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 Average/184654: Solve (x – 5)2 = 31 solutions Answer 138571 by solver91311(16897)   on 2009-03-02 20:51:42 (Show Source): You can put this solution on YOUR website! Take the square root of both sides remembering to consider both the positive and negative roots. Add 5 to both sides: John
 Average/184655: Solve x2 + 16x + 69 = 61 solutions Answer 138570 by solver91311(16897)   on 2009-03-02 20:48:28 (Show Source): You can put this solution on YOUR website! Add -6 to both sides: Then solve by factoring. Hint: and John
 logarithm/184633: Solve for N Log base 4 (Log base 3 (log base 2 N))=11 solutions Answer 138569 by solver91311(16897)   on 2009-03-02 20:45:50 (Show Source): You can put this solution on YOUR website! Remember that: So: So: And: So: And finally: A very large number indeed. 2,417,851,639,229,258,349,412,352 John
 Linear_Equations_And_Systems_Word_Problems/184635: The line Ax + By =8 passes through the points (2,1) and (4,-2). Find the values of A & B. Show work please.1 solutions Answer 138564 by solver91311(16897)   on 2009-03-02 20:15:15 (Show Source): You can put this solution on YOUR website! You need to use the Two-Point form of the equation of a straight line because you are given two ordered pairs to define your line. Where and are your given points. It really doesn't matter which point you select as #1 and #2, so I just selected: and giving us: Now all you have to do is the arithmetic and algebraic manipulation to put the equation into the requested form, namely: John
 Linear-systems/184629: I need help to solve this problem. Solve the systems of equations by substitutions 5x + y = 9 y=4x Type an ordered pair.1 solutions Answer 138562 by solver91311(16897)   on 2009-03-02 20:05:43 (Show Source): You can put this solution on YOUR website! Since you have an equation that expresses y in terms of x, just substitute the expression containing x into the other equation, thus: Solve for x to get your x-coordinate, and then substitute that value back into either of the equations and solve for the y-coordinate. Express your answer as (x,y) once you have the proper values. John
 Graphs/184630: Find the slope of the line if it exist. Type as integer or fraction. Simplifiy. Use N for no solution. (2,1) (2,-4)1 solutions Answer 138561 by solver91311(16897)   on 2009-03-02 20:01:06 (Show Source): You can put this solution on YOUR website! The slope number is a fraction where the numerator is the difference in the y values and the denominator is the difference in x values. Remember, any fraction with a denominator of zero is undefined. John
 Graphs/184625: Find the domain and the range. {(8,5),(-4,-5),(7,4),(4,7)}1 solutions Answer 138560 by solver91311(16897)   on 2009-03-02 19:58:48 (Show Source): You can put this solution on YOUR website! The domain is the set of x-coordinates. The range is the set of y-coordinates. John
 Graphs/184628: Graph the linear equation. x=31 solutions Answer 138559 by solver91311(16897)   on 2009-03-02 19:57:02 (Show Source): You can put this solution on YOUR website! The graph consists of all ordered pairs such that x = 3 and y is any real number. John
 Probability-and-statistics/184624: If there is a 30% chance of snow today and a 20% chance of snow tomorrow, what is the probability that both days will go by without any snow falling? 1 solutions Answer 138558 by solver91311(16897)   on 2009-03-02 19:54:59 (Show Source): You can put this solution on YOUR website! A 30% chance of snow today and a 20% chance of snow tomorrow means that there is a 70% chance of no snow today and an 80% chance of no snow tomorrow, so: John
 Probability-and-statistics/184623: What is the probability of rolling three 6s in a row, using a standard 6-sided die?1 solutions Answer 138557 by solver91311(16897)   on 2009-03-02 19:52:26 (Show Source): You can put this solution on YOUR website! John
 Quadratic_Equations/184612: Linear System Extension Thinking & Inquiry Questions 8. A triangle is formed by the intersection of the lines 2x+3y=14, 4x-5y=-16, and the x-axis. Find the area of the triangle Could you help me please with this question because i am really confused. Thank you very much!!!1 solutions Answer 138556 by solver91311(16897)   on 2009-03-02 19:48:49 (Show Source): You can put this solution on YOUR website! Since the x axis forms one side of the triangle, use that as the base. Find the x-intercepts of each of the two equations by substituting 0 for y in each of them. Then the length of the base of the triangle will be the magnitude of the difference between these x-intercepts. Next find the point of intersection of the two lines represented by the two given equations by solving the 2-equation, 2-variable linear system. This one lends itself readily to solution by elimination if you go for eliminating the x term. Once you have that point of intersection, the y-coordinate will be the height of the triangle. Now that you know the length of the base and the height, just use the triangle area formula: John
 Graphs/184558: I'm not sure about this. Graph the linear equation by finding and plotting its intercepts. y=-5x Thanks1 solutions Answer 138532 by solver91311(16897)   on 2009-03-02 17:26:24 (Show Source): You can put this solution on YOUR website! The process for finding the intercepts requires substituting 0 for each of the variables and then determining the value of the other variable to give you two points: (a,0) which is the x-intercept (the point where the graph intersects the x-axis and (0,b) which is the y-intercept. This would give you two points that will define the line that is the graph of your equation. For this equation: and The problem you have with the given equation is that the x- and y-intercepts are the same point, namely the origin (0,0), and one point is insufficient to define a line. Consequently, just finding the intercepts is not enough to create the graph of this equation. To find a second point on the line, you need to find a point that is not an intercept. Select a value for x other than 0, substitute that value, and determine the resulting value for y. The selected value and the resulting value can be formed into an ordered pair that you can graph to establish your second point. (I chose 1 as a value for x, but you could choose anything you like so long as it is not 0) Now you have two points, (0,0) and (1,-5). Plot them then draw a line through them to give you your graph. John
