Let's pick a number to wrap our heads around the situation.   number = 21 reversed = 12   larger/smaller = 21/12   21/12 = 1 + 9/12  where 1 is the quotient, 9 is the remainder, 12 is the divisor   Knowing how division works, the largest...

Recall the distance formula:   Distance = rate x time   In this problem the car has two different parts of its journey. First part: "A car travels at 30 km/h for 10 minutes" D1 = 30 km/hr  x  10 min  (we need time to be in hours) D1...

First, let's break the problem down & identify variables and relationships between the variables:   "445 people paid a total of \$1578 to attend" total people = 445 total cost of all people = \$1578   "Each adult paid \$6, while each student paid...

he brought 8 notebooks and 3 pens for isha and spent 365pesos . N= cost of one notebook P= cost of one pen 8N + 3P = 365 {1} for any he brought 3 notebooks and 2 pens and spent 150 pesos. 3N + 2P = 150 {2} How much the notebook and pen? Find...

mike age is 3 less then twice the age of his brother nuke. M = Mike's age now N = Nuke's age now M = 2N - 3   Ten years ago, four times nuke's age was one more mike's age. M-10 = Mike's age 10 years ago N-10 = Muke's age 10 years ago 4(N - 10) = 1 + M -10   what...

[ 15x3−10x2+25x  ] / [5x]     (split up the numerator by using the common denominator with each term)   [15x3]/[5x]  − [10x2]/[5x] + [25x]/[5x]    (simplify each term)   3x2 - 2x + 5    (this is the quotient)   check: (5x)(3x2...

We can define variables and find useful information from the problem:   he Ole Paint Shop sold 34 paintbrushes, 34 brushes total   one kind at \$8.20 each x = # of brushes that sell for \$8.20   and another at \$9.15 each. y = # of brushes that sell...

the square root is the inverse of the square   a number squared is number multiplied by itself: 12 = 1x1 = 1 22 = 2x2 = 4 32 = 3x3 = 9 ... n2 = nxn = perfect square   a square root is the inverse of this √1 = √(1x1) = 1 √4 = √(2x2)...

The number of lawns that you would like to mow per week is 8. THIS IS THE IDEAL NUMBER     You have to mow at least 4 lawns each week THIS IS THE MINIMUM NUMBER     and you can't now more than 12 lawns each week. THIS IS THE MAXIMUM NUMBER   LET'S...

Total cost DEPENDS on the number of centerpieces purchased. So, n = number of centerpieces purchased is INDEPENDENT C = total cost is DEPENDENT   C = 75 + 16.75n

recall that 100 cm = 1 m   so, 322 cm = 3.22 m   \$4.48/m x 3.22m = \$14.43 before tax   \$14.43 x 1.07 = \$15.44 after tax   William will have to pay \$15.44.

red stripes: 6 red and no stripes: 3 yellow with white stripes: 7 TOTAL: 16   P( stripes OR yellow ) = [all but the no stripes ] / TOTAL = (6 + 7) /16 = 13/16

entire set {1,2,...,20} 20 members even set {2,4,6,...,18,20} 10 members black set {11,12,...,20} 10 members even AND black set {12,14,16,18,20} 5 members   P(even OR black)  = P(even) + P(black) - P(even AND black) = 10/20 + 10/20 - 15/20 = 5/20 =...

5x2 -9x -18 5x2 + 6x -15x -18 x(5x+6) -3(5x-6)   <-- in this step where you factored out -3, the parentheses should be (5x + 6) because -18/-3 = +6   Then you can see that you factor out the common factor of (5x + 6)!

entire set: {1,2,3,4,5,6,7,8,9,10} 10 members less than 5 set: {1,2,3,4} 4 members odd set: {1,3,5,7,9} 5 members less than 5 AND odd set: {1,3} 2 members   P(less than 5 OR odd) = P(less than 5) + P(odd) - P(less than 5 AND odd)   = 4/10 + 5/10...

Another way to write (fog)(x) is f[ g(x) ]. You are embedding the g function into the f function.   So, f[g(x)] = f[ -2x+2 ]   3[ g(x) ] - 9 = 3( -2x+2 ) - 9   = -6x + 6 - 9   = -6x - 3

Just think of numbers whose sum is 8:   0 + 8 = 8 1 + 7 = 8 2 + 6 = 8 3 + 3 = 8 6 + 2 = 8 7 + 1 = 8 8 + 0 = 8   There are infinite possibilities! Every point on the line x + y = 8 is a possibility.   Can...

You can only add radicals that have the same number under the radical sign. This number is called the radicand.   The goal is to simplify each radical by rooting out the perfect square factors in hopes of common radicands:   √48 + √75     [since 48...

First, let's differentiate:   d/dx (sin(2x)) = d/dx (2sin(x)cos(x) )   cos(2x) · 2 = 2cos(x) · cos(x) + 2sin(x) · -sin(x)   [using product rule]   cos(2x) = cos2(x) - sin2(x)     [dividing both sides by two & simplifying...