear inequality 2x+y-5>0. (answer)

The meaning of the question: Show a set of all points which satisfy the equation 2x + y - 5 > 0.     For instance, the point (1,1) does not belong in this set because it does not satisfy the above equation as shown below by plugging in 1 and 1 for x and y   2*1...

# If y varies inversely with x and y = 6 when x = 3, then what is y when x = 2? (answer)

When a variable y inversely varies with another x, it means that when y is doubled x is halved, when y is tripled x reduces to a third of original value.  This is shown below:   Suppose x is 4 when y is 2, then x is halved 2 when y doubled to 4.  When x is reduced to 1 (1/4th...

# in a population with a mean of 50, a score of 55 would have a deviation of ? (answer)

http://en.wikipedia.org/wiki/Deviation_(statistics)   The above article defines deviation as    In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign...

Let's start by defining the imaginary number i as √-1.  Therefore √-1 = i, so √-2 = 2 . i etc.    (2√-3+3√-2) . (4√-3-5√-2) = (2 . √3 . i + 3 . √2. i) . (4 . √3 . i - 5 . √2 . i)   Using the long multiplication technique, we multiply each...

# Solve. Write the solution set in interval notation. (Enter EMPTY or Ø for the empty set.) 3x + 7 < 10 or 6x - 14 > 4 (answer)

The question is asking for all real values of x for which the two inequalities are true.     As an example, let's try a value of 4 for x.  Plugging that value in the first inequality we have    3*4+7<10   Since 14 is greater than 10 (or...

# graph and solve x+y=3 and x-y=5 using algebra (answer)

When an equation in first degree is given in the form y=mx+b then this can immediately be graphed with a slope of m and y intercept of b.  A first degree equation is an equation that does not contain any variables raised to second power or greater.   The given equation is x+y=3...