 Exponential-and-logarithmic-functions/184514: A plane's air speed is 450 km/h, With a tail wind , the plane traveled 1050 km/h. On the return trip, the plane flew witha head wind that was 20km.h less than the tail wind. If the total flying time was 4.6 h, find the speed of the head wind1 solutions Answer 138499 by solver91311(16897)   on 2009-03-02 12:57:07 (Show Source): You can put this solution on YOUR website! This makes no sense at all. If the plane has an air speed of 450 km/h, and the plane traveled at 1050 km/h with a tail wind then the tail wind had to be 600 km/h. The fastest wind ever recorded in a hurricane is 190 miles per hour which is about 305 km/h hence a 600 km/h tail wind is utterly absurd. Check your work and repost your question written properly please. John
 Mixture_Word_Problems/184467: A school district is combining 2 schools that will have a total of 1000 students, 42% of whom are african american. 90% of one school is african american and 10% of the other is african american. How may students are in each school. I've tried solving it several different ways x/2 + 420 = 1000 and x + y - 420 = 1000 for example and just can't figure this out! Please help - thank you very much!1 solutions Answer 138466 by solver91311(16897)   on 2009-03-02 02:42:01 (Show Source): You can put this solution on YOUR website! If 42% of the new school is african-american, then out of the 1000 students at the new school, 420 are african-american. If x represents the number of students at one school and y represents the number of students at the second school. We can establish three things: 1. The sum of the students from the 2 schools must equal 1000: (1) 2. 90% of the first school is african-american, so you can say the number of african american students at school 1 is: 3. Likewise, the number of african american students at the second school is: And we know that 420 is the sum of the african-americans at both schools, so: (2) Now (1) and (2) form a system of linear equations that can be solved by either substitution or elimination. John
 Square-cubic-other-roots/184453: This question is from textbook Blitzer 3 square root minus 4 equal 21 solutions Answer 138465 by solver91311(16897)   on 2009-03-02 02:27:43 (Show Source): You can put this solution on YOUR website! What you said was: Which is an utterly false statement because a complex number with a non-zero imaginary component cannot be equal to a real number. What you really might have meant was: In which case: Divide both sides by 3: Square both sides: Add 4 to both sides: John
 Triangles/184450: How do you find out if two triangles are similar? I know that the triangles' angles must be congruent, and their sides must be proportional. How do you determine if the sides are proportional? Here is the problem: Are any of these triangles similar? If so, write the appropriate similarity statement. 1st triangle-CAB CA=4; CB=4; AB=5/angles A and B are congruent. 2nd triangle-PRQ PR=8; RQ not listed; QP=10 3rd triangle-XYZ XZ=8; XY not listed; ZX=8 On triangles PRQ and XYZ, angles Z and P are congruent. 1 solutions Answer 138464 by solver91311(16897)   on 2009-03-02 02:17:36 (Show Source): You can put this solution on YOUR website! If you have two triangles that have 2 congruent angles, then the third angles must be congruent because the angles of a triangle always sum to 180. If you have three congruent angles, then the sides must be related with a common constant of proportionality and therefore are at least similar (congruent if the constant of proportionality is 1) John
 Polygons/184462: How do I find a missin angle in a heptagon? I am given angles 142 130 122 105 and 1101 solutions Answer 138463 by solver91311(16897)   on 2009-03-02 01:27:37 (Show Source): You can put this solution on YOUR website! The sum of the interior angles of a n-sided polygon in degrees is given by: So any heptagon (7-sided polygon) must have interior angles whose measure totals: degrees. The only problem is, you only specified the measure of 5 of the angles. So, either you really meant hexagon, or you simply failed to specify all of the given angles. The best that can be done with the given information is to determine the sum of the two missing angles. Add the measures of the angles you have, then subtract from 1260. The result will be the sum of the two missing angles in your heptagon. On the other hand, if you actually meant hexagon, then subtract the sum of the given angles from 720. John
 Polygons/184463: How do I proove that to lines are parallel if I am given a transversal and the angles that transversal is going through the lines?1 solutions Answer 138460 by solver91311(16897)   on 2009-03-02 01:03:34 (Show Source): You can put this solution on YOUR website! Opposite interior angles formed by a transversal that intersects two lines are equal if and only if the lines are parallel. John
 Graphs/184416: Solve the inequality |2x -4| < 10. Write the solution in interval notation and graph it.1 solutions Answer 138413 by solver91311(16897)   on 2009-03-01 19:20:55 (Show Source): You can put this solution on YOUR website! Means: or Note change of inequality sense when multiplying by . So your interval is: In interval notation: (-3,7). Note use of parentheses vice square brackets because equals was not included in the original inequality relationship. You can draw your own graph. Remember to use open circles on the endpoints. John