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Recent problems solved by 'stanbon'

stanbon answered: 57217 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

Linear-equations/645085: Through (4, 5); perpendicular to the line y = 5 1 solutions Answer 405352 by stanbon(57285)   on 2012-09-03 18:16:39 (Show Source): You can put this solution on YOUR website! Through (4, 5); perpendicular to the line y = 5 ---- y = 5 is a horizontal line. Draw it. ----- Plot the point (4,5) Draw a vertical line thru (4,5) ------ Equation: x = 4 =========== Cheers, Stan H.

�t�e�s�t/645086: Use the point-slope form to write the equation of the line that has the indicated slope and contains the indicated point. Express the final answer in standard form. m = 3/2, (−2, 4) 1 solutions Answer 405350 by stanbon(57285)   on 2012-09-03 18:13:28 (Show Source): You can put this solution on YOUR website! Use the point-slope form to write the equation of the line that has the indicated slope and contains the indicated point. Express the final answer in standard form. m = 3/2, (−2, 4) ------ Form: y = mx + b You know y = 4, when x = -2, and you know m = 3/2. Solve for "b": 4 = (3/2)(-2) + b 4 = -3 + b b = 7 ------- Equation: y = (3/2)x + 7 ==================== Cheers, Stan H. =============

Parallelograms/645090: How can you find the area of a parallelogram if you don't have the height? 1 solutions Answer 405348 by stanbon(57285)   on 2012-09-03 18:09:51 (Show Source): You can put this solution on YOUR website! What information do you have?

logarithm/645091: Write 2/3[logt-5logn+logy] as a single logarithm 1 solutions Answer 405347 by stanbon(57285)   on 2012-09-03 18:08:10 (Show Source): You can put this solution on YOUR website! 2/3[logt-5logn+logy] as a single logarithm ----- = (2/3)log[(ty/n^5] ------ = log[(ty)n^5]^(2/3) ====================== Cheers, Stan H. =============

Linear-systems/645073: The line passes through the point (7,9) but has no slope. 1 solutions Answer 405346 by stanbon(57285)   on 2012-09-03 18:05:19 (Show Source): You can put this solution on YOUR website! The line passes through the point (7,9) but has no slope. ------ No slope means the line is vertical. --- Plot the point (7,9) and draw a vertical line thru it. --- That line passes thru all the points where x = 7. ---- Equation: x = 7 ====================== Cheers, Stan H. ======================

Polynomials-and-rational-expressions/644953: In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be x + 3 = 48 => x = 45 or (x + 1) = 48 => x = 47 However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning. 1 solutions Answer 405329 by stanbon(57285)   on 2012-09-03 14:16:03 (Show Source): You can put this solution on YOUR website! In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be x + 3 = 48 => x = 45 or (x + 1) = 48 => x = 47 However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning. --- Although the product of the 2 factos is 48, one of the factors does not have to be 48. The factors could be 6 and 8, or 2 and 24, or any other combinations factors whose product is 48. ---------------------- Solution: (x+3)(x+1) = 48 x^2 + 4x + 3 = 48 x^2 + 4x - 45 = 0 --- Factor x^2 + 9x-5x - 45 = 0 Factor: x(x+9) -5(x+9) = 0 (x+9)(x-5) = 0 --- Since this product is zero, at least one of those factors MUST be zero. --- x+9 = 0 OR x-5 = 0 x = -9 OR x = 5 ====================== Cheers, Stan H.

