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Question 996561: I've been trying to figure this question:
Find conditions on k that will make the following system of equations have a unique solution. Then give a formula in terms of k for the solution to the system, when it exists.
3kx+18ky = 4
x+3ky = 4
I feel as if I should know this but I'm not getting anywhere. Any help would be appreciated.
Click here to see answer by ikleyn(52781)   |
Question 997046: Use the given conditions to write an equation for the line in point-slope form and slope-intercept.
When entering the point-slope form, keep terms with y on the left and keep terms with x on the right.
Simplify any fractions as much as possible and do not use decimals.
Passing through (-1, 9) and parallel to the line whose equation is 6 x + 5 y - 5 = 0.
The point-slope form is ???? = ????
The slope-intercept form is y = ????
Click here to see answer by josgarithmetic(39617) |
Question 997046: Use the given conditions to write an equation for the line in point-slope form and slope-intercept.
When entering the point-slope form, keep terms with y on the left and keep terms with x on the right.
Simplify any fractions as much as possible and do not use decimals.
Passing through (-1, 9) and parallel to the line whose equation is 6 x + 5 y - 5 = 0.
The point-slope form is ???? = ????
The slope-intercept form is y = ????
Click here to see answer by lwsshak3(11628) |
Question 997044: Write the slope-intercept equation of a function f whose graph satisfies the given conditions.
Simplify any fractions as much as possible and do not use decimals.
The graph of f passes through (-5, 8) and is perpendicular to the line whose equation is x = 10.
The slope-intercept form is y = ????
Click here to see answer by josgarithmetic(39617) |
Question 997045: Use the given conditions to write an equation for the line in point-slope form and slope-intercept.
When entering the point-slope form, keep terms with y on the left and keep terms with x on the right.
Simplify any fractions as much as possible and do not use decimals.
Passing through (2, -10) and perpendicular to the line whose equation is x - 3 y + 7 = 0.
The point-slope form is ???? = ????
The slope-intercept form is y = ????
Click here to see answer by josgarithmetic(39617) |
Question 997544: Boy and Girl sells mixtures of almonds and raisins. A kilogram of almonds and raisins cost $300 and $125, respectively. If the final cost of the mixture is $1,400 and the mixture contaion 7.5kg of the raisins, how many kilograms of almonds were mixed?
Click here to see answer by josgarithmetic(39617) |
Question 997568: 1.Answer the following questions by deciding on your variable and then using the given information to write an equation which you can solve.
1.1 Two times a number is three less than ½ of the number. Find the number.
1.2 Jan is 6 years older than Mary. If the sum of their ages is 32. Find their ages.
1.3 In 4 years Ali will be 3 times older than he is today. How old is Ali today?
1.4 I think of a number, triple it and subtract 12. If the answer is 60, what is the number?
1.5 Yoshi had some money. He spent half and then earned R12. He had R96 left. How much did he start with?
1.6 Four more than two-thirds of a number is 22. What is the number?
1.7 A man is 32 years old and his son is 4 years old. In how many years’ time will the father be 3 times as old as his son?
1.8 When I multiply some number by 3 and then subtract 5, I get the same answer as when I add 3 to the number. What is the number?
1.9 One number is 8 more than another number.
The sum of the two numbers is 26.
Find the numbers.
1.10 Find two numbers which obey the following conditions:
The first number plus 5 is equal to 3 times the second number.
The sum of the two numbers is 7.
1.11 The average of two numbers is 7.
Three times the difference between them is 18.
Find the numbers.
1.12 John has four times as many marbles as Peter. If he gives Peter 8 marble he will have twice as many marbles as Peter. How many did each have originally.
1.13 A teacher bought pens for R4 each and pencils for R2.80 each. If she bought a total of 24 pens and pencils for R84, how many pens and pencils did she buy?
1.14 A woman is six times as old as her son. In 9 years she will be three times as old as her son. How old are they now?
1.15 Find the fraction which becomes 1/2 if 1 is added to its denominator but which becomes 2/3 if 2 is added to its numerator.
1.16 Two cyclists start 60km apart. If they cycle towards each other, they meet in an hour and if they cycle in the same direction they meet in five hours. Find their average speeds. (Hint: Draw a sketch)
1.17 A person has R5 000 to invest and decides to invest part of it at 4% and the rest of it at 6% (simple interest). If the total interest for the year from the amounts is R245, how much does the person have invested at each rate?
1.18 47% of a number is 2 914. What is the number?
1.19 A father is 60 years old. His son is twice as old as the father was when the son was born. Find out how old the father was when the son was born.
1.20 A number is 8 less than that number times 3. What is the number?
1.21 A tin contains 65 coins, some of which are 10c pieces and some of which are 2c pieces for a total of R 4.50. How many 10c pieces are there?
1.22 A man is 15 years older than twice his daughter’s age.
In 2 years he will be 3 times as old as his daughter.
How old are they now?
1.23 John and James together have 20 sweets. If James gave half of his sweets to John, John would have 16 sweets. How many sweets does each have?
1.24 Find the positive number such that its square is three times the number plus 40.
Click here to see answer by addingup(3677)  |
Question 997561: 1. 7x+2y=1 and 4x+3y=8
2. x+y=5 and x-y=3
3. x+3y=-30 and y=3x
4. 2x+5y=9 and x+3y=5
5. (a+b)/3=2+2b and (2a-4b)/5= 23/5-b
6. y=2x+3 and y=-3x–7
7. x+2y+3 =7x–y and 2x–3y+16 =7x–y
8. (x+y)/(3-y)=1/2 and (x-y)/(3+2y)=4
Click here to see answer by addingup(3677) |
Question 997562: 1. Solve the following simultaneous equations for x and y.
1.1. 7x+2y=1 and 4x+3y=8
1.2. x+y=5 and x-y=3
1.3 x+3y=-30 and y=3x
1.4. 2x+5y=9 and x+3y=5
1.5. (a+b)/3=2+2b and (2a-4b)/5= 23/5-b
1.6. y=2x+3 and y=-3x–7
1.7.x+2y+3 =7x–y and 2x–3y+16 =7x–y
1.8. (x+y)/(3-y)=1/2 and (x-y)/(3+2y)=4
Click here to see answer by Alan3354(69443)  |
Question 997825: 1.18 47% of a number is 2 914. What is the number?
1.19 A father is 60 years old. His son is twice as old as the father was when the son was born. Find out how old the father was when the son was born.
1.20 A number is 8 less than that number times 3. What is the number?
1.21 A tin contains 65 coins, some of which are 10c pieces and some of which are 2c pieces for a total of R 4.50. How many 10c pieces are there?
1.22 A man is 15 years older than twice his daughter’s age.
In 2 years he will be 3 times as old as his daughter.
How old are they now?
1.23 John and James together have 20 sweets. If James gave half of his sweets to John, John would have 16 sweets. How many sweets does each have?
1.24 Find the positive number such that its square is three times the number plus 40.
''.
Click here to see answer by addingup(3677) |
Question 997768: I have 5 homework problems I am really struggling with. Since 5 is the limit per day, I'll post them all here:
Solve each inequality and graph its solution.
1) 6x - 2x > -12
2) 5k + 4k ≥ 0
3) 6 – 2n +3 > -1
4) 3n – n > 12
5) –(1 + 6x) ≤ 2 – 3x
Click here to see answer by Alan3354(69443) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 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