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Answers by Kurt T.

Simplify (2p)^-4=? (answer)

A number raised to a negative exponent is the reciprocal of the same number raised to the absolute value of the exponent.  So, for example, x^-4 = 1 / x^4. (2p)^-4 = 1 / (2p)^4 = 1 / 16p^4.

Solve D=ABC for A (answer)

You want to isolate A, and the way to do this here is to divide both sides by BC.  So A = D / BC.

(X+4)(X+5)=0 (answer)

Remember FOIL ... First, Inner, Outer, Last First ... multiply the first terms of the two binomials ... x * x = x^2 Outer ... multiply the first term of the first binomial and the second term of the second binomial ... x * 5 = 5x Inner ... multiply the second term of the first binomial...

I need help on solving functions. (answer)

In all cases, you would substitute the number in parentheses for x and solve the equation.  For example.. f(4) = 3/4 * 4 + 2 f(4) = 3 + 2 f(4) = 5 f(-4) = 3/4 * -4 + 2 f(-4) = -3 + 2 f(-4) = -1

Evaluate the expression. Write the answer in standard form. (answer)

The easiest way to answer this type of question is to multiply all four terms together.  You can do this because multiplication is commutative; it doesn't matter how the terms are organized as long as all are included in the final product. (-4) (10^-6) (2) (10^4) First, multiply -4...

Simplify (7x)^-2 (answer)

A negative exponent indicates a reciprocal of the positive exponent, so x^-3 = 1 / x^3.  That said... (7x)^-2 = 1 / (7x)^2 = 1 / 49x^2  

how to do logarithms (answer)

The logarithm is the power to which the base is raised to get a certain number.  What's that?  You want it in English?  Well, OK... Let's start with base 10 logarithms.  (For this paragraph, "log" will mean base 10 log.)  If I say the log of 1,000 is 3, this...

The upper quartile of a set of data is a number that (answer)

The upper quartile - also known as the third quartile and the 75th percentile - is the point that divides the top quarter and bottom three quarters of a distribution.  So, if your IQ score is at that point, you did better than three quarters (75%) of the norming sample. If your data...

What is the difference between intersecting and perpendicular lines? (answer)

Perpendicular lines intersect at a 90 degree angle.  For this to be true, either one line is horizontal (e.g., y = 5) and the other is vertical (e.g., x = 4) or the slopes are negative reciprocals of each other (e.g., 3 and -1/3). y = 2x and y = 3x intersect at the origin.  (In both...

Using the XY Coordinate system (answer)

Both lines pass through (7, -2), therefore that is the intersection point. The linear equations that define these two lines are: y = -2/3 x + 8/3 y = 1/4 x -15/4 In both cases, substituting 7 for x will yield -2 for y.  (7, -2) is the solution for this system of equations...

How do I solve systems by substitution? (answer)

In this case, you could substitute (6x-5) for y in the first equation, solve for x, and substitute the new x value into both equations to make sure you get the same answer for y... 4x + 2 (6x - 5) = -2 4x + 12x - 10 = -2 16x = 8 x = 1/2 Now substitute 1/2 for x in...

What is the quadratic formula? What is it used for? (answer)

The quadratic formula provides the roots (also called zeroes or x-intercepts) of a quadratic equation.  A quadratic equation is a second-degree equation; its highest term is raised to the second power.  Quadratic equations take the form of a parabola.  They open upward if...