Quadratic_Equations/644951: Find all numbers for which the rational expression is not defined: 2x - 7 / x2 + 5x - 24 1 solutions Answer 405323 by stanbon(57285)   on 2012-09-03 14:03:02 (Show Source): You can put this solution on YOUR website! Find all numbers for which the rational expression is not defined: 2x - 7 / x2 + 5x - 24 ------ The denominator cannot be zero. ---- Solve x^2+5x-24 = 0 Factor: (x+8)(x-3) = 0 x = -9 or x = 3 ---- Those are the values for which the rational expression is not defined. Cheers, Stan H. ==============

Mixture_Word_Problems/644926: the rhine river is 160 km shorter than the st. lawrence river. the amazon river is 800 km longer than five times the length of the rhine river. the zambezi river is twice as long as the st. lawrence river. how long id the amazon if it is 1440 km longer than the sum of the other three rivers? 1 solutions Answer 405320 by stanbon(57285)   on 2012-09-03 13:57:39 (Show Source): You can put this solution on YOUR website! the rhine river is 160 km shorter than the st. lawrence river. the amazon river is 800 km longer than five times the length of the rhine river. the zambezi river is twice as long as the st. lawrence river. how long is the amazon if it is 1440 km longer than the sum of the other three rivers? -------------------------- Equations: R = L-160 A = 5R+800 Z = 2L --- A = R+L+Z + 1440 ----- Substitute for "A: 5R + 800 = R+L+Z+1440 4R = L+Z+640 ---- Substitute for "R" and for "Z" : 4(L-160) = L + 2L +640 4L - 640 = 3L +640 --------------------------- L = 1280 km (length of the St. Lawrence) Z = 2L = 2560 km ( length of the Zambezie R = L-160 = 1120(length of the Rhine) A = 5R+800 = 5*1120 + 800 = 6400 km (length of the Amazon) ================================================================ =============================================== Cheers, Stan H. ===============

Functions/644923: An open box is to be made from a flat square piece of material 15 inches in length and width by cutting equal squares of length from the corners and folding up the sides. Write the volume of the box as a function of . Leave it as a product of factors; you do not have to multiply out the factors. If we write the domain of the box as an open interval in the form , then what is a ? and what is b? 1 solutions Answer 405316 by stanbon(57285)   on 2012-09-03 13:26:06 (Show Source): You can put this solution on YOUR website! An open box is to be made from a flat square piece of material 15 inches in length and width by cutting equal squares of length from the corners and folding up the sides. Write the volume of the box as a function of x . Leave it as a product of factors; you do not have to multiply out the factors. Volume = x*(15-2x)^2 If we write the domain of the box as an open interval in the form (a,b), then what is a ? and what is b? a = 0 ; b = 7.5 ======================== Cheers, Stan H. ========================

Equations/644917: You buy some calla lilies and peonies at a flower store. Calal lillies cost $3.50 each and peonies cost $5.50 each the total cost of 12 flowers is $52. How many calla lilies and how many peonies did you buy? I tried setting the problem up and solving: 12 (x-5.50)=52 1 solutions Answer 405314 by stanbon(57285)   on 2012-09-03 13:19:48 (Show Source): You can put this solution on YOUR website! You buy some calla lilies and peonies at a flower store. Calal lillies cost $3.50 each and peonies cost $5.50 each the total cost of 12 flowers is $52. How many calla lilies and how many peonies did you buy? ---- Quantity: P + C = 12 Value:: 5.5P+3.5C = 52 ---- Modify: 35C + 35P = 35*12 35C + 55P = 520 ------ 20C = 100 P = 5 (# of Peonies) ----- Solve for "C": C + P = 12 C + 5 = 12 C = 7 (# of Cala lilies) ========================= Cheers, Stan H.

test/644910: Determine weather the given value of x is a zero of the given function x=5 P(x)=x-5 True or not? I think it is a 0 yes 1 solutions Answer 405308 by stanbon(57285)   on 2012-09-03 12:57:35 (Show Source): You can put this solution on YOUR website! Yes P(5) = 0 ---------------- Cheers, Stan H.

Rational-functions/644892: I need help finding the zeros of: F(x)= 4x^3-24x^2-x+6=0 1 solutions Answer 405303 by stanbon(57285)   on 2012-09-03 12:46:50 (Show Source): You can put this solution on YOUR website! help finding the zeros of: F(x)= 4x^3-24x^2-x+6=0 ----- Factor: 4x^2(x-6)-(x-6) = 0 (x-6)(4x^2-1) = 0 x = 6 or x = 1/2 or x = -1/2 =============== Cheers, Stan H.

