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Answers by Philip P.

Linear program (answer)

Let s = the number of soldiers produced each week and t = the number of trains,  The Profit equation is:   P = $4s + $2.5t   The constraints are:   3s + 2t ≤ 120  (No more than 120 hours of finishing labor available per week) 2s +...

The equation of a parabola is a quadratic.  Use the vertex form:   y = a(x-h)2 + k  where "a" is a constant (to be determined) and (h,k) is the location of the vertex.  The problem tells you the location of the vertex, (h,k) = (2,1) so the equation is:   y...

Explain E=mc2 (answer)

E = mc2 E = energy m = mass c = the speed of light   E = mc2 is the mass-energy equivalence equation.  It tells us that mass and energy are the same thing (energy) and provides the exchange rate between the two (c2).  It's like dollars and euros are both types...

Average cost = 8000/x + 35 + 0.7x. (a) Express the average-cost formula as a single fraction.  You need to put all three terms over a common denominator, in this case x: Average cost = 8000/x + 35x/x + 0.7x2/x = (0.7x2+35x+8000)/x (b) Write...

It is a "function" because each x-value has one and only one y-value.  However, it is a non-linear function.  A linear function has a constant rate of change, Δy/Δx.

polynomial (answer)

t is the elapsed time since the athlete stopped exercising.  So when he first stops exercising the elapsed time is zero.  Plug t=0 into the polynomial to get the heart rate

The answer is B.  If you multiply or divide both sides of an inequality by a negative number, it reverses the inequality.  This is an important rule that you need to remember when working with inequalities.   Example:   -4x > 24   -4x/-4 < 24/-4     ...

Geometry Math (answer)

You don't say whether the rotation is clockwise or counterclockwise - it makes a difference.  Here are the rules: For 270o CW, (x, y) rotates to (-y, x) For 270o CCW, (x, y) rotates to (y, -x) Check out this Wyzant resource on geometric transformations. https://www.wyzant.c...

Just replace the x with 3a then do the operations   f(x) = 2x4 - x3 + 6x2 - 7x - 5 f(3a) = 2(3a)4 - (3a)3 + 6(3a)2 - 7(3a) - 5   Can you finish it from here?  Hint: (3a)4 = 34*a4 = 81a4

3√(8x4/y)   Note that 8 = 23 and x4 = x3*x        = 3√(23x3x/y)      = 2x 3√(x/y)   Rationalize the denominator        = 2x 3√(x/y)  * 3√(y2/y2)      =...

The term "essential" comes from the word "essence", meaning "the basic, real, and invariable nature of a thing ..." (from Dictionary.com).  So what is "the invariable nature" or essence of an atom?  In other words, what makes an atom an atom? ...

√(-4 - 13k) = 10   Square both sides to get rid of the square root:        -4 - 13k = 100   Add 4 to both sides        -13k = 104   Divide both sides by -13:       ...

Volume= width*length*height.  Let x = width, y = height.  Since V = 10 m3:        10 = x*2x*y = 2x2y      5/x2 = y  (This is your substitution equation)   The cost of the container is:       ...