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## BRUCE S.'s Resources

ASSUME THE DIVIDENDS ARE PAID ANNUALLY AFTER THE CAPITAL GAIN IS ADDED TO THE STOCK VALUE.( HOW THE DIVIDENDS ARE PAID IS NOT SPECIFIED.)   RETURNS                 dividend yields          capital gain   TOTAL...

# Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -7x^2 + 9x + 9. (answer)

YOU ARE GIVEN THE FUNCTION   f(x) = -7x^2 + 9x + 9  AND 4 (X,Y) PAIRS.  FOR EACH PAIR, SUBSTITUTE THE X INTO F(X) AND CALCULATE TO SEE IF THE RESULT EQUALS THE Y (OR F(X) ) VALUE FOR THE PAIR.  A MATCHING ANSWER INDICATES THAT PAIR IS A VALID SOLUTION.   THIS...

See the previous question's solution. Use the form of the quadratdic equation and it's solution equation for s to find a, b, c.

QUADRATIC EQUATION FORM IS:     a*x^2 + b*x + c =0   IF YOU CAN'T FACOTOR THIS THEN USE THE FORMULA FOR x IS:     x = [ -b ±√{ b ^2 - 4*a*c } ] /2*a   BY INSPECTION:       b = -4.51     a =...

# What is 9% of22? (answer)

9% in fractions is 0.09 9% of 22 is   0.09 * 22 = 1.98  or with significant digits only, 2.0

# If you had \$100.00 invested in a savings account that is compounded annually and yields 3% interest, how much interest would you have accumulated in 30 years? A (answer)

3% interest is 1.03 mathematically   Each year yields 3% or 1.03 times the previous year's balance.   So it becomes Principal * 1.03 * 1.03 * 1.03 .... for 30 times.  Or the concise way to write it is:   Principal * (1.03^30) = Principal * 2.4273   For...

arctan(3/4) means 'What angle has a tangent of 3/4 or 0.75'   The sec of that means 'What is the secant of that angle.   arctan(0.75) = 36.86 degrees   sec is the reciprocal of the cosine function   sec(36.86) = 1/cos(36.86) = 1/0.8 = 1.25...

This is an application of the the definition of tangent function:   tan ( angle of sun light) = Opposite side / Adjacent side    tan ( angle of sun light) = Object height / Shadow length   Initial case:  Tan ( angle of sun ) = 5.7 / 17.1    2nd...

# The perimeter of a rectangular floor is 180 feet. Find the dimensions of the floor if the length is five times the width (answer)

DEFINITION:    2*W + 2*L = PERIMETER OF A RECTANGLE,  W= WIDTH, L= LENGTH   GIVEN:  L= 5*W   2*W + 2*(5*W) = 180   2*W + 10*W = 180   12 * W = 180   W= 180 / 12   W=  15     L=5*W   L...

Break up one factor into individual factors and then multiply, as follows:   (8m7c9)(3m9c7) = (8m7c9)(3)(m)(9)(c)(7)                            = {(8m7c9)(3)} (m)(9)(c)(7)   Note that (8m7c9)(3)...

# Solve for X: | 2x/3-1 |=3/5 (answer)

ABS(2/3*X -1) =3/5   TAKE THE POSITVE FORM OF THE ABS, IE   2/3*X -1 =3/5   REARRANGE AND SIMPLIFY TO FIND X=12/5   CHECK THIS ANSWER BY SUBSTITUTING INTO THE ORIGINAL EQUATION   ABS( 2/3*12/5 -1) = 3/5   2/3*12/5 -1 =...

# solving application linear equations (answer)

For lack of a drawing tool, the planets look like this:   SUN <-- D2 --> P2 <--29.3 --> P1 <-- 25.4 --> P3   where the P's are the planets and the # are the distances between as given.   We need to find D2, distance of P2 from the sun.   The...

# If x=5 , then x+7 = 5+7 . (answer)

It is already done.  Here is how it is done (and usually presented):   Basically you have a relationship  x+7=y. The problem asks " If x = 5, what is y?"   Do the problem by substituting the value 5 for x in the original equation, ie: x+7=y 5+7=12=y...

# between 1950 and 2000 the annual growth rate for the worlds population averaged 1.8%. The U.S census bureau estimates the world population now to be 7.1 billion (answer)

At first glance you might say the population will be additive, ie      Base population + annual fractional growth * 25years      Projected Population = 7.1B + 7.1B*0.018*25      Projected Population = 7.1B ( 1 + 0.018*25...

Ruby,    You can expand the square and rearrange into the standard form for a polynomial: y-4=(x+2)^2 y-4= x^2 + 4x + 4 y = x^2 + 4x + 8 And then you can plot it.  Turns out to be a parabola, open upwards with a minimum at x=-2 and y=4...

# y=x+2 in coordinate plane (answer)

Tina,   Look at the answer to y=-x.   again use the generic straight line formula and/or plot it! Good Luck, BruceS

# y=-x in coordinate plane (answer)

Tina,     Think of the generic straight  line equation:   y = mx + b.    In this case b = 0 (the y intercept).    m, the slope, equals -1.   So this is just a straight line, passing through x=0,y=0 and sloping from lower right to upper...

# Which ordered pair does not satisfy the system 2x + y > 0 and -2x - y > -8? (answer)

Ricky,   Substitute the x,y pairs into the expressions!                      2x + y > 0?                 -2x - y > -8?             Both satisfied?? (3,...