Numbers_Word_Problems/644889: 1The measure of Angels of a triangel are 3 consecutive integers. Find the measure of the three angels. 2. Two angels are supplementary if their sum is 180 degrees. One angle measure four times the measure of an angel supplementary to it. Find the measure of the angle. 3. The measure of the angles of a trapezoid are 4 consecutive odd integers. Find the integers. 1 solutions Answer 405296 by stanbon(57285)   on 2012-09-03 12:33:01 (Show Source): You can put this solution on YOUR website! 1The measure of Angels of a triangel are 3 consecutive integers. Find the measure of the three angels. ----- 1st x-1 2nd: x 3rd: x+1 ----- Equation: sum = 180 degrees 3x = 180 degrees x = 60 (2nd) x-1 = 59 (1st) x+1 = 61 (3rd) =========================== 2. Two angels are supplementary if their sum is 180 degrees. One angle measure four times the measure of an angel supplementary to it. Find the measure of the angle. Equation: x + 4x = 180 5x = 180 x = 36 degrees (smaller angle) 4x = 144 degrees (larger angle) -------------------------------------- 3. The measure of the angles of a trapezoid are 4 consecutive odd integers. Find the integers. ----- 1st: 2x-3 2nd: 2x-1 3rd: 2x+1 4th: 2x+3 ---- Equation: sum = 360 degrees 8x = 360 x = 45 degrees ----- 1st: 2x-3 = 87 degrees 2nd: 89 degrees 3rd: 91 degrees 4th: 93 degrees =================== Cheers, Stan H.

Probability-and-statistics/644887: A traffic light is green for 50 seconds yellow for 10 seconds and red for 40 seconds A. P(green) in simplified fraction and decimal form 1 solutions Answer 405290 by stanbon(57285)   on 2012-09-03 12:15:59 (Show Source): You can put this solution on YOUR website! A traffic light is green for 50 seconds yellow for 10 seconds and red for 40 seconds A. P(green) in simplified fraction and decimal form ----- P(green) = 50/100 = 1/2 = 0.5000 ------------------------------------ Cheers, Stan H.

Polygons/644886: THE SIZE OF EACH INTERIOR ANGLE OF A REGULAR POLYGON IS 11 TIMES THE SIZE OF EACH EXTERIOR ANGLE. WORK OUT THE NUMBER OF SIDES THE POLYGON HAS. 1 solutions Answer 405289 by stanbon(57285)   on 2012-09-03 12:12:00 (Show Source): You can put this solution on YOUR website! THE SIZE OF EACH INTERIOR ANGLE OF A REGULAR POLYGON IS 11 TIMES THE SIZE OF EACH EXTERIOR ANGLE. WORK OUT THE NUMBER OF SIDES THE POLYGON HAS. ====== Equation: x + 11x = 180 12x = 180 x = 15 degrees (size ofr each exterior angle) --- Fact: Sum of all the exterior angles is 360 degrees --- # of sides = # of exterior angles = 360/15 = 24 -------------------- Cheers, Stan H. ======================

Equations/644704: find the domain of the composite function f of g. f(x)=x^2+9;g(x)=sqrtx-7 please show work 1 solutions Answer 405220 by stanbon(57285)   on 2012-09-02 22:43:04 (Show Source): You can put this solution on YOUR website! find the domain of the composite function f of g. f(x)=x^2+9;g(x)=sqrtx-7 ---- f[g(x)] = f[sqrt(x)-7] =(sqrt(x)-7)^2+9 = x-14sqrt(x)+49 + 9 = x -sqrt(x)+58 ------ Domain: x >= 0 ==================== cheers, Stan H.

test/644705: find the functions f and g so that f of g =H. H(x)=(6x+9)^4 please show work so i understand this better. thank you 1 solutions Answer 405219 by stanbon(57285)   on 2012-09-02 22:37:33 (Show Source): You can put this solution on YOUR website! find the functions f and g so that f of g =H. H(x)=(6x+9)^4 ------- H(x) = fog(x) Notice that g is the 1st function to work on "x". Let g(x) = 6x+9 ---- Notice that f does its work on g(x) Let f(x) = x^4 ---- Then H(x) = fog(x) = f[6x+9] = (6x+9)^4 ============================================== Cheers, Stan H.

