find the slope of the line that passes through (-5,3) and (-1,-9)   m = (-9-3)/(-1 --5)    = -12/4  = -3   a perpendicular line has a slope that is the negative reciprocal of the slope found with the two points   slope of perpendicular...

5(x + 3) =8x - 6   5x + 15 = 8x - 6   5x + 21 = 8x   21 = 3x   x = 7

= (1 4/9) (9000)   = (13/9)(9000)   = 13,000 ft

Ana's rate per hour = 5 products/4 hours     =5/4   Boy's rate per hour = 5 products/ 2 hours    = 5/2   x=hours it takes them working together to complete 15   5/4(x) + 5/2(x) = 15   5x/4 + 10x/4 = 15   15x/4...

Create ordered pairs from the data given   (4,400) = (x1, y1)   (5,450) = (x2, y2)   slope = (y2-y1)/(x2-x1)      = (450-400)/(5-4)     = 50/1 = 50   Now use point slope equation   (y-y1) =...

breadth or width = x   length = 2x   (x)(2x) = 578   2x2 = 578   x2 = 289   x = 17   breadth = 17   length = 34

distance formula = √(x2-x1)2 +(y2 -y1)2   You would have to use this formula 3 times   for WX: √(-3-4)2 +(-2 --6)2 = √49 + 16 = √65 ≅ 8.1   for XY: √(4 - -3)2 + (3- -2)2 =√49 + 25 = √74 ≅ 8.6   for...

distance formula = √(x2-x1)2 +(y2 -y1)2    = √(-8 - 3)2 + (3 --4)2   =√(-11)2 + (7)2   =√121 + 49   = √170   =approx 13.04   = 13.0 to the nearest tenth

If Tessa made 150 each day, she earns \$320 for the week   If she makes over 175 in one day, she earns \$3 for each one over 175   The extra she earned last week = \$515 - \$320 = \$195   so \$195 ÷ \$3 = 65   she made 65 bracelets over 175 last...

if you're asking how much to pay for a product so you can sell it at a 45% markup and that price will be \$85 then this is how to solve:   x(1.45) = 85   divide both sides by 1.45   \$58.62

her average velocity wlll be the total distance/total time   calculate the distance traveled during each of the three parts    going 20 m/s for 30 seconds = (20)(30) = 600 meters   going 40 m/s for 60 seconds = (40)(60) = 2400 meters   going...

her total miles = 16 + 3 + 22 + 7   = 48   she ran 16 miles   the part of the total = 16/48   reduce this by dividing numerator and denominator by 16   = 1/3

40% of the people receiving the questionnaire wil not throw it out   (2/3)(.40)  will fill it out   (2/3)(2/3)(.40) will then mail it   x = the number of people on the mailing list   (4/9)(.4)(x) = 2560   (4/9)(x) = 6400   4x...

let x = the top base   x + 4 = the bottom base   x + 2 = the altitude   area of a trapezoid = (1/2)(top + bottom)(altitude)   100 = (1/2)(x + x + 4)(x + 2)   100 = (1/2)(2x + 4)(x + 2)   100...

x = the amount of first type (which is \$5.20 per pound)   \$5.20 times the amount of that type + \$5.80 times 5 pounds = a mix of (5 + x) pounds that costs \$5.35   (5.20)x + (5.80)(5) = (5.35)(x + 5)   5.20x + 29.00 = 5.35x + 26.75   5...

10% of 400 pounds is 40 pounds   so there's 40 pounds of salt in the solution   total amount of solution new 16% = x   16% of the new solution is equal to the 40 pounds of salt   (.16)(x) = 40   x = 40/.16   x = 250   if...

A∪B = A + B - A∩B   {a,c,d,1,2,4} = {a,c,1,2} + B - {c,1,2}   B = {c,d,1,2,4}   B' = elements of U that aren't in B   B' ={a,b,3}   you might get another tutor's input if this isn't clear

sum of interior angles of a polygon = (n-2)(180)   when you have a regular polygon, you can divide this sum by the # of angles to get the measure of one interior angle   for a regular HEXAGON:   sum of the interior angles = (6-2)(180) = 4(180) = 720°   one...

use -6 to represent losing 6 yards   use -5 to represent losing 5 yards   add these together   (-6) + (-5) = -11   when adding two negative values, make sure your sum is negative

let x = the amount of money Joel has to start with = the amount of money he spent altogether   cost of shirt = 3x/4   cost of towel = x/4   cost of shirt = 60 more than the towel   3x/4 = 60 + x/4   multiply through by 4   3x...