Linear_Algebra/644709: I cannot figure out how to set this question up, so please help! A machine that originally cost $15,600 has a value of $7,500 at the end of 3 years. The same machine has a value of $2,800 at the end of 8 years. a. Find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years. Please help if you can! Thank you. 1 solutions Answer 405218 by stanbon(57285)   on 2012-09-02 22:30:36 (Show Source): You can put this solution on YOUR website! A machine that originally cost $15,600 has a value of $7,500 at the end of 3 years. The same machine has a value of $2,800 at the end of 8 years. --- You have 2 points: (0,15,600) and (3,7500) and (8,2800) ---- a. Find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years. average = (2800-15,600)/(8-0) = -1600 ============================================= Cheers, Stan H.

Expressions-with-variables/644679: Simplify the following algebraic expressions and show all work: I need to figure out how to do this problem step by step but it's eluding me. Can someone please show me? (8​x^​3/​27​y^​6))^​1/​3 1 solutions Answer 405207 by stanbon(57285)   on 2012-09-02 20:31:36 (Show Source): You can put this solution on YOUR website! (8​x^​3/​27​y^​6))^​1/​3 ----- = (2x/3y^2) =================== Cheers, Stan H.

Angles/644670: if the degree measures of the four angles of a quadrilateral are in the ration 1:2:3:4 what is the degree measure of the largest angle 1 solutions Answer 405202 by stanbon(57285)   on 2012-09-02 19:58:01 (Show Source): You can put this solution on YOUR website! if the degree measures of the four angles of a quadrilateral are in the ration 1:2:3:4 what is the degree measure of the largest angle ---- Equation: x + 2x + 3x + 4x = 360 degrees 10x = 360 x = 36 ---- Largest = 4x = 4*36 = 144 degrees =================================== Cheers, Stan H. ===============

sets-and-operations/644666: Please help with this, it is only one problem with several parts to it. marilyn cazayoux, financial aid director of a small private southern college surveyed the records of 100 sophomores and found the following: 49 receive government grants, 55 receive private scholarships, 43 receive aid from the college, 23 receive government grants and private scholarships, 18 receive government grants and aid from the college, 28 receive private scholarships and aid from the college, 8 receive from all 3 sources. how many of the students in the survey a) have government grants only. b) have private scholarships but not government grants, c) receive financial aid from only one of these two sources, d) receive aid from exactly 2 of these sources, e) receive no financial aid from any of the sources and f) receive no aid from college or from the government. 1 solutions Answer 405201 by stanbon(57285)   on 2012-09-02 19:55:47 (Show Source): You can put this solution on YOUR website! marilyn cazayoux, financial aid director of a small private southern college surveyed the records of 100 sophomores and found the following: 49 receive government grants, 55 receive private scholarships, 43 receive aid from the college, ----- Procedure: Draw a Venn Diagram: Draw a rectangle; label it U = 100 --- Draw 3 intersecting circles inside the rectangle, labeling them rgg = 49, rps= 55, rca = 43, ---- Fill in numbers from the inside (intersection) of all the circles to the outside. --------------------------------------------------------- Start with 8 in the inner-most intersection. ---------------------- 23 receive government grants and private scholarships, Put 23-8 = 15 in the intersection of rgg and rps --------- 18 receive government grants and aid from the college, Put 18-8 = 10 in the intersection of rgg and rcs ----------------------------------- 28 receive private scholarships and aid from the college Put 28-8 = 20 in the intersection of rps and rcs ----------------------- 8 receive aid from all 3 sources. --------------------------------- how many of the students in the survey a) have government grants only. 49-(10+15+8) = 16 ----------------------------- b) have private scholarships but not government grants, 55 -(15+8) = 32 ----------------------------- c) receive financial aid from only one of these two sources, Ans: 12 + 16 = 28 ------ d) receive aid from exactly 2 of these sources, Ans: 10 + 15 + 20 = 45 ------------------------------------- e) receive no financial aid from any of the sources 100 - [8 + 10 + 15 + 20 + 16 + 12 + 5] = 14 --------------------------------------------- f) receive no aid from college or from the government. Ans: 12 ----- ====================== Cheers, Stan H.

Rectangles/644665: The perimeter of a rectangle equals the sum of the lengths of it's four sides. If the width of a rectangle is 6 inches and it's perimeter is 46inches, find the length of the rectangle. I need to show how this problem is solved, and other than using addition (I think) I don't know how to solve it. Thank you very much for your time. 1 solutions Answer 405198 by stanbon(57285)   on 2012-09-02 19:35:28 (Show Source): You can put this solution on YOUR website! The perimeter of a rectangle equals the sum of the lengths of it's four sides. If the width of a rectangle is 6 inches and it's perimeter is 46inches, find the length of the rectangle. I need to show how this problem is solved, and other than using addition (I think) I don't know how to solve it.----- --------------------- Draw a rectangle. Let the width be 6. Let the length be "L". Perimeter is 46 ----- Equation: P = 2(L + 6) 46 = 2L + 12 2L = 34 Length = 17 inches ======================= Cheers, Stan H.

Expressions-with-variables/644663: solve the linear system by using substitution: x=4y+14 , y=-3x+3 ? 1 solutions Answer 405197 by stanbon(57285)   on 2012-09-02 19:32:15 (Show Source): You can put this solution on YOUR website! solve the linear system by using substitution: x=4y+14 , y=-3x+3 ? Substitute for "x" and solve for "y": y = -3(4y+14)+3 y = -12y - 42 +3 13y = -39 y = -3 ----- Solve for "x": x = 4y+14 x = 4*3+14 x = 26 ================ Cheers, Stan H. ================

Linear_Equations_And_Systems_Word_Problems/644655: tialParking in a student lot costs $3 for the first half and $1.25 for each hour thereafter. A partial hour is charged the same as a full hour. What is the longest time that a student can park in the lot for $8? I have to show how this problem is solved, and don't even know where to start other than I think it should start as an equation to figure out the number of hours. Thank you. 1 solutions Answer 405195 by stanbon(57285)   on 2012-09-02 19:28:51 (Show Source): You can put this solution on YOUR website! Parking in a student lot costs $3 for the first half and $1.25 for each hour thereafter. A partial hour is charged the same as a full hour. What is the longest time that a student can park in the lot for $8? -------- You need an equation relating time and cost. ---- cost = 1st hr cost + 1.25*(# of additional hours) ---- C = 3 + 1.25x ------ What is the longest time that a student can park in the lot for $8? You need to solve for time. 8 = 3 + 1.25x 1.25x = 5 x = 4 hrs. =============== Cheers, Stan H. ==============

Inequalities/644652: Use the multiplication property of inequalities to solve the inequality. Graph the solution set. 1/4x≥-7/8 I think the answer is x≥-7/2 but am not positive, nor do I know how to graph the solution set. I would appreciate any help, as I need to show my work on this too. 1 solutions Answer 405193 by stanbon(57285)   on 2012-09-02 19:20:55 (Show Source): You can put this solution on YOUR website! Use the multiplication property of inequalities to solve the inequality. Graph the solution set. 1/4x≥-7/8 ----- Multiply both sides by 4 to get: x >= 4(7/8) --- x >= 7/2 --- x >= 3.5 ================ Draw a number-line. Plot the value x = 3.5 on the line. Put a solid circle at that point on the line. Sketch an arrow from that point to the right. The point and the arrow comprise the graph of x >= 3.5 =================== Cheers, Stan H. ======================

Probability-and-statistics/644650: A set of 50 data values has a mean of 34 and a variance of 25. I. Find the standard score (z) for a data value = 23. II. Find the probability of a data value < 23. 1 solutions Answer 405191 by stanbon(57285)   on 2012-09-02 19:16:50 (Show Source): You can put this solution on YOUR website! A set of 50 data values has a mean of 34 and a variance of 25. I. Find the standard score (z) for a data value = 23. z(23) = (23-34)/5 = -11/5 ------------------------------------- II. Find the probability of a data value < 23. P(x < 23) = P(z < -11/5) = normalcdf(-100,-11/5) = 0.0139 ==================== Cheers, Stan H. ==================== -------

absolute-value/644642: I am trying to find the intercepts of f(x) is equal to the absolute value of x+2. 1 solutions Answer 405189 by stanbon(57285)   on 2012-09-02 19:13:08 (Show Source): You can put this solution on YOUR website! find the intercepts of f(x) is equal to the absolute value of x+2. ---- y = |x+2| ---- y-intercept ? Let x = 0, then y = |2| = 2 y-intercept is (0,2) ----- x-intercept ? Let y = 0, then |x+2| = 0, and x = -2 x-intercept is (-2,0) ----- Cheers, Stan H. ----------

Polynomials-and-rational-expressions/644620: Divide and simplify to lowest terms. 2x^2-2x/6x-7 divided by x-1/6x-7 1 solutions Answer 405181 by stanbon(57285)   on 2012-09-02 18:40:16 (Show Source): You can put this solution on YOUR website! 2x^2-2x/6x-7 divided by x-1/6x-7 ------ Invert the denominator and multiply: ----- 2x^2-2x/6x-7 times 6x-7/x-1 ------ Cancel the 6x-7 factor common to numerator and denominator: --- = (2x(x-1))/(x-1) ---- = 2x ======================= Cheers, Stan H. ==============

Inequalities/644607: Convert into set notation (x+16)/(3x+2)<=5 1 solutions Answer 405178 by stanbon(57285)   on 2012-09-02 18:20:22 (Show Source): You can put this solution on YOUR website! Convert into set notation (x+16)/(3x+2)<=5 (x+16)/(3x+2) -5 <= 0 --- x cannot be -2/3. ---- Solve (x+16)/(3x+2) > 5 x+16 > 15x+10 14x < 6 x < 7/3 Draw a number line and plot x = -2/3 x = 7/3 -------- Check a test value in each of the number line intervals. Let x = -10; you get (5/-28)-5 <= 0 ; true So solutions in (-oo,-2/3) -------------------------- Let x = 0; you get (16/2)-5 <= 0 ; false So no solutions in (-2/3,7/3) ------------------------------ Let x = 3; you get (19/11)-5 <= 0 ; true So solutions in (7/3,+oo) ================================== ====================================================== Cheers, Stan H. =============

logarithm/644599: Solve. log(base4)(x+4)-log(base16)x=1 1 solutions Answer 405164 by stanbon(57285)   on 2012-09-02 17:04:04 (Show Source): You can put this solution on YOUR website! Solve. log(base4)(x+4)-log(base16)x=1 ----------------- log4(x+4) - log(x)/log(16) = 1 ----- log4(x+4) - log4(x)/log4(16) = 1 ---- log4(x+4) - (1/4)log4(x) = 1 ---- (3/4)log4(x) = 1 log4(x) = 4/3 --- x = 4^(4/3) ---- x = 6.35 =========================== Cheers, Stan H. ===========================

Graphs/644590: SOLUTION: Write an equation of the line that is parallel to y= 3x + 4 and passes through (-2,3)need help, thanks 1 solutions Answer 405161 by stanbon(57285)   on 2012-09-02 16:55:55 (Show Source): You can put this solution on YOUR website! Write an equation of the line that is parallel to y= 3x + 4 and passes through (-2,3) ----- The given line has slope = 3 --- All parallel lines must have slope = 3. ---- Form: y = mx + b You know y = 3 when x = -2 and m = 3 ; Solve for "b": 3 = 3(-2) = b b = 9 ------ Equation: y = 3x + 9 ====================== Cheers, Stan H.